Light Shift Measurements in a Cesium Fountain without the use of Mechanical Shutters

Transcription

1 Light Shift Meaurement in a Ceium Fountain without the ue of Mechanical Shutter D. G. Enzer, W. M. Kliptein, and R. L. Tjoelker Jet Propulion Laboratory, California Intitute of Technology, Paadena, California USA Daphna.G.Enzer@jpl.naa.gov Abtract We preent meaurement confirming operation of a ceium fountain frequency tandard with light hift below - 15 (and with evidence uggeting it i everal order of magnitude below thi level) but without the ue of mechanical hutter. Suppreion of the light hift i realized uing a mater-lave laer configuration by reducing the overall optical power delivered to the phyic package a well a poiling the injection of the lave, cauing it to lae far off reonance (1- nm) a propoed by the author everal year ago [1]. In the abence of any mitigation, thi (AC Stark) hift, due to nearreonant laer light reaching the atom during their microwave interrogation period, i the larget hift in uch frequency tandard ( -11 for our fountain). Mechanical hutter provided adequate light attenuation but have been prone to failure. Keyword- ceium fountain, light hift, frequency tandard, atomic clock, injection locked laer I. INTRODUCTION Several year ago we propoed operating a Ceium fountain without mechanical laer hutter while keeping the light hift below -17 [1], []. In the abence of any mitigation, thi (AC Stark) hift, due to near-reonant laer light reaching the atom during their microwave interrogation period, i potentially the larget hift in uch frequency tandard ( -11 for our fountain). Therefore, light intenity i typically reduced during thi interrogation period uing acouto-optic modulator (AOM) to rapidly deflect the majority of light away from the main path. Complete attenuation i guaranteed by the additional ue of mechanical hutter. Without hutter, mall amount of leakage light through the AOM can till potentially caue hift detrimental to the -15 level of preciion of many Ceium fountain. While effective and imple, mechanical hutter are prone to failure on a time cale of month. The imple annoyance of replacing mechanical hutter intead become a failure mode for clock meant to operate in pace uch a the PARCS experiment (Primary Atomic Reference Clock in Space) for which thi new technique wa originally conceived, and alo for long-term rugged operation of clock on the ground. In addition, mechanical vibration caued by hutter create operational difficultie in many laer ytem. In our new approach, the light hift i reduced beyond what can be achieved via imple light attenuation by additionally cauing the laer to run off reonance. In our mater-lave laer configuration (Fig. 1), thi i achieved uing the double pa (DP) AOM between mater and lave originally preent for adjuting the lave laer frequency without varying it output amplitude. If the RF power on thi AOM i cut, the lave laer no longer injection lock and intead free run. The lave i alo followed by a ingle pa (SP) AOM for amplitude control. Cutting the RF power to the SP AOM attenuate the beam reaching the atom, while cutting the RF power to the DP AOM further reduce the light hift by detuning the lave laer to it free-running wavelength, often nanometer away from the atomic reonance. Mater Laer Frequency Control AOM (DP) Slave Laer Amplitude Control AOM (SP) To atom collection zone Optical fiber for beam delivery/patial filtering Figure 1. A mater laer beam goe through a double pa AOM and injection lock a lave laer. The lave beam goe thorough a ingle pa AOM for amplitude control before being coupled to a ingle mode fiber for delivery to the atom. Either the double pa or the ingle pa AOM can be ued to attenuate the reonant light a decribed in the text. Experimental verification of thi concept wa deired to confirm that the lave laer doe not till output mall amount of light at the mater laer frequency or produce a broadband pectrum of light that add to the light hift unexpectedly /05/$ IEEE. 79

