A high stability semiconductor laser system for a 88 Sr-based optical lattice clock
Marco. G. Tarallo, Nicola Poli, Marco Schioppo, Guglielmo M. Tino
AA high stability semiconductor laser system for a Sr-based optical lattice clock
M. G. Tarallo, N. Poli, M. Schioppo, G. M. Tino ∗ Dipartimento di Fisica and LENS–Universit`a di Firenze,INFN–Sezione di Firenze,Via Sansone 1, 50019 Sesto Fiorentino, Italy (Dated: June 4, 2010)We describe a frequency stabilized diode laser at 698 nm used for high resolution spectroscopyof the S - P strontium clock transition. For the laser stabilization we use state-of-the-art sym-metrically suspended optical cavities optimized for very low thermal noise at room temperature.Two-stage frequency stabilization to high finesse optical cavities results in measured laser frequencynoise about a factor of three above the cavity thermal noise bewteen 2 Hz and 11 Hz. With thissystem, we demonstrate high resolution remote spectroscopy on the Sr clock transition by trans-ferring the laser output over a phase-noise-compensated 200 m-long fiber link between two separatedlaboratories. Our dedicated fiber link ensures a transfer of the optical carrier with frequency sta-bility of 7 · − after 100 s integration time, which could enable the observation of the strontiumclock transition with an atomic Q of 10 . Furthermore, with an eye towards the development oftransportable optical clocks, we investigate how the complete laser system (laser+optics+cavity)can be influenced by environmental disturbances in terms of both short- and long-term frequencystability. PACS numbers: 06.30.Ft, 42.62.Fi, 32.70.Jz, 37.10.Jk, 42.62.Eh, 42.55.Px
I. INTRODUCTION
Optical frequency standards based on strontium atomshave demonstrated tremendous advantages in terms ofshort term stability (approaching 10 − at 1 s [1–3]) andultimate accuracy (approaching 10 − level [4]) with re-spect to the microwave atomic counterparts. This im-proved level of precision enables new and more stringenttests of fundamental physics [5], and many new appli-cations including improved timing for space travel andaccelerator centers, as well as perhaps a new type ofrelativity-based geodesy [6]. Bosonic Sr-based opticalclocks have demonstrated good features for compact andpossibly transportable devices: easily accessible transi-tions for diode-based lasers for cooling and trapping theatoms, high natural abundance for high signal-to-noiseratio spectroscopy signals, low dead time for high dutycycles and a simplified spectroscopy scheme[7].Presently, the optical local oscillator is the limiting fac-tor for the Sr optical clock stability [2] via the Dick effect[8, 9]. Thus, improving the frequency pre-stabilization ofthese oscillators is a source of intense research in an effortto approach and surpass the 10 − stability goal.Rigid optical cavities are the most common devicesused as short-term frequency references for optical stan-dards. The employment of ultra-low thermal expan-sion materials as spacers between the cavity mirrors andthe increasing level of engineering in their shape designhave allowed several optical cavities to reach a stabil-ity level σ y . · − [10, 11] at 1 s. This instabil-ity level is limited by thermal fluctuations of the mirror ∗ Electronic address: Guglielmo.Tino@fi.infn.it substrates and coatings [12]. Although some theoreticalideas have been proposed to reduce or circumvent thethermal noise[13, 14], it currently sets the ultimate limitfor cavity frequency stabilization techniques. Neverthe-less environmental (acoustic, seismic, etc.) disturbances,poor spectral purity of the free running laser source, andthermal drifts can limit the optical local oscillator sta-bility to much higher σ y values. Reaching the thermal-noise limit at the 10 − level may require a complicatedsetup and considerable table space to isolate the refer-ence cavity from environmental effects [15], which couldbe incompatible with the goal of transportable or space-based optical clocks [16]. These considerations have ledus to develop a high-stability, compact clock laser for theSr clock transition.In this paper we describe in detail the clock lasersource that we are developing as part of a compact opti-cal frequency standard based on neutral strontium atoms[7]. Its main feature is its ultra-high finesse, vibration-insensitive design, and rigid optical cavity used as theshort-term frequency reference. Our clock laser setupis one of the first to employ a rigid Fabry-Perot res-onator with ULE spacer for thermal stability and high-reflectivity fused silica mirrors for low thermal noise, witha best expected instability value σ y = 3 . · − [17].Other compact interrogation lasers have also been real-ized for strontium optical clock spectroscopy [18, 19].This paper is organized as follows: in section II wepresent the setup of the clock laser system, in section IIIwe describe the ultra-high-finesse cavities for stabiliza-tion of the clock laser at 698 nm, and in section IV weshow and discuss the characterization measurements ofthe clock laser system. Finally, we show in the last sec-tion (V) the results of spectroscopy of S - P clock tran-sition with Sr and we present the achieved frequencyinstability of the active optical fiber link.
