A Review of Contemporary Atomic Frequency Standards
11 A Review of Contemporary Atomic FrequencyStandards
Bonnie L. Schmittberger and David R. Scherer
Abstract —Atomic frequency standards are used to generateaccurate and precise time and frequency, enabling many com-munications, synchronization, and navigation systems in modernlife. GPS and other satellite navigation systems, voice and datatelecommunications, and timestamping of financial transactionsall rely on precise time and frequency enabled by atomicfrequency standards.This review provides a snapshot and outlook of contemporaryatomic frequency standards and the applications they enable.We provide a concise summary of the performance and physicsof operation of current and future atomic frequency standards.Additionally, examples of emerging frequency standard technolo-gies and prototype demonstrations are presented, with a focus ontechnologies expected to provide commercial or military utilitywithin the next decade.We include a comparison of performance vs. size and powerfor current atomic frequency standards, and we compare earlyprototypes of next-generation frequency standards to currentproduct trends. An empirical relationship between frequencystandard performance and product size is developed and dis-cussed. Finally, we provide a mapping between applications andfrequency standard technologies.
Index Terms —atomic clock, atomic frequency standard, clock,timing, frequency, oscillator, review
I. I
NTRODUCTION A TOMIC frequency standards enable enhanced auton-omy, resiliency, and integrity for critical navigation,communications, sensing, and other applications. Commercialfrequency standards that have emerged within the past tenyears, such as the chip-scale atomic clock (CSAC), representextraordinary advances in engineering and have enabled theexpansion of autonomous timekeeping to a wider range ofmobile platforms. Next-generation atomic frequency standardscould further reduce reliance on Global Navigation SatelliteSystems (GNSS), enable novel tests of fundamental physicswhich require extreme levels of precision, and are expected tochange the definition of the second.Here we present a survey of current and future atomicfrequency standards. We analyze how frequency standardperformance scales with physical parameters, project futurefrequency standard performance, and identify key applicationswhere we anticipate these frequency standards will make asubstantial impact. Time and frequency terminology and anoverview of atomic frequency standard operation are presentedin Sections I-A and I-B. Section II includes a descriptioncurrent atomic frequency standards, including physics of op-eration and performance characteristics. This section includes
B. Schmittberger is with The MITRE Corporation, McLean, VA. D. Schereris with The MITRE Corporation, Bedford, MA. e-mail: [email protected] a list of commercial products that can be purchased in volumeat the time of writing, as well as a few recent productintroductions and preliminary data sheets, based on currentpublicly available information. Emerging technologies such asresearch and development prototypes developed by universi-ties, national laboratories, and private industry are described inSection III. Quartz and other types of non-atomic oscillatorshave been omitted.In order to provide tangible comparisons, specific prod-uct names, vendors, prototypes, and research programs areincluded. The reader is cautioned, however, that productspecifications can change over time, and that data sheets maynot be indicative of actual performance. Regarding emergingtechnologies, we emphasize those that appear to have the mostpromise for development as commercial products or usefulprototypes within the next decade.Reviews of atomic frequency standards can be found inseveral articles [1–5] and books [6, 7]. Additionally, severalreviews have highlighted recent progress in specific areas,such as optical frequency standards [8], frequency standardsbased on coherent population trapping [9], atomic fountains[10], and space frequency standards [11, 12]. This reviewprovides a modern update to the literature, and differs fromprevious reviews in the quantity of information on currentcommercially available frequency standards and the intro-duction of novel comparison charts quantifying frequencystandard performance.
A. Time and Frequency Terminology
Standard terminology used in the field of time and frequencyis defined in several sources in the literature [13, 14]. In thissection, we summarize the most important terms relevant toatomic frequency standards.An oscillator, or frequency standard, is a device that pro-duces a periodic signal. An atomic frequency standard is afrequency standard whose basic resonant system is an atomor molecule experiencing a transition between two quantizedenergy levels. An atomic frequency standard provides a stablefrequency output, typically at 10 MHz. An atomic clock isa continuously operating atomic frequency standard coupledwith a counter and initialization time, providing the user withtime as well as frequency. Commercial frequency standardproducts typically have two outputs: one is an oscillatorysignal at 10 MHz, the other is a square-wave one pulse-per-second (1 PPS) output. When powered on, these productsoperate as frequency standards, and the 10 MHz output istypically used for applications that require a stable frequency. a r X i v : . [ phy s i c s . a t o m - ph ] A p r The same device can be operated as an atomic clock bycounting cycles since an initialization time on a counter. Forapplications that require time, the 1 PPS output is commonlyused.Frequency is the rate at which repetitive phenomena occurover time. Current atomic frequency standards generate an out-put in the radio frequency (RF) region of the electromagneticspectrum. The dimensionless, normalized frequency y ( t ) isrelated to the instantaneous frequency f ( t ) and the nominalfrequency f by y ( t ) = f ( t ) − f f . (1)In Eq. 1, f is typically 10 MHz, so if the instantaneousfrequency is off by 1 mHz, the fractional frequency (orfractional frequency offset) y is × − .Instability is a characteristic of an oscillator that describeshow well it produces the same frequency over a given timeinterval [13]. In the time and frequency literature, this charac-teristic is referred to as instability, fractional frequency insta-bility, or fractional frequency stability. The terms instabilityand stability are often used interchangeably, with instabilityfavored by the high-performance frequency standard commu-nity and stability favored by the commercial vendor base.Instability is typically characterized by the Allan Deviation(ADEV), denoted by σ y ( τ ) , equal to the square root of theAllan Variance (AVAR), denoted by σ y ( τ ) [14], where τ is theinterval time. For the characterization of frequency standardsand oscillators, the Allan variance, rather than a standardvariance, is used because the noise behavior displayed byfrequency standards is non-stationary. A detailed description ofADEV, along with other variances used in time and frequencymetrology, can be found in the literature [15].The ADEV σ y ( τ ) describes the instability of the fractionalfrequency y over a given time interval τ . This can be looselyunderstood as follows: for a frequency standard with a spec-ified instability (ADEV) of × − at 1 second, one canexpect a fractional frequency change of × − on averageafter 1 second of operation; i.e. if the frequency standardoutput frequency is exactly 10 MHz at t = 0 , one can thenexpect it to have changed by about 1 mHz after 1 second. Theflicker floor is the minimum value of ADEV as a function of τ .For longer measurement times the ADEV degrades (increases)due to frequency drift, or aging.Accuracy refers to the degree of conformity of a measuredor calculated value relative to its definition. In the time andfrequency literature, accuracy is referenced to the SI definitionof the second. The current SI definition of the second is theduration of 9 192 631 770 periods of the radiation correspond-ing to the transition between the two hyperfine levels of theground state of the Cs atom (at a temperature of 0 K). Inthe case of a commercial Cesium Beam Tube, for example theMicrochip 5071A, the accuracy specification of ± × − describes the range of fractional frequency offset about thenominal 10 MHz output frequency.High-performance optical frequency standards are insteadcharacterized by the term uncertainty. For example, if twoYb optical lattice frequency standards are compared againsteach other, one can establish a relative uncertainty, which can approach numerical values of − [16]. Because the currentSI definition of the second is established with reference to amicrowave atomic energy level difference in Cs, one cannotdefine an “accuracy” for optical frequency standards. If thecurrent SI definition of the second were defined in terms ofthe Yb optical transition, an accuracy could be established.When characterizing instability, accuracy, and uncertainty,lower numbers indicate better performance. Instability refersto how much a frequency standard varies with respect to itselfover some time interval, whereas accuracy refers to how mucha frequency standard differs from an accepted definition. It ispossible for a frequency standard to have good instability andpoor accuracy, and vice versa.Retrace is defined as the fractional frequency offset after cy-cling an oscillator through a power sequence. While differentmanufacturers specify this power cycling sequence differently,a common definition is the fractional frequency offset (forexample ± × − ) after an on/off/on period of 24 hours/48hours/24 hours at constant temperature.The temperature coefficient, or tempco, is defined as themaximum fractional frequency change over a specified tem-perature, for example × − over 0 ◦ C to 70 ◦ C. It isnot valid to assume that the frequency change with respect totemperature is linear over the specified range.Time Deviation (TDEV, or ∆ T ) describes the expected timeerror of a clock (in units of seconds) after some holdover timeand is defined as ∆ T ( τ ) = T + ∆ ff τ + 12 Dτ + τ √ M σ y ( τ ) + (cid:15) ( τ ) , (2)where τ is the time interval (or holdover time), T is theinitial time error, ∆ f /f is the initial frequency error, D isthe frequency drift (typically quoted in units of fractionalfrequency drift per month, sometimes called aging), M σ y ( τ ) is the modified ADEV, and (cid:15) ( τ ) describes the integratedenvironmental errors over time [17]. The modified ADEV isgenerally equal to the ADEV for τ (cid:38) s. In a laboratoryenvironment, a clock’s initial time and frequency offsets can beset to a known value with respect to a calibrated standard, andenvironmental effects can be neglected. In this case, the thirdand fourth terms in Eq. 2 can be used to calculate the predictedtime error of a free-running clock after some holdover time τ . In mobile applications, the environmental effects (cid:15) ( τ ) , suchas tempco, magnetic field sensitivity, and vibration sensitivityusually dominate over the other terms, and this expression isof limited utility. Nevertheless, it is used in the comparisoncharts to follow because it incorporates both the clock’s short-term ADEV as well as drift.Phase noise L ( f ) provides a frequency-domain represen-tation of oscillator instability and is expressed as a spectralquantity in dB below the carrier (or nominal output frequency)at a specified frequency offset. For example, a phase noise of-120 dBc/Hz at 10 Hz offset implies that, for a nominal carrierfrequency of 10 MHz, the total integrated power within a 1-Hz measurement bandwidth, centered at an offset frequencyof 10 Hz from the carrier (i.e. at 10.000 010 MHz) is 120 dBbelow the carrier power. B. Overview of Atomic Frequency Standards
An atomic frequency standard consists of a control loopin which a local oscillator (LO) is periodically referencedto an atomic transition frequency. In a microwave frequencystandard, the LO is a quartz crystal oscillator. In an optical fre-quency standard, the LO is a laser. Schematics of microwaveand optical frequency standards are shown in Figs. 1(a) and(b).