2 II. i delivered for the three beam whoe propagation vector point down and one fiber for the three beam whoe propagation vector point up. Thi technique ha the advantage of implifying the laer ytem, providing more optical power throughput, and implifying intra-beam power balancing. All data for the current paper are taken uing the recirculation configuration. APPARATUS We teted the new light hift mitigation technique on a Ceium fountain built a a tetbed for the PARCS experiment, originally lated to fly on the International Space Station. The fountain i hown in Fig. and decribed in more detail in [3]. Ditinguihing feature include: magnetic hielding of the entire phyic package (no magnetic trim coil in the atom collection chamber), all laer beam delivered to the phyic package via optical fiber, no mechanical adjutment of optic on the fountain (everything bolt on a built), welded re-entrant window in titanium and copper wall, and a re-entrant pill proof ceium ource operated at room temperature. Typical Allan deviation are ( 3) -13 τ -0.5 down to the tability of the ditributed maer local ocillator ignal (near -15). III. In order to verify that the lave laer detuning technique i effective at eliminating light hift we operate the fountain in different mode in which reonant laer light i attenuated uing one of four method: free running lave (FR), imple attenuation of the lave (AT), FR plu AT, or AT plu hutter. We aume the mode that ue hutter i free of light hift and therefore compare the meaured clock frequency in each of the firt three mode to thi lat mode. Note that the free running mode i achieved by cutting the RF power to the DP AOM uch a the one hown in Fig. 1, while the AT mode i achieved by cutting the RF power to the SP AOM uch a the one hown in the ame figure. (a) Free-flight region Ramey microwave cavity To eliminate long-term drift uch a that of the local ocillator (a maer ignal table to ~-15 from 00-,000 econd and ditributed from a nearby building via fiber optic cable), we cycle through all four mode making all frequency comparion within 1600 econd. In thi time we perform 0 clock frequency meaurement in each mode ( launche per frequency meaurement; 1.96 per launch). Thi proce i then repeated, and the full data et reported here include 334 repetition over the coure of 15 day (not all contiguou). The experimental cycle wa pecifically choen to take advantage of the maer local ocillator tability and to ue it a a flywheel. Note that attenuation method other than the four above were alo teted and diagnotic were performed o that the total repetition time from one et to the next wa actually 800, even though the frequencie of interet were all determined within Optical detection region State election microwave cavity (b) (c) 1 Titanium atom collection chamber MEASUREMENT TECHNIQUE Frequency meaurement are performed in a tandard way (ee for e.g. [6] and [7]). Atom are cooled, collected and launched at 4.1 m/ in all F=4 tate, and then tateelected to the F=3; mf=0 tate. Launched atom pa through the Ramey cavity twice, once on their way up and once on their way down with a total Ramey time of 470 m in between. We phae modulate the microwave by changing their phae during the econd pa to either +90 or -90 from that of the firt pa and then compare the percentage of atom coming back in the F=3 tate for alternate phae. With thee meaurement and knowledge of the Ramey fringe lope, we determine how cloe the applied microwave frequency i to the Ceium clock reonance, and monitor change in the clock frequency due to light hift or other caue. Figure. (a) Bottom ection of C fountain ued for thee meaurement how all the crucial region. (b) Fully aembled C fountain within three layer of magnetic hielding and with laer ytem mounted on compact frame. (c) Schematic howing that only collimator are required for the recirculation technique.. After recirculation occur via the polarizing beamplitter cube hown, collimator 1 provide three beam whoe reultant propagation vector point down, and collimator provide three beam whoe reultant propagation vector point up. The ix orthogonal laer beam ued to trap and cool atom into a lin lin 3-D optical molae (ee e.g. [4], [5]) in the atom collection region are arranged in a typical geometry but delivered in a nontraditional way. Fig. a how the original (more traditional) way thee beam had been delivered, via ix independent (polarizing maintaining) fiber injecting light into ix eparate collimator. A decribed in [3], however, we later witched to a recirculation configuration hown in Fig. c where one fiber Fig. 3 how a ample time-of-flight fluorecence ignal a the downward going atom pa through a mm heet of reonant, circular-polarized probe light. The detection area ha two detector with a repump beam in-between. The 80