698 nmECDL
MASTER l /4 l /4 UHFcavity UH F c a v i t y AOM2
AOM3
EOM2
Beat noteanalysis
PNCSystem
Pre-stab.cavity
SMFto atomsFast PD
PZT
ServoElectronics SERVO
EOM1
PDHdetector PDHdetector PDHdetector l /2 (b)(a) (c) SLAVE
SERVO c : to PZT grating c : to laser diode c c FIG. 1: Experimental setup for the 698 nm clock laser fre-quency stabilization and characterization. Block (a): masterdiode laser with two-stage frequency stabilization; (b): secondindependently-stabilized ultra-high finesse cavity and beat-note interferometer to make laser characterization studies; (c)noise-compensated fiber link which deliver interrogation laserto the atoms. UHF: ultra-high finesse; AOM i : acousto-opticmodulators; EOM i : electro-optic modulators; SMF: single-mode optical fiber; PNC: phase noise cancellation system. II. FREQUENCY-STABILIZED DIODE LASERSYSTEM SETUP
The clock laser used to probe the S - P strontiumclock transition is a frequency stabilized diode laser at698 nm. A schematic diagram of the system is shown inFig.1. The whole system is housed in a clean room (class10’000 ÷ ◦ C and delivers about 10mW of optical power at 83 mA driving current. Thefree running ECDL exhibits a frequency noise spectraldensity S ν ( f ) ≃ . · /f (Hz /Hz) up to few MHzuntil it reaches its white noise plateau at 10 (Hz /Hz)[20, 21]. Non-linear response and poor power coupling can occur when one attempts frequency stabilization ona high-finesse cavity. In particular, frequency noise belowabout 750 Hz yields large phase-modulation depths, whilefor frequencies higher than 20 kHz the frequency velocitybecomes higher than the critical value for kHz-wide op-tical cavities[22]. We reduce the laser linewidth with twostages of Pound-Drever-Hall (PDH) frequency stabiliza-tion to optical cavities [23]. A one-step stabilization to anultra-high finesse cavity is in principle possible by meansof conventional servo electronics, but this would require180 dB gain while keeping the same signal-to-noise ratioand the same amplifier fidelity level. Hence we use a firststabilization step to reduce the linewidth to < and the resonance is about 150 kHz wide.The cavity length is tunable because one of the two endmirrors is attached to a piezoelectric transducer (PZT).In order to suppress externally-induced vibrations, thecavity is hermetically enclosed in a metallic pipe withanti-reflection (AR) coated wedges for optical access anda leaded-rubber layer to damp the transmitted vibrationfrom the pipe. The servo correction signal is sent to twoactuation channels. As shown in Fig. 1, one is sent to aPZT attached to the extended cavity grating, while thesecond goes directly to the diode current. The first loophas a single pole at zero and a gain of about 75 dB @ 10Hz. The crossing frequency between the two loops occursat about 100 Hz, with a combined servo bandwidth ofabout 2 MHz [21, 25].For the second stage of frequency stabilization, theerror signal generated by the PDH detector is sent totwo parallel servo loops. One loop dominates at low fre-quencies (up to 1 kHz) and acts on the PZT of the pre-stabilization cavity, thereby compensating low frequencydrifts. The second loop dominates at higher frequencies(up to 50 kHz) by acting on the double-pass AOM (seeFig.1). The measured servo bandwidth of this secondstep of frequency stabilization is 54 kHz.The frequency of the master laser can stay locked tothe ultra-high finesse reference cavity for several hoursas is needed for the remote spectroscopy of strontiumatoms. Environmental thermal drifts limit the lockingtime by causing a pre-stabilization cavity drift that sat-urates the servo amplifier. A tight stabilization of theroom temperature is achieved by two parallel tempera-ture conditioning units. The room and the cavity tanktemperatures are both recorded by a digital data loggingsystem. For 24 hours data acquisition, the temperaturedistribution width of the temperature stabilization sys-tem in one day reaches almost the logger resolution ( ∼ ◦ C). The effect on the cavity error temperature showsa full-width half-maximum distribution close to the digi-tization resolution ( ∼ ×