Control
Loop Comb User
Output (RF)Physics Package Laser
SystemOptical field
Control
Loop RF
User
Output (RF)
Physics Package LO
OCXO
MicrowavesTuning voltage Tuning voltageMicrowave
Synthesizer (a) (b)
Fig. 1. Schematic of general frequency standard control loop for (a) amicrowave frequency standard, and (b) an optical frequency standard. Thebandpass filter nature of the atomic resonance response is shown in the physicspackage. LO = local oscillator, OCXO = oven controlled quartz oscillator.
The quartz oscillator has a frequency output in the RF regionof the spectrum (typically 10 MHz). A microwave synthesizermultiplies this RF signal’s frequency up to the appropriate mi-crowave frequency that is resonant with the atomic transition.The microwaves are used to interrogate a collection of atomsin the physics package. An error signal is generated based onthe difference between the synthesized microwave frequencyand the natural atomic resonance frequency. A control loopintegrates this error signal and applies a control voltage tosteer the LO and ensure that the microwaves are tuned to theatomic resonance. In this way, the long-term stability of theRF output is dictated by the ability of the control loop to adjustthe microwaves to atomic resonance, rather than the propertiesof the LO itself.Optical clocks work in much the same way, except thatthe LO is in the optical region of the spectrum (a laser), andan optical frequency comb is required to convert the outputsignal from the optical domain into the RF domain, as shownin Fig. 1(b). These frequency standards are described in moredetail in Section III.There is a time constant, often referred to as the clock‘loop tau’ or loop attack time, which governs the timescalefor regulation of the LO. This timescale is typically on theorder of 1 s or less and describes how quickly the controlloop can respond to errors. For timescales less than the clockloop tau, the instability is dictated by the short-term instabilityof the LO. For timescales longer than the clock loop tau, theinstability is dictated by the quality of the physics package.The frequency standard instability (ADEV, or σ y ( τ ) ) at timescales longer than the loop tau can be expressed as σ y ( τ ) = K Q × SN R τ − / , (3)where K is a unitless constant of order unity and dependson the type of interrogation, Q is the atomic resonance linequality factor (defined as the ratio of the carrier frequency tothe linewidth, also unitless), and SNR is the ratio of the signalpower to the noise power spectral density. We note that σ y ( τ ) is a dimensionless quantity, and SNR in Eq. 3 has units of √ Hz due to the dependence of the noise on the measurementbandwidth.II. C
URRENT A TOMIC F REQUENCY S TANDARDS
A. Overview
In this section, we describe the physics of operation of cur-rent atomic frequency standards and outline their performancein terms of the quantities defined in Section I-A. Currentatomic frequency standards can be divided into three main cat-egories. Hydrogen masers are floor-mounted laboratory instru-ments capable of achieving excellent instability. Cesium BeamTube (CBT) atomic frequency standards are rack-mountedinstruments with excellent accuracy and instability. Gas cellfrequency standards range from hand-held to rack-mounteddevices and achieve moderate performance. A comparisonof ADEV vs. τ of four different current frequency standardtechnologies is shown in Fig. 2. [s]10 A D E V h o u r d a y ADEV vs. for different atomic clocks
CSACRbCBTH Maser
Fig. 2. Comparison of ADEV for different frequency standard technologies.The curves shown from top to bottom are the Microchip CSAC, SRS PRS10Rb frequency standard, Microchip 5071A Cesium Beam Tube, and VremyaActive Hydrogen Maser.
B. Hydrogen Maser1) Physics of Operation:
There are two types of hydrogenmasers that serve as atomic frequency standards. The activehydrogen maser is the largest and most stable product on themarket today, and the passive hydrogen maser is a smaller andlower-performance variation. The atomic transition involvedis the ground-state hyperfine transition | F = 1 , m F = 0 (cid:105) →| F = 1 , m F = 1 (cid:105) of atomic hydrogen, with a transition fre-quency near 1420 MHz. Here, F denotes the hyperfine energylevel and m F denotes its sublevel.In a hydrogen maser, a beam of atomic hydrogen is pro-duced via RF excitation and directed into a cavity. Atoms areconfined within a quartz bulb with a characteristic dimensionless than the wavelength of microwave radiation (21 cm), satisfying the Dicke criterion [18] and eliminating the first-order Doppler effect. An active hydrogen maser operates onthe principle of self-sustained oscillation [1]; if the cavitylosses are low enough and the intensity of the state-selectedhydrogen beam is high enough, the collection of atoms andthe microwave cavity interact in such a way as to sustain self-oscillation.After microwave frequency synthesis, a quartz oscillator isphase-locked to this microwave frequency. A passive hydrogenmaser operates on the same basic principle, but with sub-threshold gain of the cavity. In this case, a smaller storagebulb and/or lower-Q cavity are used, resulting in a smallersize device with comparatively poorer performance.
2) Product Description and Performance:
Active hydrogenmasers are the on the order of 300 L in volume and havethe best performance in terms of short-term instability, phasenoise, and flicker floor of any established products on themarket. In the short term (on the order of 1-10 s), their σ y ( τ ) degrades as τ − , which is characteristic of white phasenoise. This is due to the fact that in an active device theLO can be phase-locked, rather than frequency-locked, to theappropriate atomic transition. As can be seen in Fig. 2, allother frequency standards shown are characterized by a σ y ( τ ) that degrades as τ − / in the short term, characteristic ofwhite frequency noise. The intrinsic accuracy of a hydrogenmaser is limited by the storage chamber wall properties, cavitydetuning, and hydrogen density, which give rise to the long-term drift of these frequency standards. Commercial productsexhibit a flicker floor of 10 − or less and a long-term drift of × − /day. At present, hydrogen masers are available fromthree vendors: Microchip (USA), T4Science (Switzerland, alsoavailable through Orolia), and Vremya-CH (Russia).An active hydrogen maser is the instrument of choice forapplications requiring exquisite short-term stability such asradio astronomy and frequency metrology. One application ofhydrogen masers is in maintaining precision phase stabilityamong widely separated telescopes for Very Long BaselineInterferometry (VLBI), which were recently used in the EventHorizon Telescope to capture an image of a black hole [19]. C. Cesium Beam Tube1) Physics of Operation:
In Cesium Beam Tube (CBT)atomic frequency standards, the atomic transition involvedis the ground-state hyperfine transition | F = 3 , m F = 0 (cid:105) →| F = 4 , m F = 0 (cid:105) in Cs, with a transition frequency of9.192 631 770 GHz. These levels are referred to as “clocklevels,” or “field-independent transitions” and are used becausethey have no first-order dependence on external magnetic fields(only a small quadratic dependence).Cesium is used in a beam tube frequency standard due to thefact that it has a high vapor pressure at reasonable oven tem-peratures, a small second-order Zeeman shift, a large hyperfinefrequency, and atomic energy levels that are amenable toatomic state preparation, interrogation, and detection. Becauseof all these factors, it is also the basis of the SI definition ofthe second.A schematic of a Cs beam tube frequency standard isshown in Fig. 3 [20, 21]. Atoms effuse from a thermal
Vacuum System 9 192 631 770 Hz Input
A-Magnet
Getter B-Magnet
C-Field Power
SupplyCs Oven Getter Hot Wire Ionizer
Mass
Spectrometer and Electron Multiplier
Oven Heater
Power Supply Magnetic Shield
Cavity
C-Field DC
Cs Beam Detector
Signal OutDetector
Power
Supply
Fig. 3. Schematic of a Cesium Beam Tube atomic frequency standard (adaptedfrom [20]). oven towards the microwave cavity. The strong magnetic fieldgenerated by the A-Magnet deflects only one state into theU-shaped microwave cavity. Inside the microwave cavity, themicrowaves cause a fraction of atoms to make a transition tothe other clock state. Those atoms are then deflected by theB-Magnet onto a hot-wire detector and registered as signal.
2) Product Description and Performance:
In commercialproducts [20], atoms effuse from a thermal oven at a temper-ature on the order of 100 ◦ C. Atoms pass through a Ramseycavity with a length on the order of 10 cm, which results ina transit-time limited linewidth of ∼
500 Hz and a line Q of ∼ × . The atomic linewidth is inversely proportional tothe spacing between the two arms of the cavity. Based onEq. 3, an SNR of ∼ √ Hz will result in an instabilityof × − at 1 s. The instability of commercial CBTs islimited by shot noise in the beam current [20].Accuracy limitations in commercial Cs beam tubes arisefrom an inability to exactly compensate for offsets in the mea-sured clock frequency, including the C-field bias, the second-order Doppler shift, any residual phase difference betweentwo arms of the cavity, and the servo system controlling theoscillator. These effects each contribute on the order of a fewparts in to the device’s specified accuracy [4]. D. Gas Cell Frequency Standards
Traditionally, the low-performance category of atomic fre-quency standards (typically based on Rb) have been catego-rized as “Rb frequency standards.” However, the introduc-tion of cesium-based Coherent Population Trapping (CPT)frequency standards such as the Microchip CSAC into thecommercial marketplace renders this name inaccurate. Be-cause frequency standards of this category are all based oninterrogation of a gas cell of atoms, we refer to this categoryas gas cell frequency standards. There are two main types ofgas cell frequency standards: lamp-pumped rubidium vaporcell frequency standards, and laser-pumped CPT frequencystandards. Both rely on an optical source (lamp or laser) foratomic state preparation, and both rely on the technique ofmicrowave-optical double resonance (MODR).
1) Physics of Operation:
A gas cell frequency standardincludes a vapor cell of alkali atoms (rubidium or cesium)that is simultaneously interrogated by both a light source and microwave radiation. In gas cell frequency standards, a lightsource is used for both atomic state preparation as well asstate detection. The light source is responsible for preparingatoms in one of the two clock states via a process referredto as optical pumping. The “double-resonance” technique isnamed for the requirement that the optical and microwavefields are both resonant with the appropriate atomic transitions.When this condition is met, the atomic state population istransferred to a new energy state, which causes a changein how much light is absorbed in the gas cell and hencedetected by a photodetector. The microwave radiation must beresonant with the transition frequency of the hyperfine clocklevels (approximately 6.8 GHz in Rb or 9.2 GHz in Cs). Theoptical radiation is stabilized to an appropriate optical (ground-to-excited state) transition in the atoms and is used both toprepare the atomic state and to detect whether the microwavesare on resonance.The core component of a gas cell frequency standardphysics package is the gas cell (alternatively referred to asa vapor cell or alkali cell). This is a mm to cm-scale chambermade of a transparent glass such as quartz or borosilicate.Inside the vapor cell is a small amount of alkali metal. Thegas cell is heated to a temperature on the order of ∼ ◦ Cto increase the vapor pressure, resulting in measurable lightabsorption in the vapor cell. In order to reduce the frequencyof depolarizing collisions with the chamber walls, an inertbuffer gas is introduced into the chamber to slow down thecollision rate. The buffer gas introduces a pressure shift on theclock transition, which in turn depends on the temperature ofthe buffer gas. Due to this environmental sensitivity as wellas long-term drift from gas cell effects, these devices are notintrinsically accurate and need to be periodically calibrated.
