A Single-Ion Trap with Minimized Ion-Environment Interactions
P. B. R. Nisbet-Jones, S. A. King, J. M. Jones, R. M. Godun, C. F. A. Baynham, K. Bongs, M. Doležal, P. Balling, P. Gill
““ECTrap_20102015_arXiv” — 2015/10/22 — 0:20 — page 1 —
Noname manuscript No. (will be inserted by the editor)
A Single-Ion Trap with Minimized Ion-Environment Interactions
P.B.R. Nisbet-Jones · S.A. King · J.M. Jones · R.M. Godun · C.F.A. Baynham · K. Bongs · M. Doležal · P. Balling · P. Gill
21 October 2015
Abstract
We present a new single-ion endcap trap for highprecision spectroscopy that has been designed to minimizeion-environment interactions. We describe the design in detailand then characterize the working trap using a single trapped Yb + ion. Excess micromotion has been eliminated to theresolution of the detection method and the trap exhibits ananomalous phonon heating rate of d (cid:104) n (cid:105) /dt = 24 +30 − s − . Thethermal properties of the trap structure have also been mea-sured with an effective temperature rise at the ion’s position of ∆T (ion) = 0 . ± . K. The small perturbations to the ioncaused by this trap make it suitable to be used for an opticalfrequency standard with fractional uncertainties below the − level. Trapped single atomic ions can provide a near-idealized sys-tem in which a quantum object is decoupled from its en-vironment, and any interactions can be precisely tailored.Many uses for such traps have been found, from frequencymetrology and tests of fundamental physics [1,2,3], to simu-lations of quantum systems [4,5] and quantum informationprocessing [6,7], however the imperfections inherent withany physical system introduce perturbations and uncertainties
P.B.R. Nisbet-Jones · S.A. King · J.M. Jones · R.M. Godun · C.F.A. Baynham · P. GillNational Physical Laboratory, Hampton Rd, Teddington, Middlesex,TW11 0LW, UKE-mail: [email protected]. Doležal · P. BallingCzech Metrology Institute, V Botanice, 150 72, Prague, CZJ.M. Jones · K. BongsSchool of Physics and Astronomy, University of Birmingham, Birming-ham, B15 2TT, UK to the experiments being performed. In many cases these canlimit the operational capability of the trapping system.This paper presents a new single-ion endcap trap specif-ically designed to reduce the ion’s interaction with its en-vironment. Particular care has been taken to minimize dcand rf phase-offset induced micromotion, thermal effects,and ion heating rates, and also to maximize optical access,resulting in significant improvements over existing designs.Although this trap was developed with a particular interest inprecision spectroscopy of the S / − F / electric octupole(E3) transition in Yb + for frequency metrology and testsof fundamental physics, its performance is applicable to iontrapping for a wide variety of applications.The requirements on an ion trap for fundamental frequencymetrology with fractional uncertainty at the − level arepresented in Section 2. Details of the design and fabricationof the trap which meets these requirements are given inSection 3. Characterization of the trap using a single Yb + ion is performed in Section 4. An ion trap and vacuum system for high precision frequencyspectroscopy must:1. Minimize the thermal black-body radiation (BBR) emis-sions from the trap, resulting in the BBR environment atthe ion’s position being dominated by the well controlledambient field;2. Minimize the anomalous phonon heating rate, Γ h of theion;3. Minimize stray electric fields which result in rf-inducedmicromotion;4. Minimize collisions with background gas;5. Maximize fluorescence collection from the ion to improvethe state detection signal-to-noise ratio (SNR). a r X i v : . [ phy s i c s . a t o m - ph ] O c t ECTrap_20102015_arXiv” — 2015/10/22 — 0:20 — page 2 —