80 cm which can easilybe further reduced and acoustically isolated for trans-portable purposes. Nevertheless the results presented inthis paper can be regarded as a full test for such appli-cations. III. ULTRA-HIGH FINESSE CAVITIES FOR AHIGH STABILITY LASER
The key feature of our frequency-stabilized clock laseris the ultra-high finesse Fabry-Perot resonator used as alocal frequency reference. The design of our two (iden-tical) resonators meets three main requirements to min-imize both the short- and long-term instability: high-reflectivity and very low mechanical loss mirrors, engi-neered geometry to reduce the impact of environmentalvibrations, and low sensitivity to temperature fluctua-tions.The ultra-high finesse cavity consists of a 10 cmlong ULE (High grade Corning 7972 glass) spacer withtwo optically contacted fused silica mirrors. An ultra-narrow cavity resonance is ensured by the dielectric high-reflection coatings of the mirrors ( T mir ∼ τ =43(2) µ s and bydirectly observing the linewidth ∆ ν =3.7(0.5) kHz of theTEM mode of the cavity. The two independent mea-surements give for both cavities a finesse of 4 . · withina 4% error. We also measured the on-resonance cavitytransmittance T F P = 0.33 which leads to L mir = 2 . ± . . · , which represents the best result for an opticalresonator at 698 nm to our knowledge [26]. This valuealso sets an upper limit on the mirror absorption andhence to the heating-induced frequency instability.We have made an estimate of the thermal noise limitof our cavities based on the values reported for ULE,fused silica and mirror coatings in reference [12]. Theresulting limit, ∼ . · − , is about three times smallerthan the noise level in all-ULE vertical cavities realizedat the same wavelength for a similar purpose [24].Fig. 2 shows a schematic drawing of the cavity andits mechanical setup. The ultra-stable cavity sits onthe aluminum-iron support inside a cylindrical vacuumchamber, which has maintains a pressure of 10 − Torrwith a 20 l/s ion pump. The cavity is supported hor-izontally with two aluminum arms connected by threelow-expansion INVAR shafts. The effective supportingpoints are four square areas (about 2 mm in size) with (a)(b) (c) FIG. 2: Schematic drawing (to scale) of the ultra-high finessecavity inside the vacuum system. The cavity (a) sits on four2 mm area on the aluminum support plate (b). To equi-librate the forces, small pieces of viton have been insertedbetween the cavity and the aluminum supporting areas. Thealuminum plates are connected with three INVAR shafts andrest on the internal surface of the vacuum can on three pointsalong three grooved lines (0.5 mm depth) that define the ver-tical direction inside the vacuum can (c). The thick aluminumvacuum chamber has an external diameter of 30 cm. Viton square pieces (0.5 mm thickness) between the alu-minum supporting points and the ULE spacer surface.The vacuum chamber is made of thick aluminum walls(5 cm) to increase the thermal inertia of the system.The temperature of the outside surface of the vacuumcan is actively stabilized at 25 ◦ C by controlling the cur-rent passing through a high resistance (Alumel) wire thatis wound around the can. Further insulation from en-vironmental temperature gradients is provided by two-layers of polystyrene-and-plastic foil, which completelycovers the tank. Finally the whole structure is containedin a 3 cm thick, extruded polystyrene box. This setup al-lows our heating system to keep a constant cavity temper-ature with a few tenths of a Watt flowing in the Alumelwire. The measured time constant of the system is about3 hours. The amplitude of the residual control overshootdepends on the room temperature T room fluctuations.When ∆ T room is about 2–3 ◦ C, the temperature vari-ations of the external cavity tank are about 50 mK.As with other state-of-the-art optical cavities used forlaser frequency stabilization, our cavity geometry hasbeen designed to reduce vibration sensitivity[27–29]. TheULE spacer has a ”mushroom slotted shape” obtainedby cutting an ULE cylinder along its longitudinal z-axis.The positions of the cuts along the horizontal and verticaldirection are respectively x = 46 .