2) Physics of Lamp-Pumped Rb Frequency Standards:
A detailed description of the physics of operation of Rbfrequency standards is provided in the literature [2, 4]. Inprinciple, the MODR technique can be achieved by opti-cally pumping atoms into one of two clock states via anarrow-linewidth optical source. Traditionally RF dischargelamps, rather than lasers, are used for optical pumping andstate detection because spectroscopic-grade lasers with thenarrow linewidth and tunability required for integration intocommercial products have only recently become available.The broadband lamp emission can be filtered into a narrowlinewidth source via a scheme that was developed before theadvent of the laser.The atomic energy levels of Rb have a partial overlapwith those of the Rb levels used in the frequency standard.This overlap can be exploited to generate laser-free opticalpumping in an architecture shown in Fig. 4. An RF dischargelamp made of Rb emits light at the resonances of Rb.This light is directed towards a filter cell made of Rb. Dueto the fortuitous overlap of energy levels, one of these linesemitted from the Rb lamp is absorbed in the Rb filter cell.Therefore, light arriving at the Rb absorption cell, which isthe core of the frequency standard, contains radiation at onlyone of the Rb (D1 transition) lines, which results in opticalpumping into the | F = 2 (cid:105) state.To accomplish MODR, microwave radiation is then applied to the absorption cell and transfers atoms from | F = 2 (cid:105) to | F = 1 (cid:105) . This causes more atoms in the absorption cell toabsorb the filtered light, which results in less light arriving atthe photodetector. The electrical signal from the photodetectoris then used as the input to the control loop for the frequencystandard. In a simplified scheme, the filter cell is removed,resulting in distributed filtering within the absorption cell [4]. Lamp
Filter Cell
Absorption Cell
Temperature Sensors and HeatersLampExciter Coil Rb RbMagnetic Shield
C-Field Coil
Signal out
Photo-detector
C-Field Coil
CurrentRF Excitation
Fig. 4. Schematic of a lamp-pumped Rb frequency standard (adapted from[22]) where the output of a Rb lamp is first filtered by a Rb cell beforeentering the absorption cell. The optical output from the absorption cell ismeasured by a photodetector.
3) Physics of Coherent Population Trapping:
The princi-ples of Coherent Population Trapping [23] and its use in chip-scale atomic clocks (CSACs) have been covered in severalreviews in the literature [9, 24, 25]. In principle, CPT is similarto the underlying physical mechanism of lamp-based Rbfrequency standards; an optical and a microwave source bothneed to be tuned to the appropriate transitions in alkali atoms,which generates a change in the amount of light incident on aphotodetector. In practice, CPT is best understood as a three-level quantum mechanical interaction, as described in Ref. [25]and illustrated in Fig. 5.When the two hyperfine ground states are simultaneouslyresonantly excited by two coherent optical frequencies, a typeof destructive interference phenomenon occurs. Atoms arepumped into a so-called dark state, and there is an increase inoptical transmission through the vapor cell. In practice, ratherthan two laser sources, a single laser source is used whichis modulated at exactly half the hyperfine frequency. Atomsexperience the laser modulation as an effective frequencydetuning, which induces the CPT phenomenon. In this way,the microwaves are applied to the atoms indirectly via fastmodulation of the laser current. This eliminates the need fora tuned microwave cavity and further simplifies the design ofthe physics package.In practice, the technique of CPT is particularly amenable tominiaturization because the clock physics package can consistprimarily of a single laser and a millimeter-scale microfabri-cated vapor cell. CSAC is based on an extreme example ofminiaturization that includes a vertical cavity surface emittinglaser (VCSEL) along with a Micro-Electro-Mechanical System(MEMS) microfabricated vapor cell [26].
4) Product Description and Performance: Lamp-PumpedRb Frequency Standards:
Rb frequency standards are theworkhorses of the telecommunications and tactical militarymarkets, and there are more variations of this type of frequency
VCSEL Rb ∆ 𝑀𝑊 /2 modulation Control loop ∆ 𝑀𝑊 Rb Energy Levels ȁ ۧ𝐹 = 1,𝑚 𝐹 = 0ȁ ۧ𝐹 = 2,𝑚 𝐹 = 0 (a) (b) Fig. 5. Schematic of a CPT frequency standard (adapted from [25]). standard on the market than any other frequency standardarchitecture. Rb frequency standard products vary and includeexquisite devices currently used in the GPS constellation, rack-mounted devices in the telecom industry, and handheld unitsthat consume a few Watts of power.
5) Product Description and Performance: CPT FrequencyStandards:
The first CSAC physics package was demonstratedby NIST in 2004 [27], and the first commercial CSAC wasintroduced by Microchip (then Symmetricom) in 2011. Now,there are a handful of products on the market today basedon CPT. Some of these are advertised as CSACs with apower consumption of a few hundred mW. However, someCPT frequency standards are larger devices with a powerconsumption on the order of a few Watts.
E. Comparison of Current Atomic Frequency Standards
A comparison of specifications from many current com-mercially available frequency standards is shown in Table I.We have included long-established commercial products fromcompanies such as Microchip, Accubeat, FEI, Spectratime,SRS, Excelitas, IQD, and Vremya. For the purposes of com-parison, we have also included recent and emerging prod-ucts from companies such as Teledyne, Chengdu Spaceon,Muquans, and Spectradynamics.We generated figures showing the trends of ADEV () σ y ( τ ) ), L ( f ) , drift, retrace, tempco, and TDEV for all the frequencystandards listed in Table I as functions of size, weight, power,and the combined metric SWaP (a linear product of size,weight, and power), summarized in Ref. [28]. We found thatmany of the observed trends are repetitive, and thus in theinterest of space, here we show only TDEV after 1 day vs.size and power in Figs. 6(a) and (b), respectively. TDEV after1 day was chosen because it is a compromise between short-term and long-term behavior, and it incorporates both thefrequency standard’s ADEV and monthly drift specification.To calculate TDEV at 1 day, Eq. 2 was used, neglecting initialtime error, frequency error, and environmental effects. If theproduct did not quote ADEV at 1 day, the contribution fromADEV was extrapolated as τ − / from the largest τ valuelisted on the data sheet. The monthly drift specification wasalso extrapolated to 1 day. In practice, TDEV after 1 day forlow-performance clocks is dominated by the drift spec.The estimated TDEV(1 day) vs. size shown in Fig. 6(a)fits well to a straight line on a log-log plot, indicative of apower-law relationship. This scaling relationship is also visiblein plots of σ y (1 s ) vs. size, monthly drift vs. size, σ y (1 s ) vs. weight, and monthly drift vs. weight [28]. The straight-line fit is shown in Fig. 6, this is determined empirically to be TDEV(1 day) = C × ( size in cc ) slope ; which yields C = 8 . × − and slope of − . . This trend persists acrossfive orders of magnitude in size and encompasses compara-tively old technologies as well as modern CPT-based devices,including CSAC, low-performance Rb frequency standards,high-performance Rb frequency standards, CBT frequencystandards, passive and active hydrogen masers, and emergingtechnologies such as cold atom frequency standards. This indi-cates empirically that an improvement in product performancecan be expected from larger (or heavier) products accordingto a known power-law scaling.The TDEV at 1 day vs. steady-state power consumptionplot is shown in Fig. 6(b). In contrast to the trend of TDEVvs. size, a saturation effect appears to be involved here, wheregains in performance are no longer correlated with an increasein steady-state power consumption beyond 50-100 W. We notetrends of σ y (1 s ) vs. power and monthly drift vs. power exhibitthe same saturation effect [28].Because of the redundancy involved in comparisons vs.size and weight, we conclude that analyzing performanceparameters such as TDEV vs. the combined metric SWaP isnot optimal. We conclude that comparisons of performanceparameters vs. size and power separately are the most useful.III. N EXT -G ENERATION A TOMIC F REQUENCY S TANDARDS
Despite ongoing advances in the performance and minia-turization of atomic frequency standards, portable microwavefrequency standards appear to be approaching a practical limitdue to the performance of quartz oscillators. It is difficultto find a volume source of quartz crystal oscillators with ashort-term instability of better than ∼ × − at 1 s. Byintegrating a quartz LO and a microwave physics package witha clock loop tau on the order of ∼ × − / √ τ . For performance beyond this limit,it is necessary to either radically improve quartz oscillatorsor employ an architecture based on a fundamentally differentLO and physics package, e.g. , an optical transition. In thissection, we describe a range of next-generation microwave fre-quency standards followed by an overview of optical frequencystandards under development. We analyze their current andprojected performance relative to current frequency standardcapabilities. A. Future practical microwave frequency standards
There are a number of efforts underway to improve the per-formance of portable microwave frequency standards, whichinclude both modifications to existing warm atom systems aswell as the development of ion and cold atom-based frequencystandards. Each of these platforms has exhibited short-terminstabilities approaching − / √ τ , as shown in Table II. Thislevel of instability is sufficient to enable applications such asdeep-space autonomous navigation [29] and measurements ofthe gravitational redshift with an accuracy of 2 ppm [30]. Inthis section, we will provide an overview of each of theseplatforms in terms of current performance and outlook forminiaturization. Vendor Product ADEV ( τ = 1 s) L (dBc/Hz,10 Hzoffset) Drift (monthly)
Retrace( ± ) T range ( ◦ C ) Tempco Size (cm ) Weight (kg)
Power (W)Microchip SA45.sCSAC × − -70 × − × − -10 to 70 × −
17 0.035 0.12Microchip SA35.mMAC × − -87 × − × − × −
50 0.086 5Microchip SA22.c × − -90 × − × − -10 to 75 × −
208 0.43 10Microchip 5071A × − -130 0 to 55 29700 30 50Microchip CsIII4310B . × − -130 0 to 50 16544 13.5 30Microchip MHM × − -138 × − × − -86 × − -20 to 65 × −
32 0.075 1.2Accubeat AR133A × − -116 × − × − -20 to 65 × −
146 0.295 8.25FEI FE-5669 × − -140 × − × − -20 to 60 × −
669 1.69 20FEI FEI RAFS × − -138 × − -4 to 25 4902 7.5 39Spectratime LP Rb × − -100 × − × − -25 to 55 × −
216 0.29 10Spectratime iSpaceRAFS × − -120 -5 to 10 3224 3.4 35Spectratime miniRAFS × − -84 -15 to 55 388 0.45 10T4Science iMaser-3000 × − -136 × − × − -130 49820 33 90SRS PRS10 × − -130 × − × − -20 to 65 × −
155 0.6 14.4Excelitas RAFS × − -105 × − × − -20 to 45 1645 6.35 39IQD IQRB-1 × − -95 × − × − × −
66 0.105 6IQD IQRB-2 × − -138 × − × −
230 0.22 6Vremya VCH-1003M × − -135 × − × − -95 × − -30 to 65 × −
65 0.2 6ChengduSpaceon XHTF1021Rb × − -100 × − × − -20 to 60 × −
189 0.27 7.8ChengduSpaceon TA1000OPC . × − -125 48266 40 100ChengduSpaceon CPT × − -90 × − -45 to 70 × −
24 0.045 1.6Teledyne TCSAC × − -85 × − × − -10 to 60 × −
23 0.042 0.18Muquans MuClock × − -151 682000 135 200Spectradynamics cRb × − -138 39806 30.5 75 TABLE I: Summary of current frequency standard product key performance parameters. Tempco across T range is listed.Many high-performance microwave frequency standardshave already undergone miniaturization efforts, and theirADEV at 1 second vs. size is shown in Fig. 7. Technologydemonstrations that have reached the prototype stage are rep-resented by closed symbols with the full size of the frequencystandard included. For other advanced laboratory-based de-velopment efforts, only the approximate size of the physicspackage is included (represented by open symbols), with theassumption that future prototype frequency standards based on these technologies will undergo further miniaturization. Thesolid red curve in Fig. 7 shows the best fit of the TDEV vs. sizeof current microwave frequency standards from Fig. 6(a).