The first two of these requirements are in conflict. Thedominant thermal heating mechanism of the ion trap struc-ture is dielectric loss in the insulators which isolate the rfand ground sections of the trap. This loss takes the form P = V (cid:15) (cid:48) r (cid:15) tan δΩ rf E , where the power P dissipated intoa dielectric of volume V depends on the dielectric’s relativepermittivity (cid:15) (cid:48) r and loss tangent tan δ when an electric field E of frequency Ω rf is applied across it. Whilst selecting materi-als which have a low loss tangent and relative permittivity isimportant, the easiest way to reduce the thermal heating of thetrap structure is to operate the trap with the lowest possiblevalues for Ω rf and E . However, to achieve a low phononheating rate Γ h the trap should be operated at the highestpossible drive frequency and electric field to provide tight ionconfinement and hence high secular frequencies ω r,z .The anomalous heating rate also has a z − α dependence onthe ion-electrode separation z . The exponent α depends onthe noise process involved but comparison between traps pro-duced in different laboratories indicate a range of < α < [8] making it highly beneficial to have a large electrodespacing. To maintain a given secular frequency ω r,z whenchanging z , E must be increased as z . These effects make itclear that careful design is required to find a suitable compro-mise configuration in which the trap can operate successfullywithin the above constraints.The other requirements are more straightforward to meet.Relative phase delays between the rf voltage on the two end-caps will result in micromotion that cannot be compensatedusing only dc fields. The trap structure must therefore betotally symmetric to ensure that the effective path lengthbetween the endcaps and the rf feed, including all possiblecapacitive and inductive delays, is equal. Likewise the ionmust be shielded from any rf field that does not come from theendcaps. The ion trap must be contained within an UHV/XHVenvironment to reduce pressure-dependent shifts on the orderof ∼ Hz Pa − [9]. Finally, any apertures in the imagingsetup should be placed as close to the ion as possible to in-crease the numerical aperture (NA) and hence fluorescencecollection efficiency. Fast state detection is necessary fortransitions with short excited state lifetimes to avoid losingexcitation probability [10], increasing the clock instability viareduced live time, and introducing the Dick effect from theresulting under-sampling of the local oscillator noise. A highSNR also allows easy use of photon correlation spectroscopyto minimize the excess micromotion. The trap presented in this paper is based on the endcap design[11], and consists of two cylindrical electrodes that are heldat an equal rf potential facing one another whilst containedwithin a pair of independent dc electrodes. This basic design isin use in multiple laboratories, [1,12,13] and has the benefit of excellent optical access in the radial plane. Recent experimentswith fiber-optics contained within the endcap electrodes haveextended this access into the axial direction [13].
Molybdenumrf endcap electrodeAluminaBolt Molybdenumdc endcap electrodeFused SilicaSpacer
Fig. 1: Vertical cross-section through the trap structure. Therf endcaps are secured into the OFHC copper with M2 set-screws and sit within hollow dc endcap electrodes that aresupported by fused silica spacers and recessed alumina bolts.A schematic of the trap is shown in Figure 1. The supportstructure for the trap, which also acts as the high voltagerf feed, is made of oxygen-free, high thermal conductivity(OFHC) copper. OFHC copper has both high electrical andthermal conductivity, and exhibits low out-gassing which willreduce ion loss via chemical reactions of the ion with oxygen.The two 99.9% purity molybdenum rf endcap electrodesare secured into the copper mount using an interference fitand M2 set-screws. Molybdenum has good electrical andthermal conductivity, is non-magnetic, and can be polishedto a high surface quality. Material properties are also thoughtto contribute to Γ h and whilst the mechanism behind this isunclear, traps with cleaned Mo electrodes have demonstratedexcellent results [14]. The faces of the rf electrodes whichsubtend the ion were mechanically polished to achieve amirror quality finish as shown in Figure 2. The mean surfaceroughness was measured via focal-variation microscopy to be R a = 20 nm, resulting in an emissivity of (cid:15) ≈ . at 300 K.As the inner endcap electrodes represent the largest solidangle contribution to the ion’s field of view, the low emissivityreduces the thermal radiation that the ion will experience fromthe temperature of these endcaps. The polished surface alsohas the potential to reduce Γ h as it removes any possiblepoints for field emission of electrons and ensures a uniformsurface free from adsorbates which have been proposed asa source of electric field noise [8]. The electrode tips have adiameter of µ m and a separation of µ m.ECTrap_20102015_arXiv” — 2015/10/22 — 0:20 — page 3 — A Single-Ion Trap with Minimized Ion-Environment Interactions 3