19 mm and y = − . − ) for acceleration alongthe vertical axis and 10 kHz/(ms − ) for horizontal ac-celeration. For a typical vibration noise spectrum in alaboratory approaching 1 µ g/ √ Hz, these values for thefrequency sensitivity set a limit on the frequency noiseof the order of 10 mHz/ √ Hz, more than a factor tensmaller than the calculated single cavity thermal noise p S T Nν ( f ) = 145 / √ f mHz / √ Hz.Good long-term frequency stability is due the smalllinear coefficient-of-thermal expansion (CTE) of the cav-ity, which result from the very low CTE’s of the ULEspacer (0 ±
30 ppb/ ◦ C from 5 ◦ C to 35 ◦ C with a 95%confidence level[30]) and the fused silica mirrors ( ∼ ◦ C). We measured the cavity CTE near room tem-perature to be 7 · − / K and the length-change periodto be about 3 hours. These values agree (within a factor2 for the CTE) with a 2-dimensional FEM simulation ofthe cavity heat-transfer equation [31].
IV. FREQUENCY STABILITY OF THE 698 NMDIODE LASER
In fig.3 the measurement of the frequency noise of the698 nm clock laser source is shown. It has been measuredby sending part of the light, frequency shifted by AOM in Fig.1, to the second cavity, which rests on the same op-tical table, and analyzing the error signal obtained whenthe frequency of the beam is steered near the resonanceof the second cavity.The measured frequency noise reaches its minimumvalue of p S ν ( f ) = 210 mHz / √ Hz at 10 Hz and thenexhibits a slow rise up to the servo bump at 50 kHz. Atlower frequencies, the laser noise has a slope of 1 / √ f which is a factor of three higher than the thermal noisecontribution of the cavity in the 2-11 Hz frequency band.This discrepancy maybe due to the influence of residualair currents in the beam path through the presence ofparasitic etalons coupled to the high finesse cavity. Thiseffect could be enhanced either by the quite large modu-lation frequency used for the PDH lock (14 MHz) and thelong optical path between AOM and the second high-finesse cavity (about 2 m)[10]. From the integration ofthis noise spectrum, we calculated a laser linewidth ofabout of 2 Hz.To convert these noise measurements directly into fre-quency deviations and to check the residual relative cav-ity drifts, we also locked the frequency of the beam de- -1 F r e qu e n cy no i se [ H z / H z / ] Frequency [Hz]
TN limit
FIG. 3: Frequency noise of the stable 698 nm laser sourcelocked to its ultra-high finesse cavity. The dashed line rep-resents the calculated thermal noise (TN) limit due to thecontribution of the ULE spacer, the fused silica mirror sub-strate and the Ta O / SiO coating. The spectrum takes intoaccount the cavity pole. livered from the source to the second cavity using AOM and generated a beatnote between the two beams. Forconvenience the resultant beat frequency has been down-converted from 200 MHz to about 3 kHz. The beatnotelinewidth, recorded by a digital signal analyzer, is 3 Hzwith a resolution bandwidth of 1.8 Hz. This value agreeswith the spectrum in Fig.3. We measured the Allan devi-ation by counting the beatnote frequency with differentgate times. The result (see Fig.4) is calculated by remov-ing the linear drift with a computer controlled RF gen-erator. The minimum σ y ( τ ) is 1 . × − at τ = 67s. We checked the the stabilized laser system’s sensitivityto acceleration by observing the frequency noise imposedon the laser by accelerations in the vertical and horizon-tal direction. The results of the measurements are shownin Fig. 5. In the upper part of the figure the vibrationnoise spectra are included. The acceleration noise hasbeen measured with a triaxial accelerometer (Kinemet-rics Episensor), while the frequency noise has been mea-sured using a resonance of the second ultra-high finessecavity as a frequency discriminator. For comparison thefrequency noise has been recorded with and without anair damping system applied to the optical table wherethe laser is mounted. With this floating system off, itis possible to recognize an excess of noise between 10and 30 Hz, corresponding to the two main accelerationnoise peaks in the horizontal and vertical directions. Welooked for the peak values of the vibration noise whichshowed the highest spectral coherence between the singleaccelerometer channel signal and the frequency discrimi-nator by means of a digital signal analyzer. We found the -1 -17 -16 -15 -14 Laser beatnote Drift removed Fiber link TN limited beatnote A ll a n d ev i a t i on y () Integration time [s]