1) Warm vapor microwave frequency standards:
Owing tothe implementation of novel optical pumping techniques andincreasingly stable narrow-linewidth semiconductor lasers [44,45], warm atomic vapor-based microwave frequency standardshave achieved substantial performance improvements in recentyears, as shown in Table II.
LegendCSAC = Microchip SA.45s CSAC
TCSAC = Teledyne CSAC (preliminary)
CPT = Chengdu Spaceon CPT
NAC = Accubeat Rb NAC1
IQRB1 = IQD IQRB-1
Ch Rb = Chengdu Spaceon XHTF1031
MAC = Microchip SA.35m
SA22 = Microchip SA.22c
PRS = SRS PRS10 LP = Spectratime low profile Rb AR133A = Accubeat AR133A Rb miniRAFS = Spectratime miniRAFS
IQRB2 = IQD IQRB-2 = FEI FE-5669 Rb
FS725 = SRS FS725
RAFS = Excelitas space RAFS iRAFS = Spectratime iSpace RAFS
CsIII = Microchip CBT 4310B CsIII
FEI RAFS = FEI RAFS = Microchip 5071A CBT
OPC = Chengdu Spaceon TA1000 OPC c-Rb = Spectradynamics cold Rb c-Rb
PHM = T4Science pHMaser 1008 mu = Muquans cold-atom MuClock (preliminary) MHM = Microchip MHM 2010 H Maser
Vremya = Vremya VCH-1003M H Maser T4 = T4Science iMaser-3000 H Maser CSAC CPTNACIQRB1, Ch RbMAC SA22PRSLPAR133A miniRAFS5669IQRB2 FS725RAFS iRAFS CsIIIFEI RAFS 5071AOPCc-Rb PHM muMHMVremya T4TCSAC CSAC CPTNAC MACIQRB1 , Ch Rb SA22PRSAR133ALP, miniRAFS5669IQRB2 FS725RAFSiRAFSCsIIIFEI RAFS 5071AOPCc-Rb PHM muMHMVremya T4TCSAC (a) (b)
Fig. 6. TDEV at 1 day vs. (a) size and (b) power for the frequency standards listed in the legend.
Optical lattice clockThermal atom physics package
Ion physics package
Ion clock
Cold atom clockFuture practical optical clocksFuture practical microwave clocks
IMPACTDSAC SOC Ion physics packageCSAC Commercial clock Cs Fountain Microwave systemsOptical systems5071A PHARAOSpectradynamics μquans
O-RAFS
Ca beam Ca ion
Fig. 7. TDEV after 1 day vs. size for next-generation microwave and optical clocks. Solid filled symbols indicate clocks whose size includes theelectronics package. Empty filled symbols indicate clocks whose size only includes the physics package. The red solid line is the fit TDEV( day) = . × − (size in cc) − . used in Fig. 6(a). The established commercial clocks (stars) are the Microchip CSAC and 5071A. The remainder of clocksshown are prototypes, technology demonstrations, or early-stage products. The cold atom microwave clocks are from SpectraDynamics [31, 32], Muquans [33],and projections for the PHARAO payload [30]. The ion microwave clock is the JPL DSAC [29]. The ion microwave physics package is from IMPACT(Sandia) [34] (reported breadboard size × cm , assumed third dimension size of 10 cm). The thermal atom optical clock physics packages are AFRLO-RAFS [35, 36] (with size estimated from Ref. [37]) and the calcium thermal beam clock from Peking University [38]. The compact ion clock physicspackage is from the Chinese Academy of Sciences [39]. The optical lattice clock for the Space Optical Clock (SOC) program was developed by PTB andfits inside a trailer [40]. The gray bubble describes current microwave fountains with parameters estimated from Refs. [41–43]. Red and blue bubbles areprojections for future microwave and optical clocks, respectively, assuming further advances in stability and miniaturization. Recent demonstrations have achieved instabilities that rivalsome portable hydrogen masers [45, 46]. Although thesesystems have not yet undergone explicit miniaturization, manyengineering hurdles have already been overcome with thedevelopment of CSACs, and thus this platform holds promisefor future frequency standard applications that require ultra-low SWaP.
2) Cold atom microwave frequency standards:
Efforts toreduce the coupling of atoms to the external environmenthave motivated the development of neutral cold-atom systems,which exhibit much smaller Doppler and collisional shiftsthan warm atoms and can have a smaller SWaP than atomicfountains. In these systems, atoms are first laser-cooled andtrapped in a magneto-optical trap (MOT). This both coolsthe atoms, slowing them down to speeds on the order of10 cm/s or less, and confines them to a well-defined re-gion using magnetic field gradients. In recent years, therehave been significant efforts towards miniaturization of thesesystems [47]. This type of architecture requires a periodictiming sequence with periods of trapping, laser cooling, clockinterrogation with the optical and magnetic trapping fieldturned off, and state readout. Because atoms are untrapped(and hence free falling due to gravity), the maximum practicalduration of the clock interrogation phase is limited to 10-100 ms, which sets limits on frequency standard stability.Compact versions of cold atom frequency standards haveachieved short-term instabilities as low as (cid:46) × − / √ τ ,as shown in Table II, and it is expected that the PHARAOclocks on the ACES project of the European Space Agency(ESA) will reach (cid:46) × − / √ τ [30]. Compact cold atomfrequency standards are already operating in orbit [48] andhave flown on an aircraft [49], and they are commerciallyavailable from Muquans [33] and SpectraDynamics [32], withthe latter system depicted in Fig. 8(a).A plot of TDEV(1 day) vs. size for these cold atom clocksis shown in Fig. 7. For future practical microwave frequencystandards, we include advanced prototype demonstrations withsome level of transportability, an overall size of the frequencystandard or physics package listed, and a measured ADEVout to at least seconds. For future practical optical fre-quency standards, we include those demonstrations matchingthe conditions above but with a measured ADEV out to atleast seconds, and we calculate TDEV in the same way.From Fig. 7 it is clear that the TDEV(1 day) vs. size of theseemerging products and next-generation prototypes follows asimilar relationship as current frequency standards, whichsuggests that they are not achieving stability improvementsfor a given size compared to today’s technology.