110 120
Lateral Displacement (!m) S u r f ace P r o fi l e ( n m ) Fig. 2: Focal variation microscopy image of the polished sur-face of the upper rf endcap electrode. The inset plot shows thesurface profile along the red line. The 150 nm pit highlightedby the yellow marker (1) is typical of the other imperfectionswhich are visible as black dots in this image, although on alarger scale.Two molybdenum dc electrodes surround the rf endcapsand form the ground reference for the rf potential in thetrapping region. The gap between the rf and dc electrodes inthe trapping region is 135 µ m to ensure a good quadrupolepotential. This gap increases to 1 mm at the base to reducethe capacitance between the endcaps and thus reduce therf current required to drive the trap. This also allows the rfelectrodes to increase in thickness near the base increasingtheir mechanical ridigity. The dc electrodes are positionedusing a pair of fused silica spacers and are secured with99.9% purity alumina bolts. By placing the dielectrics in anon-critical region away from the trap center, it is possibleto have a large separation between the high voltage and dcelectrodes greatly reducing E across the lossy dielectric.The position of the high emissivity dielectric behind the dcendcap also removes any direct line of sight between it andthe ion.The C-shape of the copper mount breaks the trap’s cylin-drical symmetry. The asymmetric mounting protrusions onthe dc endcaps effectively shield the ion from the coppermount restoring the surrounding ground potential (Figure 3).Without the extra shielding the rf minimum would be shiftedfrom the geometric center of the trap, and there would nolonger be a true micromotion zero due to the phase delaybetween the rf potential from the electrode tips and the centerof the C.The dc electric field in the trapping region is controlled byapplying static voltages to the dc electrodes (axial direction)and to two fixed compensation electrodes set back from trapcenter by 5 mm in the radial plane (Figure 4) with a separationof 60 ◦ to maximize optical access in the radial plane. The Fig. 3: Illustration of the importance of extending the dcelectrodes to shield the trapping region from the rf potentialcaused by the C-shaped mount. Simulation of the rf electricpotential performed using the COMSOL software package.With the copper C-shaped mount unshielded the rf poten-tial asymmetrically distorts the quadrupole potential in thetrapping region.dc electrodes are capacitively shorted to ground via 1 µ Fcapacitors to prevent any rf pickup on the dc electrodes thatcould be re-radiated with a phase offset. These capacitorsare located 50 mm from trap center on the air-side of the dcfeedthrough. The applied dc voltages are filtered close to thefeedthrough using a combination of RC and LC π -filters Isotopically enriched neutral
Yb is contained withina resistively heated tantalum tube oven. The atomic beam isslightly collimated (opening angle of θ ≈ ◦ ) reducing theamount of Yb deposited on the trap structure during loading.Yb deposits can cause patch potentials leading to changes inthe necessary compensation voltages and might also affectthe phonon heating rate of the ion.3.1 Vacuum SystemThe vacuum system maximizes the optical access to the trapwhilst maintaining a small light-weight package. The chamberwas machined out of a single aluminum block and is fittedwith non-magnetic CF mounting flanges. The trap region ofthe chamber takes the form of a × × mm cuboidwith a central (cid:31) = 40 mm cylindrical opening (Figure 4).This opening is sealed using two (cid:31) = 50 mm viewports.The laser access and ion imaging window is anti-reflectioncoated UV-grade fused silica (UVFS). The other window ismagnesium fluoride (MgF ), which is transparent up to 8 µ mto allow direct thermal imaging of the trap structure duringoperation. Both windows are cold-welded to the chamberwith (cid:31) = 1 mm indium wire, achieving undetectable He leakrates.The indium sealed windows allow a maximum opticalaccess opening angle of θ = 112 ◦ , compared to the θ = High SRF SMD components (X7R dielectric) ensures good perfor-mance in the 1-10 MHz range.