FIG. 4: Stability curves for the clock laser system. The plotshows the Allan deviation for the frequency-stabilized clocklaser which approaches the thermal noise limit, while the fiberlink does not limit the potential stability of the laser system. values of 3 kHz/(ms − ) and 20 kHz/(ms − ) for the sensi-tivity for vertical and horizontal directions, respectively.By using these coupling coefficients we can reconstructthe frequency noise due to environmental vibrations: asshown in Fig. 5, the frequency noise spectrum matchesthe reconstructed one between 7 and 20 Hz. The couplingcoefficients are also in good agreement with the resultsof our FEM simulations.A second possible contributor to our clock laser fre-quency instability is laser amplitude modulation noise.Due to the ultra-high finesse of the cavity, the typi-cal optical power stored in the cavities is several watts.Slow laser power build-up and amplitude fluctuationscan cause optical path length shifts via mirror thermalabsorption[32]. Even assuming that the mirror losses aredue only to absorption, at this power level photothermalshot noise is negligible [33]. Nevertheless, since the timeconstant of the thermoelastic effect for our cavity mirrorgeometry is of the order of 0.1 s (which corresponds toa cut-off frequency of 1.6 Hz) slow heating effects coulddominate the nominal thermal drift.We performed a measurement of the amplitude mod-ulation noise sensitivity by locking the power of one ofthe cavities to a fixed voltage reference and looking for afrequency shift on the beatnote frequency when the refer-ence value is changed. The final sensitivity measurementresult is shown in Fig.6. The extracted slope determinedthe laser sensitivity to be k AM = 39 . ± . /µ W (1)This value can be compared with an estimate of thestatic thermoelastic effect, which depends on the mir-rors’ heating constant, its optical absorption and laser beam size. If we assume that all the mirror losses aredue to absorption we get a static amplitude sensitivity δν/δP ≃
45 Hz/ µ W [32], which is compatible with theexperimental data. This value for k AM is large enoughto require that the power of diode-based laser systems beactively controlled. For instance, for an input power of300 µ W, the relative intensity noise has to be at the levelof 10 − (-100 dB) to be equal to the TN noise limit at 1s. V. REMOTE SPECTROSCOPY OF THE CLOCKTRANSITION
We have used our stable clock laser for remote spec-troscopy of the Sr S - P transition [7]. The experi-mental system is shown in Fig.7. In this section we de-scribe the details of the coherent fiber link and the remotespectroscopy results. A. Low-noise optical frequency transfer by meansof hundreds meter-long optical fiber
To deliver the 698 nm light from the stabilized laser tothe Sr trap for spectroscopy on the S - P clock transi-tion we use a 200 m long, single mode optical fiber thatconnects two laboratories located in separated buildings. F r e qu e n cy no i se s p ec t r u m [ H z / H z / ] Frequency [Hz]
UHF 2 Sqrt[ (k i a i ) ] -6 -5 A cce l e r a t i on no i se s p ec t r u m [ g / H z / ] x y z FIG. 5: Measurements of the clock laser sensitivity to ac-celerations. The upper plot shows the recorded accelerationnoise spectra on the optical table without the air dampingsystem (here z indicates the vertical with respect to the ta-ble). The lower plot shows the corresponding measured laserfrequency noise (black line). Here the red line is the recon-structed frequency noise by using as sensitivity coefficients k y = 3 kHz/(ms − ) and k z =20 kHz/ (ms − ) respectively forvertical and horizontal directions.