3) Trapped ion microwave frequency standards:
Ion-basedsystems are also making substantial progress in SWaP re-duction [51]. Ions that are used in frequency standards arepositively charged, i.e. , they are atoms that are missing an elec-tron. Ions can be trapped by applying certain configurations ofelectric and/or magnetic fields that confine charged particles.Ion traps can consist of a single or few ions or a cloudof up to approximately 10 million ions. Single ions trappedin deep potential wells operate under exquisite conditionsthat are well-isolated from many external perturbations. As (a) (b)
Fig. 8. (a) The Spectradynamics cold atom clock (height = 48 cm) reproducedwith permission from Ref. [50]. (b) The DSAC system (volume = 17 L) fromRef. [29]. a result, even though there can be far fewer ions used in ion-based frequency standards than there are atoms in vapor-basedfrequency standards, they can still provide a large SNR. Inaddition, ion traps are highly stable with lifetimes of up tomonths, thus enabling long interaction times during clock in-terrogation, whereas cold atoms must be continually re-cooledand trapped (typically every 10-100 ms). The ion platformis under development using a number of atomic species, asshown in Table II, with one of the most advanced beingthe mercury Deep-Space Atomic Clock (DSAC) depicted inFig. 8(b).The DSAC developed by the Jet Propulsion Laboratory(JPL) and NASA has reached an
SNR × Q -limited short-terminstability of . × − / √ τ [29]. The ion interrogation cyclebegins by applying light from a mercury lamp to opticallypump the trapped ions into a magnetically insensitive groundstate. A . GHz microwave field is then applied to the ions,which gives rise to enhanced rates of fluorescence when itsfrequency is tuned to resonance with the hyperfine splitting.The fluorescence is collected with a photomultiplier tube [29],the output of which is used to generate an error signal thatfeeds back to the microwave source. The DSAC system iswell-suited for long-term operation in space because it uses alamp instead of a laser and does not require cryogenics or amicrowave cavity.The DSAC performs better than the current product trend-line for its size, i.e. , compared to the red solid curve in Fig. 7.We expect that this system is near the limit of next-generationmicrowave frequency standard performance vs. size, whichwe represent in Fig. 7 by the red bubble. We estimate theparameters of this bubble by noting that, while we expect somefurther advances in performance and size relative to currentfrequency standards (as demonstrated in the DSAC, for exam-ple), we do not expect future microwave frequency standardsto reach sizes that are substantially smaller than current CSACsnor for practical frequency standards to reach short-terminstabilities much better than − at 1 second (limited bythe instability of high-performance quartz oscillators). Somehigh-performance microwave ion systems have been shownto reach sub- − / √ τ instabilities, but these systems aregenerally more complex and require laser cooling of the ionsor high-SWaP local oscillators ( e.g. , superconducting cavitymasers [52]). To surpass the current trends in performance vs. size of microwave frequency standards, it is necessary toutilize a completely different frequency standard platform withan intrinsically higher Q —one referenced to atomic transitionsseparated by optical, rather than microwave, frequencies. B. Optical frequency standards
Future compact frequency standards based on opticaltransitions are expected to reach short-term fractional fre-quency instabilities of approximately × − / √ τ to × − / √ τ [8]. These frequency standards will enablelonger-term autonomous navigation and improved phase pre-cision for applications including distributed coherent radar,beamforming, and geolocation.Optical frequency standards offer fundamentally improvedperformance over microwave frequency standards. This im-provement can be understood from Eq. 3, where it is clear thatemploying a higher reference frequency (higher Q ) improvesthe stability of the frequency standard. Optical frequencystandards use an optical field ( ν ∼ hundreds of THz) asa frequency reference, which offers an immediate projectedimprovement in stability over microwave frequency standards(typically ν ∼ ∼
1) Thermal atom optical frequency standards:
Thermalatoms remain a promising platform for a wide range offuture practical optical frequency standards because they en-able access to a larger number of atoms with a relativelysimple physics package. Systems based on vapor cells andatomic beams are under development, some examples areoutlined in Table II. Warm vapor-based clocks must employschemes to minimize Doppler effects, such as Doppler-freespectroscopy [64] or, more recently, a two-photon transition inrubidium [35]. The demonstrated short-term instability of thesesystems is already better than a number of compact microwavefrequency standards, as shown in Fig. 7.We expect thermal atom optical frequency standards, alongwith ion-based optical frequency standards, to eventually pop-ulate the smaller-size region of the “Future practical opticalfrequency standards” blue bubble in Fig. 7, where technolo-gies including ultra-small vapor cells, like the one shown inFig. 9(a), and chip-integrated frequency combs [65] will enablesubstantial further miniaturization.Optical frequency standards based on thermal atomic beamscan eliminate some collisional effects present in vapor cellsystems and take advantage of some of the techniques usedfor cesium beam microwave frequency standards. Laboratory-scale optical atomic beam frequency standards have alsoreached fractional frequency instabilities of less than − at1 s [66], and miniaturization efforts are underway [38]. Evenwith first-order Doppler-free spectroscopy techniques, thermalbeams still suffer from second-order Doppler effects [63], andthus a number of systems have begun to employ laser coolingand magneto-optical trapping.Frequency standards based on freely expanding laser-cooledatoms can achieve longer coherence times and a negligiblesecond-order Doppler shift compared to warm atom sys-tems. However, technical challenges of optimizing the coolingschemes ( e.g. , mode mismatch between the cooling fieldsand the atoms) are expected to limit the performance ofthese frequency standards to fractional uncertainties of about − [63]. State-of-the-art setups have therefore moved tolattice-based schemes [16], and some future practical op-tical frequency standards, including the Space Optical Clocks(SOC) project [67] of ESA, have also been commissionedowing to their promise of enhanced performance.
2) Optical lattice frequency standards:
Counterpropagatingoptical fields applied to a vapor of cold neutral atoms forman “optical lattice,” which imparts a dipole force that attractsatoms to the minima of the dipole potential wells. For suffi-ciently cold atoms and deep potential wells, the atoms becomespatially confined at the minima of the potential wells, eachof which can be much smaller than the wavelength of light.Under conditions of very tight confinement, the light-atomsystem can enter the so-called “Lamb-Dicke regime,” in whichDoppler effects and atomic recoil due to photon scatteringare suppressed. In this regime, optical lattice-based frequencystandards are highly insensitive to residual atomic motion andcan surpass the performance of frequency standards which usefreely expanding atoms.Atoms that are exposed to strong optical fields experienceinternal energy shifts (Stark shifts). By employing a carefully Platform
Advantages
System information Atom Short-terminstability Long-termperformance Uncertainty Performer(s)
CPT (Mclocks projectresult) Rb . × − / √ τ Flicker floor = × − at300 s, Drift = × − /month Not reported LNE-SYRTE,INRIM,UFC [44], [45] Warm vapor
Projected lowSWaP, Highatomicdensities CPT, Physics packagecontained on2.54 mm ×
30 mm board Rb × − / √ τ , 1to 100 s Flicker floor = × − (100-1000 s) Not reported Universit´e deNeuchˆatel,SpectraTime(SpT) [53]Double-resonancepumping scheme Rb . × − / √ τ ,1 to 100 s Not reported Not reported Universit´e deNeuchˆatel [46]CAMPS program result Rb . × − / √ τ ,1 to s Not reported Not reported Honeywell [54]Commercial cRb,22 × ×
32 cm , 28 kg Rb × − / √ τ , 1to s Flicker floor ≈ × − at s, Drift < × − /day Not reported SpectraDynamics,NIST [31], [32] Cold vapor
ReducedDoppler andcollisionaleffects Commercial MuClock,155 × ×
80 cm ,135 kg Rb × − / √ τ , 1to s Flicker floor ≈ × − at10 days few parts in − Muquans [33]Cold atom clockexperiment in space(CACES) demonstratestests in orbit Rb × − / √ τ measured onground, 1 to s( × − / √ τ predicted in orbit) Not reported Not reported Chinese Academyof Sciences [48]HORACE clock forGalileo GNSS Cs . × − / √ τ ,1 to s Not reported Not reported LNE-SYRTE [55]Projection for theACES (PHARAO)payload Cs . × − / √ τ out to × s Not reported . × − LNE-SYRTE,CNES, ESA,ENS-PSLResearchUniversity [30]
Fountain
Well-establishedhighperformance Physics packagedesigned forcommercialdevelopment offountains Cs × − / √ τ , 1to s Not reported Not reported National PhysicalLaboratory, As-trogeodynamicalObservatory,National ResearchCouncil ofCanada, PennState [56]DSAC (Deep-spaceatomic clock),17,000 cm , 16 kg, 47W Hg . × − / √ τ ,1 to s Drift < × − /day Not reported JPL, NASA [29] Trapped ion
Well-isolatedfromenvironment Sympathetically cooledCd ions andlaser-cooled Mg ions inPaul trap Cd . × − / √ τ ,4 to × s Not reported × − TsinghuaUniv. [57]Ultra-small vacuumpackages underdevelopment for theIMPACT program Yb × − / √ τ , 10to s Not reported Not reported Sandia, JPL [58]Micro-MercuryLamp-Pumped clockunder development forthe ACES program (30cm vacuum package) Yb . × − / √ τ ,10 to 1000 s Flicker floor = × − at1000 s Not reported JPL [59]Laser-cooled ion clockcontained in volume of51 × ×
28 cm Yb . × − / √ τ ,30-1500 s Not reported Not reported National PhysicalLaboratory, Univ.of Oxford [60] TABLE II: Examples of microwave atomic frequency standards under development. (a) (b) Fig. 9. (a) The vapor cell on a chip used in the two-photon thermal atomoptical frequency standard [68] (image from press release [69]) shown nextto a coffee bean. (b) The PTB optical lattice frequency standard on an air-conditioned car trailer [40]. chosen wavelength [70], referred to as the “magic wavelength,”some of those shifts can be canceled, leaving only residualeffects such as those due to wavefront distortions. Under theseconditions, laboratory optical lattice frequency standards havereached record levels of instability (ADEV of . × − at1 s) and fractional uncertainty ( . × − after 1 hour of aver-aging) [71]. The SOC program is supporting the developmentof transportable optical lattice frequency standards (Sr and Yb)with goals of a fractional instability below × − / √ τ and afractional uncertainty below × − for the next generationof frequency standards beyond PHARAO [67].To our knowledge, the Sr lattice frequency standard fromPTB is currently the only full lattice frequency standard thathas been constructed on a transportable platform [40], i.e. ,an air-conditioned trailer shown in Fig. 9(b). Its fractionalfrequency instability is two orders of magnitude better than thecold-atom-based transportable microwave frequency standardsshown in Fig. 7. We expect that further miniaturization andintegration of system components will shift this platform intothe high-performance area of the blue bubble defining “futurepractical optical frequency standards” in Fig. 7.