3 upper detector (DET) detect F=4 atom; the lower detector (DET1) detect F=3 atom. The number of atom detected in a given tate (proportional to area under curve in Fig. 3) i alway normalized by the total number of atom een in both detector. In thi way we generate the normalized Ramey fringe curve hown in Fig. 5 from the raw data hown in Fig. 4. Beide normalizing, Fig. 5 alo account for two offet, one of which i illutrated by the arrow in Fig. 4. The fringe do not reach zero on reonance, indicating that ome portion of launched atom are not taking part in the Ramey tranition (typically 4-5% of total atom number for DET1, F=3 atom). Thi lo of contrat i upected to be due to microwave leakage. Similar fringe collected with a 180 phae hift between microwave on the way up veru down, reveal the offet for DET, F=4 atom (typically -3%). Thee offet are characterized more in the ytematic dicuion. trantion probability microwave frequency - 9,19,631,770 (Hz) Figure 5. Similar Ramey fringe to thoe of Fig. 4, but with each point normalized to the total number of atom participating in ocillation (i.e. offet are removed a decribed in text). Inet how the normalized central Ramey fringe with ~1 Hz FWHM atom fluorecence ignal (V) time () Figure 3. Time-of-flight fluorecence ignal for atom going down through detection region. Area under the curve i proportional to the number of atom. IV. RESULTS Reult are hown in Table I. All frequencie are relative to the preumed light-hift-free cae (AT plu hutter). The full-light-hift wa monitored by occaionally checking the clock frequency with all laer left on (and injection locked) except the atom collection region repump laer. Thi repump wa kept off to prevent collecting atom that would fluorece and direct extra light up toward the interaction region. Abence of fluorecence/cattering wa confirmed by meauring thi full-light-hift a a function of laer detuning and verifying the expected invere linear relationhip (ee () in next ection). We alo confirmed that the light hift i predominantly due to the two trapping/cooling laer which free-run 1 and nm blue of reonance. Shift from the probe and repump beam were at leat an order of magnitude maller (tuned jut off reonance to maximize the light hift). TABLE I. MEASURED LIGHT SHIFTS detector 1 (F= 3) ignal (V m) detector 1 offet microwave frequency - 9,19,631,770 (Hz) Figure 4. Raw data howing rapidly ocillating Ramey fringe uperimpoed on a broader Rabi profile. Plotted are area under the timeof-flight fluorecence ignal (Fig. 3) a a function of applied microwave frequencie. No phae change i applied between the firt and econd pa through the Ramey microwave cavity. Arrow indicate that ome atom do not participate in the ocillation and thu contribute to an offet. Attenuation Configuration NO attenuation (i.e. full light hift).4-11 Fractional Frequency Shift (relative to AT+hutter) free running lave (FR).1 ± attenuating lave (AT) 0.3 ± FR plu AT 0.3 ± The baeline full light hift of.4-11 varied at mot 7% from it maximum to it minimum over the coure of the 15 day. The other three line of the table how that jut free running the lave laer (FR) gave ~ 4 reduction in light hift, jut attenuating the lave laer (AT) reduced the light hift by more than 4 to below our tatitical uncertainty 81

4 (± ) and uing both method did not introduce any unexpected artifact and therefore alo reduced the light hift to our meaurement limit. If the FR and AT reduction in light hift are independent, one might expect a > 8 attenuation when uing both, reducing the light hift to < -19, but thi i un-verifiable at thi time. The error bar in the table are tatitical error on the difference frequencie reported. The demontrated effectivene of thi lave laer detuning technique indicate that it can be ued for light hift reduction below -15, even in fountain with much higher light cattering or with vertical beam for which the AT method alone would not be adequate. V. COMPARISON WITH CALCULATIONS Following the calculation preented in [1], we etimate the expected light hift for far-detuned and near-reonant light. In the dreed-tate-picture, two generalized energy level are hifted by an applied light field a hown in Fig. 6 [8], [9], where Ω eff = Ω + δ i the effective Rabi frequency, δ i the detuning (laer frequency minu atomic frequency), Ω i the Rabi frequency, I γ Ω = C, ge (1) I I i the light intenity, I i the on-reonance aturation intenity, γ i the linewidth of the optical tranition, and C ge i the Clebch-Gordan coefficient that decribe the coupling between the atom and the light field. In thi picture, for poitive detuning δ, the ground tate i the upper level and ha a poitive light hift, wherea for negative detuning, the ground tate i the lower-level and ha a negative light hift. The ground tate i then hifted in energy by h δ hω E g = ( Ω eff δ ), δ 4δ where the econd expreion i valid for the weak intenity regime