10 Hz and 100 kHz respectively.
ECTrap_20102015_arXiv” — 2015/10/22 — 0:20 — page 4 —
Horizontal BeamInclined Beams mm Fig. 4: Schematic diagram of the trap and vacuum chamber. (a) Cross-section in the horizontal plane taken through the trapcenter. (b) Front view. The compensation electrodes are shown in yellow and the paths of the named co-linear laser beams areshown as blue lines. ◦ from a traditional CF optic, and allows us to probeand cool the ion in two perpendicular radial directions. Thisalso maximizes the effectiveness of the polarization spinningtechnique [15] and ensures a high fluorescence rate. Opticalaccess in the axial direction is limited by the trap structureitself at θ = 103 ◦ .Ultra-high vacuum is maintained by a SAES NexTorrD100-5 combination non-evaporable getter (NEG) and ion-getter pump. The NEG provides a pumping speed of up to100 l s − for active gases (H , H O, N , O , etc.), while inertgases are pumped by the ion getter pump at a rate of 6 l s − .After final assembly a bakeout at 125 ◦ C roughed by a turbo-molecular pump achieved a base pressure of < × − Pa( − mbar) determined by the current draw of the ion pump.For a Langevin-approximated frequency shift of 10 Hz Pa − [9] this corresponds to 100 µ Hz.3.2 Light delivery and collectionThe ion is illuminated along three optical axes which probeperpendicular radial directions and sample the axial motion ofthe ion at an angle of θ = 40 ◦ (Figure 4). The horizontal beamcontains all the wavelengths that are used in the experimentwhich range from the UV (369 nm cooling) to the IR (935 nmre-pump). These wavelengths are combined using dichroicbeamsplitters and coupled into an endlessly-single-modephotonic crystal fibre . The fibre output is brought to anachromatic focus of waist w = 19 µ m at the ion’s positionusing a pair of off-axis parabolic mirrors, ensuring perfectoverlap of all lasers onto the ion. The two beams that areraised out of the horizontal plane only supply cooling light.Atomic fluorescence is collected through the UVFS view-port using an aspheric lens pair in a 2.6:1 telescope. After NKT LMA-PM-5 spatial and spectral filtering an on-resonance fluorescencesignal of , s − is obtained for a single ion at I sat . Fora typical background count rate of s − this results in asignal to noise ratio of SNR = 400. The trap performance was characterized using single Yb + ions however the performance should be directly transferableto other elements. Ions have been loaded and trapped at rffrequencies from Ω rf / π = 3 − MHz. The secular frequen-cies of trapped single ions were measured by ‘tickling’ theion with a low-power rf field applied to one of the dc endcaps.When resonant with the ion’s secular frequency this ticklingfield heats the ion, and greatly increases the observed fluores-cence from a far red-detuned cooling laser. Secular frequencieshave been arbitrarily set from the kHz to the MHz range upto a maximum of ω ( x,y,z ) = 2 π × (1 . , . , . MHz,obtained using a helical resonator with a loaded resonantfrequency of MHz with 1 W of forward power. Ion life-times on the order of a week are routinely observed at allfrequencies. Uncooled ion lifetimes of up to 15 hrs have beenobserved on multiple occasions. Collisions with backgroundgas molecules can populate the long-lived F-state in Yb + , andwithout repumping, is equivalent to loss of the ion. We rou-tinely observe > hr lifetimes without collisional transfer tothis state which supports the low vacuum pressure measuredin Section 3.1.4.1 3D Micromotion minimizationFor ion-based atomic clocks, residual excess micromotionfrom imperfectly compensated stray potentials causes two ofECTrap_20102015_arXiv” — 2015/10/22 — 0:20 — page 5 — A Single-Ion Trap with Minimized Ion-Environment Interactions 5 the most significant trap-induced systematic shifts: the dc-Stark shift and the time-dilation shift [1,16,17]. Additionally,when pushed away from the rf potential minimum the ion isexposed to the possibility of electrical noise from the trapdrive.The projection of the ion’s micromotion in the directionof any one of the cooling beams can be measured usingthe photon correlation technique. The excess micromotioninduces a first-order Doppler shift of the cooling laser in theframe of the ion, which can be observed as a modulation of theion’s fluorescence at the trap drive frequency when