3) Trapped ion optical frequency standards:
Despite havinga lower number of atoms, trapped ion optical frequency stan-dards represented the highest performance optical frequencystandards for a number of years after the development ofoptical frequency combs, with optical lattice platforms onlysurpassing them in 2014 [72]. As is the case in microwaveion frequency standards, their excellent instability is due inlarge part to their pristine environment. In addition, laser-cooled ions can also operate in the Lamb-Dicke regimewhen using sufficiently deep trapping potentials. Even thoughoptical lattice systems have surpassed that of ions in terms ofperformance, ion-based systems have much simpler physicspackages than optical lattice systems and thus are expectedto attain a much smaller SWaP, which makes them highlyamenable to a number of strategic applications in navigationand communications. In addition, the long-lived ion traps canbe exploited to obtain a higher Q and SNR.State-of-the-art ion optical frequency standards haveachieved short-term fractional frequency instabilities nearing − / √ τ and fractional uncertainties of . × − [73], as MicrowaveOptical
Fig. 10. The evolution of the fractional frequency uncertainty of microwaveand optical frequency standards reported in Refs. [63] and [75] shown withadditional data points from Refs. [16, 43, 73]. The dashed curves are meantto guide the eye and emphasize the different trends in the state-of-the-art ofthe two types of frequency standards. shown in Table IV. Efforts to miniaturize ion optical frequencystandards are also underway [74], with one system reaching avolume of . m excluding electronics [39]. C. Comparison of High-Performance Frequency Standards
While it is still too early to define a best fit for the short-term instability vs. size of optical frequency standards, it isreasonable to infer that such a trend will be distinct fromthat for microwave frequency standards. There has also been adistinct difference in the evolution of the fractional frequencyuncertainty of microwave vs. optical frequency standards overthe past several decades, which has been analyzed in Refs. [63]and [75] and reproduced here in Fig. 10 with the inclusion ofadditional data points from Refs. [16, 43, 73]. These trendsindicate that future improvements in microwave frequencystandard performance will likely be incremental, whereas thepace of improvement of optical frequency standards will bemore rapid.Laboratory optical lattice frequency standards are likelyto serve as the primary ground frequency standards in anyfuture redefinition of the SI second. The instability and ac-curacy offered by these high-performance optical frequencystandards will also enable new tests of fundamental physicsincluding Einstein’s theory of relativity [76], which predictsthat frequency standards will tick more slowly the closerthey are to massive objects, and the variation of fundamentalconstants predicted by extensions of the Standard Model ofparticle physics [77], which can be measured by comparingthe frequencies of optical frequency standards over long timeperiods.While the present work focuses on practical frequencystandards, it is worthwhile noting the current status of record-holding instruments. In Table IV, we list recently reportedinstability and uncertainty measures for high-performanceoptical frequency standards and cesium fountains. Currently,optical frequency standards achieve approximately 1000x im- Platform
Advantages
System information Atom Short-terminstability Uncertainty Performer(s)
O-RAFS - Two-photontransition scheme in vapor cell Rb × − / √ τ ,1 to s Not reported AFRL, NIST [35],[37], [36] Warm atoms
Low SWaP+C, Highdensities Two-photon transition schemewith vapor cell on a chip andmicroresonator comb Rb . × − / √ τ ,0.1 to s Not reported NIST, UC Boulder,Cal Tech, Draper,Stanford [68]Atomic beam, miniaturizedphysics package (0.3 m ) Ca . × − / √ τ ,0.1 to s Not reported Peking Univ., BeijingVacuum ElectronicsResearch Inst. [38] Optical lattice
Higher densities,insensitive to atomicmotion Clock installed onair-conditioned trailer Sr . × − / √ τ ,3 to × s . × − PTB [40]
Trapped ion
Well-isolated fromenvironment Physics package contained involume of 0.54 m Ca . × − / √ τ ,10 to × s . × − Wuhan Inst., ChineseAcademy ofSciences, TaizhouUniv. [39]
TABLE III: Examples of optical atomic clocks under development.proved instability and 100x improved uncertainty compared totheir microwave counterparts.There are a number of efforts underway to improve the per-formance and reduce the SWaP of optical frequency standards.Drift of the laser between feedback cycles is the limiting factorin state-of-the art frequency standards [63], and a numberof techniques are under investigation to improve the stan-dalone laser system stabilization, including cavity cooling [78],vibration-insensitive cavity designs [79], and using spectralholes in cryogenically cooled crystals as a reference [80].Novel methods to probe the atoms non-destructively [81] orto build frequency standards in tandem [82] may also improvethe frequency standard stability by lengthening accessibleinterrogation times without sacrificing SNR.In addition to the efforts referenced above regarding minia-turization, there has also been substantial work towards im-proving the portability of frequency combs for optical fre-quency standards. The original titanium-sapphire laser-basedcombs have largely been replaced by fiber-based sytems [83]or whispering gallery mode resonators [84]. More recently,there have also been a number of efforts towards miniaturizingmicroresonators and integrating them on chips, which repre-sent promising engineering advances towards future practicaloptical frequency standards [65, 68, 85].Recent demonstrations showed that a master optical fre-quency standard and a quartz-based microwave frequencystandard separated by a 4 km free-space link could be synchro-nized via two-way time-frequency transfer with an ADEV at1 second of − [86], using miniaturized frequency combsas the key component facilitating the link. A hybrid networklinking optical frequency standards to microwave clocks couldsubstantially alleviate reliance on GNSS for a broad range ofapplications including radar, navigation, and communications.IV. C ONCLUSION
In summary, we have presented an overview of the currentstate-of-the-art in the field of atomic frequency standards,including a summary of the physics of operation and per- formance for many products on the market today. The com-parisons in Table I and Fig. 6 provide the most completesummary and review of current products at the time ofwriting. Additionally, we describe the state-of-the-art of next-generation frequency standards in Section III and comparethe projected performance of current and future products. Wealso discuss record performance at the time of writing formicrowave and optical frequency standards.In a broad sense, applications that require atomic frequencystandards can be divided into three general areas: low-powerapplications, tactical applications, and strategic applications.Low-power applications are those that require extremely lowpower, on the order of less than 1 W, to achieve their mission;these applications currently require a CSAC. Tactical applica-tions are those that have been serviced historically by the broadrange of Rb gas-cell frequency standards on the market today,for a variety of communications and military applications.Strategic applications are those for which an investment inthe high size, power, and cost of high-performance referencefrequency standards is required to meet system performance.Fueled by the demands of low-power commercial andmilitary applications, we expect to see a significant changein the market availability of low-power atomic frequencystandards within the next 5 to 10 years. There was only onecommercially-available product for several years (MicrochipCSAC), but the addition of a second vendor (Teledyne) as wellas continued investment from Europe [89, 90], China [91], andJapan [92] promise to continue to evolve the product land-scape in the future. Similarly, we expect the high-performanceproduct space (better than a Microchip 5071A Cesium BeamTube) to undergo evolution as well. The recent introductionof cold atom commercial products by SpectraDynamics andMuquans, other commercial efforts by Microchip [93, 94]and Honeywell [54], and research laboratory prototypes byJPL [29], NPL [60], NIST [68], AFRL [35], and others [56]point to a more varied and competitive landscape for strategicfrequency standards in the future. In comparison, we note thatthere is a comparative lack of commercial investment in novelmid-range tactical frequency standards, which suggests that FrequencyStandardType Platform Short-terminstability Uncertainty Performer(s)
Optical Sr Lattice . × − / √ τ × − JILA and NIST [87]Optical Yb Lattice . × − / √ τ . × − NIST, UC Boulder, Peking Univ.,Niels Bohr Institute, IstitutoNazionale di RicercaMetrologica, Politecnico diTorino, Korea University [16]Optical Al + QuantumLogic . × − / √ τ . × − NIST, UC Boulder, Univ. ofOregon [73]Microwave Cs Fountain . × − / √ τ . × − PTB, Penn State Univ. [43]Microwave Cs Fountain . × − / √ τ ( . to . × − NIST, INRIM, Politecnico diTorino [88]