40 50 60 70 80-5000500 AM = 39 Hz/ W C oun t e r F r qu e n cy [ H z ] Laser Power [ W]
FIG. 6: Measurement of the frequency sensitivity to laser in-tensity shifts. The frequency counter measures the frequencydisplacement for different DC values of the servo-stabilizedinput power.
The excess phase noise coming from the coupling of envi-ronmental noise to the fiber results in an effective broad-ening of the spectrum of the stabilized laser after oneround trip of about 2 kHz. To preserve the spectral pu-rity of the clock laser at the fiber end we then set up afiber phase noise cancellation (PNC) system.
Sr1D lattice
813 nmDM DM MOPA S r o v e n
698 nm
689 nm S P P
200 mSM fiber
PM fiber
SLAVE C l o ck l a s e r [Laser amplifier]OIPNC system ~ ~ DDS
10 MHz
Frequencyshift chain
922 nm MOPA+BiBO689 nm ECDL
Two-stageMOT cooling
FIG. 7: Schematic diagram of the optical and electronic setupused to deliver and probe the clock transition of the lattice-confined Sr atoms. The stabilized laser is amplified byan injection-locked slave diode. The light is then split andfrequency-shifted by an AOM inside the PNC for heterodynebeat note detection. Most of the light is sent to the fiberand coupled to the lattice light by means of a dichroic mirror(DM). The inset shows the relevant energy levels for Sr op-tical clock scheme. OI: optical isolator; MCL: programmablemicrocontroller. -9 -7 -5 -3 S (f) ( r a d / H z ) Frequency [Hz]
Open loop Closed loop
FIG. 8: Fiber phase noise cancellation servo loop perfor-mance. The plot shows the noise spectrum of the mixeroutput acquired by a digital signal analyzer. The open loopspectrum is obtained instead by converting the single sidedspectrum of the beatnote from a spectrum analyzer.
About 1 mW of light coming from the stabilized masterlaser at 698 nm is amplified to a level of 20 mW withan optically injected slave laser. Following the schemeproposed in [34] this light is split into two beams by apolarizer beam splitter. Most of the light is sent to asingle pass AOM that is used to shift the frequency ofthe master laser and cancel fiber-induced phase noise.The diffracted first order from the AOM is coupled intothe 200 m long optical fiber. Due to a 50% fiber couplingefficiency and additional losses in the fiber we have about5 mW exiting the other fiber end. A fraction of this lightis reflected by the fiber end itself which is terminatedwith a standard FC/PC connection. The second beam isused as local oscillator for phase noise detection.The interference signal is then observed on a photodi-ode on which the reference and the reflected beam arecoupled together. With typical powers of 100 nW and 1mW for the reflected power and the reference beam, re-spectively, we get a signal-to-noise ratio of about 30 dBwith 10 kHz resolution bandwidth.The error signal for the phase-locked loop is obtainedby using a digital phase and frequency detector (PFD)and a microcontroller-controlled DDS as the referenceoscillator. The error signal obtained is then fed backto a VCO that controls the AOM frequency. The servobandwidth is naturally limited by the period of the lightround-trip to a value of about 800 kHz. Actually, withabout 7 kHz servo bandwidth we were able to cancel al-most completely the phase noise added by the fiber linkpath. The effect of the noise cancellation is best illus-trated by means of the power spectral density of phasefluctuations, S ϕ ( f ) [35] measured at the output of thePFD with a digital signal analyzer. The result is shownin Fig.8.We studied the performance of the fiber link also in thetime domain, by directly measuring the Allan deviationof the counted beat note frequency of the signal comingfrom the photodiode, (see Fig. 4). The Allan deviationof this signal converted into relative optical frequencyunits corresponds to σ clocky ( τ ) = 2 . · − τ − , whichreflects the effect of the white noise-limited phase-lock.The fiber link has a final instability of 7 · − after 100s integration time. B. Probing of the Sr clock transition