the ion isilluminated with light at the cooling transition half-maximum.The observed fluorescence signal S obs from each coolingbeam can then be written as S obs = S max S mod sin( Ω rf t + φ )] , (1)where the maximum signal S max is sinusoidally modulatedat the trap drive frequency Ω rf with phase φ and fractionalamplitude S mod . To minimize the micromotion, voltagesare applied to the compensation electrodes and the resultingelectric field pushes the ion towards the rf potential mini-mum reducing the value of S mod . A complete analysis ofthis technique, including effects caused by the fluorescencetransition’s finite linewidth is given in [18]. rf Period F l u o r e s ce n ce s i g n a l [ r e l . ] Fig. 5: Photon correlation signal and sinusoidal fits for anion with a flourescence modulation of S mod = 0 . (blacktriangles), S mod = 0 . (blue squares), and S mod = 0 . (green circles).An example of the resulting correlation plot is shownin Figure 5 for three different levels of micromotion. Mi-cromotion along the two perpendicular axes of the beamsin the radial plane is shown in Figure 6 as a function ofthe voltage applied to one of the radial compensation elec-trodes. As the laser beams have components along both ofthe ion-to-compensation-electrode axes, changing one of thecompensation voltages will alter the micromotion observedalong both beams. The micromotion projection along a givenbeam is minimized using the more sensitive compensation electrode, and through an iterative process can be eliminatedto the measurement resolution of the system, resulting in S mod = 0 . .After micromotion minimization the trap has been consec-utively reloaded up to twenty times over a 5 hour period with-out noticeable changes in the micromotion at the S mod = 0 . level being observed. No long term drifts in the micromotionhave been observed suggesting that vacuum windows aresufficiently far from the ion that dielectric charging fromthe UV laser beams is insignificant [19] and that the trap iselectrically and mechanically stable. Voltage [V] M o d u l a t i o n D e p t h Fig. 6: Modulation depth of the photon correlation signal as afunction of the voltage on one of the compensation electrodesin the radial plane for the beams that are at an angle of ◦ (black) or ◦ (red) in the radial plane. The green shadedarea represents the modulation depth where the dc-Stark andtime dilation shifts are below × − . A sign change inthe modulation depth corresponds to a π phase change in themodulation signal.4.2 Anomalous heating rate of the ionIn many experiments such as optical atomic clocks or quantumcomputation based on optical qubits, it is desirable to resolvenarrow lineshapes on electric dipole forbidden transitions.The peak excitation (gate fidelity) is limited by the dephasingcaused by the thermal distribution of the vibrational quantumnumber of the ion. Even if an ion is cooled to its vibrationalground state before interrogation, electric field noise willcause the ion to heat during the probe pulse, thus reducing thefringe contrast. As the wavefunction of a hot ion is larger andit experiences more of the trapping potential a high heatingrate will also increase the dc Stark and time-dilation shiftscaused by the ion’s secular motion.ECTrap_20102015_arXiv” — 2015/10/22 — 0:20 — page 6 — The phonon heating rate of the trap was measured usingthe Doppler re-cooling technique. After a prolonged periodwithout laser cooling the cooling laser, tuned close to the un-perturbed line center, is re-applied to the ion. The temperatureof the ion before re-application of the cooling laser can bedetermined by analysis of how the fluorescence returns. Afull description of this technique can be found in [20,21,8].The trap was operated at an rf frequency of Ω rf / π =7 . MHz with a secular frequency ω r / π = 500 kHz. Thisis much lower than the natural linewidth of the cooling tran-sition Γ/ π = 19 . MHz, ensuring that the ion is within theweak-binding limit where the semi-classical Doppler coolingmodel is valid. The ion was allowed to heat for periods up to50 s before the 5 MHz red-detuned cooling laser was reappliedand the fluorescence return counted in 15 µ s time-bins. Thefluorescence return was measured 3000 times to decrease thestatistical uncertainty and the results averaged as shown in Fig-ure 7(a). There was no resolvable change