TABLE IV: Current high-performance frequency standards.these applications are well-served by the current range of Rbfrequency standards on the market today. We expect continuedchanges in the low-power as well as strategic (microwave andoptical) commercial atomic frequency standard landscape inthe years to come. A
CKNOWLEDGMENTS
This work was funded by the MITRE Innovation Program.The authors thank John Betz and Erik Lundberg for a carefulreview of the manuscript.Approved for Public Release; Distribution Unlimited. PublicRelease Case Number 20-0651.c (cid:13)
EFERENCES [1] H. W. Hellwig, “Atomic frequency standards: A survey,”
Proceedings of the IEEE , vol. 63, no. 2, pp. 212–229,1975.[2] L. L. Lewis, “An introduction to frequency standards,”
Proceedings of the IEEE , vol. 79, no. 7, pp. 927–935,1991.[3] R. E. Beehler, “A historical review of atomic frequencystandards,”
Proceedings of the IEEE , vol. 55, no. 6, pp.792–805, 1967.[4] C. Audoin and J. Vanier, “Atomic frequency standardsand clocks,”
Journal of Physics E: Scientific Instruments ,vol. 9, no. 9, p. 697, 1976.[5] A. McCoubrey, “The relative merits of atomic frequencystandards,”
Proceedings of the IEEE , vol. 55, no. 6, pp.805–814, 1967.[6] J. Vanier and C. Audoin,
The quantum physics of atomicfrequency standards . CRC Press, 1989.[7] F. Riehle,
Frequency standards: basics and applications .John Wiley & Sons, 2006. [8] A. D. Ludlow, M. M. Boyd, J. Ye, E. Peik, and P. O.Schmidt, “Optical atomic clocks,”
Rev. Mod. Phys. ,vol. 87, pp. 637–701, Jun 2015.[9] J. Vanier, “Atomic clocks based on coherent populationtrapping: a review,”
Applied Physics B , vol. 81, no. 4,pp. 421–442, 2005.[10] R. Wynands and S. Weyers, “Atomic fountain clocks,”
Metrologia , vol. 42, no. 3, p. S64, 2005.[11] N. D. Bhaskar, J. White, L. Mallette, T. McClelland,and J. Hardy, “A historical review of atomic frequencystandards used in space systems,” in
Proceedings of1996 IEEE International Frequency Control Symposium .IEEE, 1996, pp. 24–32.[12] L. A. Mallette, P. Rochat, and J. White, “Historicalreview of atomic frequency standards used in spacesystems - 10 year update,” in
Proceedings of the 38thAnnual Precise Time and Time Interval Systems andApplications Meeting, Reston, Virginia , December 2006,pp. 69–80.[13] M. A. Lombardi, “Fundamentals of time and frequency,”in
Mechatronics . CRC Press, 2005, pp. 133–150.[14] D. W. Allan, “Time and frequency (time-domain) charac-terization, estimation, and prediction of precision clocksand oscillators,”
IEEE Transactions on Ultrasonics, Fer-roelectrics, and Frequency Control , vol. 34, no. 6, pp.647–654, 1987.[15] D. Sullivan, D. Allan, D. Howe, and F. Walls, “NISTTechnical Note 1337,”
US Dept. of Commerce, NationalInstitutes of Standards and Technology , 1990.[16] W. F. McGrew, X. Zhang, R. J. Fasano, S. A. Sch¨affer,K. Beloy, D. Nicolodi, R. C. Brown, N. Hinkley, G. Mi-lani, M. Schioppo, T. H. Yoon, and A. D. Ludlow,“Atomic clock performance enabling geodesy below thecentimetre level,”
Nature , vol. 564, no. 7734, pp. 87–90,2018.[17] W. Riley, “NIST Special Publication 1065,”
Handbookof Frequency Stability Analysis, NIST , 2008.[18] R. Dicke, “The effect of collisions upon the Dopplerwidth of spectral lines,”
Physical Review , vol. 89, no. 2,p. 472, 1953.[19] K. Akiyama, A. Alberdi, W. Alef, K. Asada, R. Azulay,A.-K. Baczko, D. Ball, M. Balokovi´c, J. Barrett, D. Bint- ley et al. , “First M87 event horizon telescope results. II.Array and instrumentation,” The Astrophysical JournalLetters , vol. 875, no. 1, p. L2, 2019.[20] L. S. Cutler, “Fifty years of commercial caesium clocks,”
Metrologia , vol. 42, no. 3, p. S90, 2005.[21] S. A. Diddams, J. C. Bergquist, S. R. Jefferts, and C. W.Oates, “Standards of time and frequency at the outset ofthe 21st century,”
Science , vol. 306, no. 5700, pp. 1318–1324, 2004.[22] W. J. Riley, “A history of the rubid-ium frequency standard,” July 2019. [Online].Available: http://ieee-uffc.org/wp-content/uploads/2019/07/A-History-of-the-Rubidium-Frequency-Standard.pdf[23] N. Cyr, M. Tetu, and M. Breton, “All-optical microwavefrequency standard: a proposal,”
IEEE Transactions onInstrumentation and Measurement , vol. 42, no. 2, pp.640–649, 1993.[24] V. Shah and J. Kitching, “Advances in coherent popula-tion trapping for atomic clocks,” in
Advances in Atomic,Molecular, and Optical Physics , 2010, vol. 59, pp. 21–74.[25] S. A. Knappe, “Emerging topics: MEMS atomic clocks,”
Comprehensive Microsystems , vol. 3, 2007.[26] R. Lutwak, J. Deng, W. Riley, M. Varghese, J. Leblanc,G. Tepolt, M. Mescher, D. Serkland, K. Geib, andG. M. Peake, “The chip-scale atomic clock - low-powerphysics package,” in
Proceedings of the 36th AnnualPrecise Time and Time Interval Systems and ApplicationsMeeting, Washington, D.C. , 2004, pp. 339–354.[27] S. Knappe, V. Shah, P. D. Schwindt, L. Hollberg,J. Kitching, L.-A. Liew, and J. Moreland, “A microfab-ricated atomic clock,”
Applied Physics Letters
IEEE Transactions on Ultrasonics, Ferroelectrics, andFrequency Control , vol. 63, no. 7, pp. 1034–1043, July2016.[30] P. Laurent, D. Massonnet, L. Cacciapuoti, and C. Sa-lomon, “The ACES/PHARAO space mission,”
ComptesRendus Physique , vol. 16, no. 5, pp. 540 – 552, 2015,the measurement of time / La mesure du temps.[31] F. G. Ascarrunz, Y. O. Dudin, M. C. Delgado Aramburo,L. I. Ascarrunz, J. Savory, A. Banducci, and S. R.Jefferts, “A portable cold Rb atomic clock with fre-quency instability at one day in the − range,” in , May 2018, pp. 1–3.[32] F. G. Ascarrunz, Y. . Dudin, M. C. Delgado, J. Savory,and S. Jefferts, “Long-term frequency instability of aportable cold Rb atomic clock,” in
Proceedings of the49th Annual Precise Time and Time Interval Systems andApplications Meeting, Reston, Virginia Yb + ,” in , April 2015, pp. 752–757.[35] K. W. Martin, G. Phelps, N. D. Lemke, M. S. Bigelow,B. Stuhl, M. Wojcik, M. Holt, I. Coddington, M. W.Bishop, and J. H. Burke, “Compact optical atomic clockbased on a two-photon transition in rubidium,” Phys. Rev.Applied , vol. 9, p. 014019, Jan 2018.[36] G. R. Phelps, N. D. Lemke, K. W. Martin, C. J. Erick-son, and J. Burke, “A compact optical rubidium atomicfrequency standard,” in
Proceedings of the 47th AnnualPrecise Time and Time Interval Systems and ApplicationsMeeting, Monterey, California , January 2016, pp. 157–160.[37] N. D. Lemke, G. Phelps, J. H. Burke, K. Martin, andM. S. Bigelow, “The optical rubidium atomic frequencystandard at AFRL,” in , July 2017,pp. 466–467.[38] H. Shang, X. Zhang, S. Zhang, D. Pan, H. Chen, andJ. Chen, “Miniaturized calcium beam optical frequencystandard using fully-sealed vacuum tube with − instability,” Opt. Express , vol. 25, no. 24, pp. 30 459–30 467, Nov 2017.[39] J. Cao, P. Zhang, J. Shang, K. Cui, J. Yuan, S. Chao,S. Wang, H. Shu, and X. Huang, “A compact, trans-portable single-ion optical clock with . × − sys-tematic uncertainty,” Appl. Phys. B , vol. 123, no. 112,2017.[40] S. B. Koller, J. Grotti, S. Vogt, A. Al-Masoudi,S. D¨orscher, S. H¨afner, U. Sterr, and C. Lisdat, “Trans-portable optical lattice clock with × − uncertainty,” Phys. Rev. Lett. , vol. 118, p. 073601, Feb 2017.[41] L. Marmet, P. Dube, and C. Gigault, “Progress in build-ing NRC’s cesium fountain clock,” in
Proceedings of the2005 IEEE International Frequency Control Symposium
Metrologia , vol. 55, no. 6, pp. 789–805, Oct 2018.[44] M. A. Hafiz, X. Liu, S. Gu´erandel, E. D. Clercq, andR. Boudot, “A CPT-based Cs vapor cell atomic clockwith a short-term fractional frequency stability of × − τ − / ,” Journal of Physics: Conference Series , vol.723, p. 012013, June 2016.[45] P. Yun, F. m. c. Tricot, C. E. Calosso, S. Micalizio,B. Franc¸ois, R. Boudot, S. Gu´erandel, and E. de Clercq,“High-performance coherent population trapping clock with polarization modulation,” Phys. Rev. Applied , vol. 7,p. 014018, Jan 2017.[46] M. Gharavipour, C. Affolderbach, S. Kang, T. Bandi,F. Gruet, M. Pellaton, and G. Mileti, “High performancevapour-cell frequency standards,”
Journal of Physics:Conference Series , vol. 723, p. 012006, Jun 2016.[47] J. Rushton, M. Aldous, and M. Himsworth, “Contributedreview: the feasibility of a fully miniaturized magneto-optical trap for portable ultracold quantum technology,”
Review of Scientific Instruments , vol. 85, no. 12, p.121501, 2014.[48] L. Liu, D.-S. L¨u, W.-B. Chen, T. Li, Q.-Z. Qu, B. Wang,L. Li, W. Ren, Z.-R. Dong, J.-B. Zhao, W.-B. Xia,X. Zhao, J.-W. Ji, M.-F. Ye, Y.-G. Sun, Y.-Y. Yao,D. Song, Z.-G. Liang, S.-J. Hu, D.-H. Yu, X. Hou,W. Shi, H.-G. Zang, J.-F. Xiang, X.-K. Peng, and Y.-Z. Wang, “In-orbit operation of an atomic clock basedon laser-cooled Rb atoms,”
Nature Communications ,vol. 9, no. 1, p. 2760, 2018.[49] M. Langlois, L. De Sarlo, D. Holleville, N. Dimarcq,J.-F. m. c. Schaff, and S. Bernon, “Compact cold-atomclock for onboard timebase: Tests in reduced gravity,”
Phys. Rev. Applied , vol. 10, p. 064007, Dec 2018.[50] http://spectradynamics.com/products/crb-clock/.[51] S. Mulholland, S. Donnellan, G. P. Barwood, D. Gentle,G. Huang, H. A. Klein, P. Patel, G. Walsh, P. E. G. Baird,and P. Gill, “A portable microwave clock using laser-cooled trapped Yb + ions,” in , May 2018, pp. 1–2.[52] A. N. Lykov, “Superconducting maser,” IEEE Transac-tions on Applied Superconductivity , vol. 15, no. 2, pp.900–903, June 2005.[53] C. Schori, G. Mileti, B. Leuenbeger, and P. Rochat, “CPTatomic clock based on rubidium 85,” in
EFTF-2010 24thEuropean Frequency and Time Forum , April 2010, pp.1–4.[54] J. Sebby-Strabley, C. Fertig, R. Compton, K. Salit,K. Nelson, T. Stark, C. Langness, and R. Livingston,“Design innovations towards miniaturized GPS-qualityclocks,” in , May 2016, pp. 1–6.[55] F. Esnault, N. Rossetto, D. Holleville, J. Delporte, andN. Dimarcq, “HORACE: A compact cold atom clockfor Galileo,”