The fiber link delivers a few milliwatts of frequency-stabilized, noise-compensated laser light suitable forprobing the S - P clock transition of bosonic Sratoms. We use the technique of magnetic field-inducedspectroscopy (MIS) to quench the forbidden transition[36], while the experimental setup we used to cool andprobe the atoms has been described in Ref. [7].Following the usual scheme for optical lattice clocks,about 4 · cooled Sr atoms are trapped in an opticallattice, which allows Lamb-Dicke suppression of Dopplerand recoil shifts, near the “magic wavelength” of 813.428nm [37] to cancel AC Stark shift of the transition fre-quency. In Fig. 9 the highest resolution spectrum isshown. The atoms are probed by the clock light under astatic magnetic field B = 1.3 mT, a probe intensity I =20 W/cm and an interaction period τ = 200 ms. Theexpected Rabi frequency is Ω = 2 π ·
36 Hz and a π pulseduration of about 14 ms. Such overdriving of the clocktransition yields a Lorentzian lineshape approximativelyequal to P e (∆) = Ω2 Ω + Γ l / + (Ω + Γ l / (2)where ∆ is the frequency detuning from the atomicresonance, and Γ l is a loss coefficient that is added to thepure Rabi process [38], which can be due to laser coher-ence decay (finite laser linewidth and drifts) or collisionaleffects [39].In order to minimize the effects due to residual fre-quency drifts in the clock laser, the cycle duration is setto 1 s, and we use a photomultiplier tube to collect thefluorescence from the ground-state atoms that are excitedby resonant light at 461 nm. Further active cavity driftremoval is applied by feeding a linear frequency ramp tothe AOM (see Fig. 7) located inside the PNC systemin front of the input end of the long fiber. The valueof the ramp rate is set with a home-made front panelthat controls the microcontroller frequency by checkingthe resonance peak drift on the oscilloscope. All the RFsignals for driving the AOMs along the clock light pathare locked to a 10 MHz reference signal that comes froma low phase-noise quartz oscillator (Oscilloquarz BVA)slaved to a rubidium standard, which for long term is -400 -200 0 200 400-0.20.00.20.40.6 FWHM = 74(2) Hz S t r a n s i t i on p r ob a b ili t y Frequency offset [Hz]
FIG. 9: High resolution spectrum of the S - P transitiontaken by a single linear sweep of the probe laser frequency.The spectrum is obtained with a static magnetic field B =1.3 mT, a probe intensity I = 20 W/cm and an interactionperiod τ = 200 ms. The expected MIS Rabi frequency is Ω= 130 Hz which limits the observed linewidth (see details ontext). The signal-to-noise ratio is 7. steered by a GPS clock signal. Thus the residual laserdrift is kept at the 0.1 Hz/s level.The result shown in Fig. 9 is compatible with a Rabi-limited linewidth: the discrepancy between predicted andexperimental values is about 2 Hz, within the experimen-tal error. This means that Γ l = (2 ±
2) Hz. The peakdensity n = 2 · atoms/cm does not affect the spec-tral width of the clock transition [39], which implies thatthe measured linewidth is not collision-limited. This alsomeans that the clock laser is compatible with an atomicquality factor Q at ≤ · , which should be attainablewith minor changes in the present apparatus. The mainlimitation in the detection of the clock transition wasdue to fluctuations in the number of atoms trapped inthe optical lattice. This can be suppressed by applying anormalization process that measures the population ratioof atoms in the lower/upper clock states by means of the P – S transition at 679 nm to pump the excited atomsback to the S state. A second improvement will be theamplitude and phase stabilization of the lattice laser. VI. CONCLUSIONS
We have presented the laser source we use for pre-cision spectroscopy of S - P intercombination lineof strontium. We demonstrated that a simple, 0.8 m optical system, can be characterized and stabilized atthe Hz level for possible transportable optical clockapplications. The measured frequency noise reaches itsminimum value of 210 mHz / √ Hz at 10 Hz, a factor ofthree above the thermal noise limit. We addressed somespecific problems such as effects of environmental vibra-tion on the whole stabilization system, heating-inducenoise on ultra-high finesse cavities employing fusedsilica mirrors, and remote transfer of optical frequencycarrier over optical fibers. Remote MIS spectroscopy ofthe clock transition should not be limited by our clocklaser at the Hz-level, allowing spectroscopy on the clocktransition up to Q at = 10 . Acknowledgments
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