our meaurement all fall within Ω << δ. For a given tray light laer frequency that can couple each hyperfine level to a particular excited tate a in Fig. (6), the detuning (laer frequency minu atomic frequency) to each of the hyperfine level i lightly different, leading to a differential energy hift, C ge I ( δ4 δ3) Eg4 Eg3 h γ. (3) 8 I δδ 4 3 Here δ 4 i the detuning to the F=4 hyperfine level, δ 3 i the detuning to the F=3 hyperfine level, and (δ 4 δ 3 )/(π) i alway poitive and i the clock frequency ν = 9.GHz. Thi differential hift i what affect the clock frequency. () hδδ h Ω eff = h Ω + δ Figure 6. Two unhifted (left) and hifted (right) energy level in the dreed-tate picture. When δ i poitive, the ground tate i the upper level. For far detuned light δ >> δ4 δ3, where δ δ4 δ3. The fractional clock frequency hift i then ν Cge I γ (far-detuned), (4) ν 8 I δ where we have ubtituted the clock frequency ν for (δ 4 δ 3 )/(π). Note that the clock hift for far-detuned light i alway negative. When we do not allow the lave laer to free run, the laer light i much cloer to reonance with one of the hyperfine level and that level light hift then dominate the overall clock hift. In the cae where the dominant light ource i near reonance with F=4, δ << δ4 δ3, where δ δ 4, and including pontaneou emiion a in [4] or [5], () or (3) give ν Cge I δ (near F=4). ν I (1 + ( δ / γ) )πν Thi formula i till only valid in the weak intenity regime Ω << δ. For light near the F=3 reonance, thi nearreonance clock hift ha the oppoite ign. Notice that the magnitude of the frequency hift for far-detuned light (4) i jut the magnitude of the frequency hift for near-reonant light (5) caled by πν/ δ, (ignoring the pontaneou emiion term in the denominator which i negligible for fardetuned light). Finally, we can ubtitute parameter value from Table II to etimate the near-reonant and far-detuned light hift auming I = P/(πr ), where P i the laer power reaching the interrogation region and r i the beam-tube radiu over which the light i pread. Uing the light hift etimate in (5) to derive the meaured full-light-hift.4-11, we deduce the power reaching the interaction region to be P =.6-6 mw. For ~ mw of recirculated light input to the atom collection region, thi implie a cattering fraction of only TABLE II. VALUES USED IN ESTIMATION OF THE LIGHT SHIFT (5) 8

5 linewidth, γ/π Parameter beam-tube radiu, r Value (far-detuning) 5 MHz 0.75 cm aturation intenity, I 1.1 mw/cm average Clebch-Gordan coefficient, C ge detuning, δ/π Value (near-reonance with F=4 tate) GHz (i.e. 1 nm) MHz Taking P =.6-6 mw, (4) give an etimate for the far-detuned light hift from the trapping/cooling laer, i.e. the light hift in the FR mode. Thi calculated value of i 0 time maller than (and oppoite ign to) what we actually meaure, eaily explained by mall amount of leakage light near-reonance. Leakage can arie if zero or firt-order light from the DP AOM reache the lave laer and caue it to lae at a near-reonant frequency, or if the free-running lave laer naturally ha ome output near reonance. In general, the amount of leakage could be dependent on the opto-mechanical etup, and thu future ue of thi technique hould rely on confirming the ability of the DP AOM to reduce the light hift everal order of magnitude in the FR mode a done here. VI. SYSTEMATICS In thi ection we decribe ytematic that were checked and/or controlled including: laer intenity, temperature, colliion hift/atom number, microwave power, maer jump, and enitivity to detector offet. The colliion hift wa meaured to be ~ -14 for the number of atom typically launched, o atom number needed to be held contant to better than 4% over a 1600 data et to keep the colliion hift below the tatitical uncertainty Atom number varied with intenity of the trapping/cooling laer, and alo with room temperature (through the Ceium ource preure). Laer intenitie for trapping/cooling and probe beam were all held contant uing electronic ervo that controlled the RF input power to the SP AOM. The room remained within a 3 C temperature range over the coure of the 15 day of data. Overall, the wort-cae long term drift of atom number wa monitored to be only 0.6% per 1600 et. Shot to hot variability wa typically ±1-%. Maer local ocillator performance wa tracked by comparing it to another maer. Typical drift over a 1600 data et were 9-17 (5-15 per day), and the wort drift over the 15 day of data wa till a negligible -16 per A few much larger hort-term drift occurred, but we excluded data from thee hort time period. Shift due to the fiber frequency