Advances in Space Research
IEEE Transactions on Ul-trasonics, Ferroelectrics, and Frequency Control , vol. 66,no. 3, pp. 624–631, March 2019.[57] K. Miao, J. W. Zhang, X. L. Sun, S. G. Wang, A. M.Zhang, K. Liang, and L. J. Wang, “High accuracymeasurement of the ground-state hyperfine splitting in a Cd + microwave clock,” Opt. Lett. , vol. 40, no. 18,pp. 4249–4252, Sep 2015.[58] P. D. D. Schwindt, Y.-Y. Jau, H. Partner, A. Casias,A. R. Wagner, M. Moorman, R. P. Manginell, J. R.Kellogg, and J. D. Prestage, “A highly miniaturizedvacuum package for a trapped ion atomic clock,”
Reviewof Scientific Instruments , vol. 87, no. 5, p. 053112, 2016.[59] T. M. Hoang, S. K. Chung, T. Le, J. D. Prestage,L. Yi, R. I. Tjoelker, and N. Yu, “Performance of micromercury trapped ion clock,” in .IEEE, 2019, pp. 1–2.[60] S. Mulholland, H. Klein, G. Barwood, S. Donnellan,D. Gentle, G. Huang, G. Walsh, P. Baird, and P. Gill,“Laser-cooled Ytterbium-ion microwave frequency stan-dard,”
Applied Physics B , vol. 125, no. 11, p. 198, 2019.[61] W. F. McGrew, X. Zhang, H. Leopardi, R. J. Fasano,D. Nicolodi, K. Beloy, J. Yao, J. A. Sherman, S. A.Sch¨affer, J. Savory, R. C. Brown, S. R¨omisch, C. W.Oates, T. E. Parker, T. M. Fortier, and A. D. Ludlow,“Towards the optical second: verifying optical clocks atthe SI limit,”
Optica , vol. 6, no. 4, pp. 448–454, Apr2019.[62] F. Riehle, “Optical clock networks,”
Nature Photonics ,vol. 11, p. 25, Jan 2017.[63] N. Poli, C. Oates, P. Gill, and G. Tino, “Optical atomicclocks,”
Rivista Del Nuovo Cimento , vol. 36, no. 12,2013.[64] T. Schuldt, K. D¨oringshoff, E. Kovalchuk, J. Pahl,M. Gohlke, D. Weise, U. Johann, A. Peters, and C. Brax-maier, “An ultra-stable optical frequency reference forspace,” in
International Conference on Space Optics —ICSO 2014, 2014, Tenerife, Canary Islands, Spain , vol.10563, 2017.[65] D. T. Spencer, T. Drake, T. C. Briles, J. Stone, L. C.Sinclair, C. Fredrick, Q. Li, D. Westly, B. R. Ilic,A. Bluestone, N. Volet, T. Komljenovic, L. Chang, S. H.Lee, D. Y. Oh, M.-G. Suh, K. Y. Yang, M. H. P.Pfeiffer, T. J. Kippenberg, E. Norberg, L. Theogarajan,K. Vahala, N. R. Newbury, K. Srinivasan, J. E. Bowers,S. A. Diddams, and S. B. Papp, “An optical-frequencysynthesizer using integrated photonics,”
Nature , vol. 557,no. 7703, pp. 81–85, 2018.[66] R. W. Fox, J. A. Sherman, W. Douglas, J. B. Olson,A. D. Ludlow, and C. W. Oates, “A high stability opticalfrequency reference based on thermal calcium atoms,” in , May 2012, pp. 1–3.[67] S. Origlia, M. S. Pramod, S. Schiller, Y. Singh,S. Viswam, K. Bongs, S. H¨afner, S. Herbers, S. D¨orscher,A. Al-Masoudi, R. Schwarz, U. Sterr, and C. L. and, “Anoptical lattice clock breadboard demonstrator for the I-SOC mission on the ISS,” in . Optical Society of America,2017.[68] Z. L. Newman, V. Maurice, T. Drake, J. R. Stone, T. C. Briles, D. T. Spencer, C. Fredrick, Q. Li, D. Westly,B. R. Ilic, B. Shen, M.-G. Suh, K. Y. Yang, C. Johnson,D. M. S. Johnson, L. Hollberg, K. J. Vahala, K. Srini-vasan, S. A. Diddams, J. Kitching, S. B. Papp, and M. T.Hummon, “Architecture for the photonic integration of anoptical atomic clock,”
Optica
Phys. Rev. Lett. ,vol. 91, p. 173005, Oct 2003.[71] E. Oelker, R. Hutson, C. Kennedy, L. Sonderhouse,T. Bothwell, A. Goban, D. Kedar, C. Sanner, J. Robinson,G. Marti et al. , “Demonstration of . × − stabilityat 1 s for two independent optical clocks,” Nature Pho-tonics , vol. 13, no. 10, pp. 714–719, 2019.[72] B. J. Bloom, T. L. Nicholson, J. R. Williams, S. L. Camp-bell, M. Bishof, X. Zhang, W. Zhang, S. L. Bromley, andJ. Ye, “An optical lattice clock with accuracy and stabilityat the − level,” Nature , vol. 506, p. 71, Jan 2014.[73] S. M. Brewer, J.-S. Chen, A. M. Hankin, E. R. Clements,C. W. Chou, D. J. Wineland, D. B. Hume, and D. R.Leibrandt, “ al + quantum-logic clock with a systematicuncertainty below − ,” Phys. Rev. Lett. , vol. 123, p.033201, Jul 2019.[74] S. Hannig, L. Pelzer, N. Scharnhorst, J. Kramer,M. Stepanova, Z. Xu, N. Spethmann, I. Leroux,T. Mehlst¨aubler, and P. Schmidt, “Towards a trans-portable aluminium ion quantum logic optical clock,”
Re-view of Scientific Instruments , vol. 90, no. 5, p. 053204,2019.[75] M. S. Safronova, D. Budker, D. DeMille, D. F. J.Kimball, A. Derevianko, and C. W. Clark, “Search fornew physics with atoms and molecules,”
Rev. Mod. Phys. ,vol. 90, p. 025008, Jun 2018.[76] C. W. Chou, D. B. Hume, T. Rosenband, and D. J.Wineland, “Optical clocks and relativity,”
Science , vol.329, no. 5999, pp. 1630–1633, 2010.[77] M. G. Kozlov, M. S. Safronova, J. R. Crespo L´opez-Urrutia, and P. O. Schmidt, “Highly charged ions: Opticalclocks and applications in fundamental physics,”
Rev.Mod. Phys. , vol. 90, p. 045005, Dec 2018.[78] T. Kessler, C. Hagemann, C. Grebing, T. Legero, U. Sterr,F. Riehle, M. J. Martin, L. Chen, and J. Ye, “A sub-40-mHz-linewidth laser based on a silicon single-crystaloptical cavity,”
Nature Photonics , vol. 6, p. 687, Sep2012.[79] J. Millo, D. V. Magalh˜aes, C. Mandache, Y. Le Coq,E. M. L. English, P. G. Westergaard, J. Lodewyck,S. Bize, P. Lemonde, and G. Santarelli, “Ultrastablelasers based on vibration insensitive cavities,”
Phys. Rev.A , vol. 79, p. 053829, May 2009.[80] S. Cook, T. Rosenband, and D. R. Leibrandt, “Laser-frequency stabilization based on steady-state spectral-hole burning in Eu :Y SiO ,” Phys. Rev. Lett. , vol. 114, p. 253902, Jun 2015.[81] J. Lodewyck, P. G. Westergaard, and P. Lemonde, “Non-destructive measurement of the transition probability in aSr optical lattice clock,”
Phys. Rev. A , vol. 79, p. 061401,Jun 2009.[82] G. W. Biedermann, K. Takase, X. Wu, L. Deslauriers,S. Roy, and M. A. Kasevich, “Zero-dead-time operationof interleaved atomic clocks,”
Phys. Rev. Lett. , vol. 111,p. 170802, Oct 2013.[83] H. Inaba, Y. Daimon, F.-L. Hong, A. Onae, K. Mi-noshima, T. R. Schibli, H. Matsumoto, M. Hirano,T. Okuno, M. Onishi et al. , “Long-term measurement ofoptical frequencies using a simple, robust and low-noisefiber based frequency comb,”
Optics Express , vol. 14,no. 12, pp. 5223–5231, 2006.[84] T. J. Kippenberg, R. Holzwarth, and S. A. Diddams,“Microresonator-based optical frequency combs,”
Sci-ence , vol. 332, no. 6029, pp. 555–559, 2011.[85] H. Bao, A. Cooper, M. Rowley, L. Di Lauro, J. S.Totero Gongora, S. T. Chu, B. E. Little, G.-L. Oppo,R. Morandotti, D. J. Moss, B. Wetzel, M. Peccianti, andA. Pasquazi, “Laser cavity-soliton microcombs,”
NaturePhotonics , vol. 13, no. 6, pp. 384–389, 2019.[86] H. Bergeron, L. C. Sinclair, W. C. Swann, C. W. Nel-son, J.-D. Deschˆenes, E. Baumann, F. R. Giorgetta,I. Coddington, and N. R. Newbury, “Tight real-timesynchronization of a microwave clock to an optical clockacross a turbulent air path,”
Optica , vol. 3, no. 4, pp.441–447, Apr 2016.[87] T. Bothwell, D. Kedar, E. Oelker, J. M. Robinson, S. L.Bromley, W. L. Tew, J. Ye, and C. J. Kennedy, “JILASrI optical lattice clock with uncertainty of × − ,” Metrologia , vol. 56, no. 6, p. 065004, oct 2019.[88] T. P. Heavner, E. A. Donley, F. Levi, G. Costanzo,T. E. Parker, J. H. Shirley, N. Ashby, S. Barlow, andS. R. Jefferts, “First accuracy evaluation of NIST-F2,”
Metrologia , vol. 51, no. 3, pp. 174–182, May 2014.[89] R. Vicarini, V. Maurice, M. A. Hafiz, J. Rutkowski,C. Gorecki, N. Passilly, L. Ribetto, V. Gaff, V. Volant,S. Galliou et al. , “Demonstration of the mass-produciblefeature of a Cs vapor microcell technology for miniatureatomic clocks,”
Sensors and Actuators A: Physical , vol.280, pp. 99–106, 2018.[90] S. Karlen, J. Haesler, T. Overstolz, G. Bergonzi, andS. Lecomte, “Sealing of MEMS atomic vapor cellsusing Cu-Cu thermocompression bonding,”
Journal ofMicroelectromechanical Systems , 2019.[91] J. Zhao, P. Guo, H. Lu, R. Liu, C. Wang, J. Cui,and H. Meng, “New progress towards chip-scale atomicclock in Peking University,” in . IEEE, 2018, pp.1–3.[92] H. Zhang, H. Herdian, A. T. Narayanan, A. Shirane,M. Suzuki, K. Harasaka, K. Adachi, S. Goka, S. Yanagi-machi, and K. Okada, “ULPAC: A miniaturized ultralow-power atomic clock,”
IEEE Journal of Solid-State Cir-cuits , vol. 54, no. 11, pp. 3135–3148, 2019.[93] D. R. Scherer, C. D. Boschen, J. Noble, M. Silveira, D. Taylor, J. Tallant, K. R. Overstreet, and S. Stein,“Analysis of short-term stability of miniature Yb + buffer gas cooled trapped ion clock,” in Proceedings ofthe 49th Annual Precise Time and Time Interval Sys-tems and Applications Meeting, Reston, Virginia , January2018, pp. 95–99.[94] J. Tallant, J. Noble, D. Guan, N. Dao, and K. Overstreet,“Progress towards a commercial Yb + microwaveatomic frequency standard,” in .IEEE, 2019, pp. 1–6. PLACEPHOTOHERE
Bonnie L. Schmittberger received the A.B. degreein physics from Bryn Mawr College in 2010 and theA.M. and Ph.D. degrees in physics from Duke Uni-versity in 2013 and 2016, respectively. Her graduateresearch focused on nonlinear optics in ultracoldatoms.She is currently an Experimental Physicist atThe MITRE Corporation in McLean, VA, whereshe is working on atomic and optical sensors forapplications in communication and navigation. From2016 to 2018 she was a postdoctoral researcher atthe Joint Quantum Institute, where she worked with quantum states of lightfor applications in metrology. Dr. Schmittberger is a member of the OpticalSociety of America.PLACEPHOTOHERE