in the fluorescencelevel throughout the 10 ms counting window. The resolutionof the measurement was limited to d (cid:104) n (cid:105) /dt = 100 s − bythe signal-to-noise achieved in our 15 µ s binning of the pho-ton counter signal. This yields an upper limit on the phononheating rate of d (cid:104) n (cid:105) /dt = 50 +100 − s − with σ uncertaintycurtailed at zero.An alternative method of measuring the anomalous heat-ing rate is to observe dephasing of the Rabi oscillations onan atomic transition as a function of the time delay betweencooling the ion and starting a Rabi transition. The excitationprobability P can be calculated from the excitation proba-bility P n and Rabi frequency Ω n for each motional state n [22] along with the probe-laser-induced decoherence over theprobe time t , caused by its finite coherence time τ : P = 14 (cid:16) e − t/τ (cid:17) (cid:32) − (cid:88) n P n cos ( Ω n t ) (cid:33) (2)Ion heating during the probe pulse also affects the dephas-ing rate; however this effect is small for the conditions inthis trap. During this measurement the trap was operatedat an rf frequency of Ω rf / π = 20 . MHz with a secularfrequency ω r / π = 776 kHz. Rabi oscillations were drivenon the 467 nm: S / − F / transition following a delay ofup to 500 ms between the end of the cooling cycle and inter-rogating the transition. Fitting Equation 2 to this data (Fig. 7)determined the heating rate to be d (cid:104) n (cid:105) /dt = 24 +30 − s − ,which corresponds to an electric field noise density of S E =5 . × − V m − Hz − . This heating rate is in line withheating rates for other traps of this size. More precise measure-ments of the heating rate would require alternative techniquessuch as carrier-to-sideband ratio measurements, which are notpossible at this stage due to the necessary probe laser powers.The fundamental limit to the ion heating rate is expected to bethe Johnson noise of the LRC circuit connected to the endcapelectrodes. [8]. Time ( ms ) N o r m a li z e d F l u o r e s ce n ce (a)
50 100 150 200 00.20.40.60.81
Probe Time (ms) E x c i t a t i o n P r o b a b ili t y (b) Fig. 7: The top plot shows ion fluorescence as a function of re-cooling time for a Doppler re-cooling measurement of the trapanomalous heating rate. The ion was illuminated at I = I sat and at a detuning of 5 MHz. Fluorescence return was measuredafter 30 s without cooling. The red line shows the theoreticalfluorescence return for a heating rate d (cid:104) n (cid:105) /dt = 50 . Theinset plot shows the first 300 µ s of recooling. The bottomplot shows the Rabi oscillation decay on the E3 transitionfor post-cooling delay times of 10 ms (hollow circles), 50 ms(purple triangles), 200 ms (orange squares), and 500 ms (greencircles). Peak excitation of the first Rabi pulse was limited to85% by noise on the excitation laser.4.3 Thermal measurements of the trap structureOne of the dominant causes of uncertainty in state-of-the-artoptical atomic clocks is the Stark shift caused by the emissionof black-body radiation from the trap and vacuum chamberapparatus. It is therefore essential that any trap is designedwith good thermal properties so that any temperature riseduring operation is low, can be accurately determined, andcan be kept stable.Finite element models (FEM) were developed by CMI [23]to calculate the changes in the temperature distribution acrossthe ion trap caused by its operation, and thus the effectivetemperature of the total BBR environment seen by the ion.Models of the trap show that the maximum temperature riseof any part of the trap structure should be 0.15K at standardoperating conditions, and are shown in Fig. 8. As the solidangle subtended by the hot regions of the trap is very small,and the rf electrode, which has a very large solid angle, hasECTrap_20102015_arXiv” — 2015/10/22 — 0:20 — page 7 — A Single-Ion Trap with Minimized Ion-Environment Interactions 7 been polished to a mirror finish, the effective temperaturerise that should be seen by the ion is much lower than this, ∆T (ion) = 0 . ± . K.Fig. 8: FEM simulation of the thermal profile cross-sectionfor an applied rf potential at Ω rf / π = 15 MHz requiredto give ω r / π = 1 MHz . A maximum temperature rise of0.15 K was found in the fine wires which connect to the dcendcap electrodes.The thermal characteristics of the operating trap were mea-sured in situ through the MgF window using a Cedip Silverthermal infrared camera in the 3-5 µ m radiation band Fig. 9.The imaging setup was pre-calibrated by measuring targetsamples at known temperatures. During initial characteriza-tion of the trap [23] it was found that dielectric heating in theUHV feedthrough completely dominated the heating from thetrap structure itself, causing a temperature rise of 6.5 K whensecular frequencies of 1 MHz were generated at a drive fre-quency of 21 MHz. A simple heat sink made from a thermallyconductive ceramic post (Shapal (cid:31) = 13 mm) reduced thistemperature rise by a factor of two, and a further improvementin the feedthrough temperature was obtained by decreasingthe drive frequency by 30%. With these minor modifications atemperature rise of 1.5 K was measured both with the thermalcamera and calibrated PT100 sensors on the air-side of thefeedthrough, when an ion was trapped in a Ω rf / π = 14 MHzfield with ω r / π = 1 MHz. This results in an effective tem-perature rise at the ion of ∆T (ion) = 0 . ± . K. We have designed and constructed a trap for single ions withthe endcap topology in order to minimize trap-ion interactionsand thus approach an ideal isolated quantum system. The traphas been characterized using a single Yb + ion to investigatethe micromotion and anomolous heating rate properties of Fig. 9: IR images of the trap structure taken in the 3-5 µ m range (a) without an applied rf voltage, and (b) with Ω rf / π = 14 MHz field at ω r / π = 1 MHz. The IR imagesare not corrected for emissivity and thus show the effectivetemperature that the ion observes rather than the actual tem-perature of the trap. Reflections belong to ambient laboratoryradiation which is shielded during normal operation.the trap. The trap was operated over a range of frequenciesfrom Ω rf / π = 3 → MHz, and with secular frequencies ω r,z from kHz to the MHz range. Cooled ions remain inthe trap almost indefinitely, and the uncooled ion-retentiontime is in excess of 15 hrs. A fluorescence signal-to-noiseratio from a single ion of 400 is achieved.Excess micromotion has been minimized to the level of S mod = 0 . as determined via the rf-photon correla-tion technique. The anomalous phonon heating rate of thetrap was measured using the Doppler recooling method to be d (cid:104) n (cid:105) /dt = 50 +100 − s − and via the observation of Rabi flopdephasing to be d (cid:104) n (cid:105) /dt = 24 +30 − s − with the uncertaintylimited by the experimental methods. Further investigationof the anomalous phonon heating rate using sideband spec-troscopy is planned. The effective rise in the BBR temperatureat the ion has been determined via a combination of thermalimaging and FEM models to be ∆T (ion) = 0 . ± . Klimited by the rf loss in the vacuum feedthrough.When used for an atomic clock based on the frequencyof the E3: S / − F / transition in Yb + , perturbationsinduced by these trap parameters are presented in Table 1.These contributions, when summed in quadrature, consti-tute a fractional uncertainty on the transition frequency of . × − . This should be compared with the uncertaintycontribution from trap-based frequency shifts in recently pub-lished absolute frequency measurements of ∼ . × − [1,16]. The uncertainty could be further improved by reducingthe secular shifts through well established techniques forground-state cooling of the ion, and by fully heat-sinkingthe feedthrough. If successful, these improvements shouldreduce the uncertainty in the error budget by more than anECTrap_20102015_arXiv” — 2015/10/22 — 0:20 — page 8 — Source of Shift δν/ν (10 − ) σ/ν (10 − ) Background gas collisions 0.15 0.15Excess µ -motion scalar dc-Stark 0 0.1Excess µ -motion time dilation 0 0.1Secular motion scalar dc-Stark -0.3 0.2Secular motion time dilation 0.7 0.1BBR dc-Stark: offset from 293 K 0.2 0.2 TOTAL
Table 1: Error budget for trap induced shifts and uncertain-ties for the E3: S / − F / transition in Yb + when thetrap is operated at Ω rf / π = 14 MHz, with ω x,y,z / π =(1 , , MHz.order of magnitude.This work was funded by the European Metrology Re-search Programme (EMRP), the UK National MeasurementSystem, and the European Space Agency (ESA). The EMRPis jointly funded by the EMRP participating countries withinEURAMET and the European Union.
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