ditribution cable were not monitored but were previouly meaured and are expected to be table over uch hort time period []. We teted enitivity to the two detector offet mentioned in the Section III (one i hown in Fig. 4) which are ued in calculating the percentage of atom coming back in the F=3 veru F=4 tate. We analyzed a ubet of the data uing different value for thee input parameter to determine how enitive the final reult i to drift. Thi i akin to teting our enitivity to mall drift in Ramey fringe contrat. Fig. 7 how the reulting calculated frequency error where zero error correpond to aumed parameter for that data run. Detector offet were monitored throughout each data run, and tayed contant to within 0.% of total atom number per et, cauing a frequency error of at mot Drift of thee offet value i due to microwave power drift dicued next where thi frequency error i confirmed in a different way. frac. freq. error ( -15 ) detector offet (% of total atom number) Figure 7. When analyzing clock data, different detector offet value lead to different deduced frequencie. Fractional frequency hift a a function of detector offet are hown for detector 1 (filled circle) and detector (unfilled circle). Linear regreion (line) give y = 1.5x for detector 1 and y = 1.6x for detector. We et the microwave power a cloe a poible to that of a π/ Rabi pule. At thi power (and with no phae change between the two pae) the atom make a complete a tranition a poible from F=3 to F=4 (and thu give a minimum DET1 offet). At the end of each 800 data et, the DET1 offet wa checked and then alo meaured uing 1 db extra microwave power and 1 db le. We ued thee meaurement a diagnotic to monitor drift in microwave power. The wort-cae drift in meaured DET1 offet at ±1 db off ideal wa 0.1% of total atom number per et. Fig. 8 how meaured DET1 offet and clock hift a a function of microwave power. From Fig. 8a, DET1 offet value ha to change at leat 1.6% to indicate a 0.5 db power change when the microwave power i ±1 db off ideal. From Fig. 8b, a 0.5 db power change at up to 1 db from the ideal π/-pule power could give a much a a 5-15 clock hift. Therefore, our wort-cae DET1 value variation of 0.1% per et confirm our etimate above of a negligible 3-16 clock error. Note that thi enitivity to microwave power drift could be mitigated by teering the microwave cloer to the clock frequency. For thee meaurement, the microwave 83

6 were detuned from the clock frequency by We have ince implemented teering. detector 1 offet (%) frac. freq. hift ( -15 ) microwave power relative to π/-pule power (db) (a) (b) microwave power relative to π/-pule power (db) Figure 8. When the microwave power drift from it ideal value for a π/- pule, change occur to the detector offet and to the meaured clock frequency. Detector 1 offet (a) and fractional frequency hift (b) are hown a a function of applied microwave power. Detector 1 offet meaurement are ued to monitor the drift in the microwave power, a dicued in the text. Finally, we performed other check including revering the order of the attenuation mode and teting other attenuation mode with hutter uch a one in which the SP AOM are only turned off briefly and then turned back on once the hutter have cloed. No noticeable difference were oberved. We removed occaional glitche in the data where the number of atom detected wa many tandard deviation from the mean; however, we kept all other data which included 4 clock frequency meaurement that were >4 tandard deviation from the mean (8 are expected for 334 et of 400 frequency meaurement). ACKNOWLEDGMENT A a tetbed for the PARCS experiment the apparatu ued for thee meaurement benefited from contribution by many of the PARCS team member. Command and control with traceability to the flight ytem were implemented by a team at JPL including Steve Cole, Brian Franklin, Tom Garvey, Richard Guerrero, Vahag Karayan, Erik Peteron, George Well, and Phil Yate. Electronic upport included contribution by Ted Ozawa, Tom Radey, and Rudy Varga, from JPL. John White provided coniderable laboratory upport. The microwave cavitie were built by Steve Jeffert at NIST, Boulder. Fiber-optic ditribution of the JPL Frequency Standard Tet Laboratory Hydrogen Maer reference ignal were provided by Robert Hamell, Malcolm Calhoun, and William Diener. The reearch decribed in thi paper wa carried out at the Jet Propulion Laboratory, California Intitute of Technology, under contract with the National Aeronautic and Space Adminitration. REFERENCES [1] W. M. Kliptein and D. G. Enzer. Mitigation of the light hift in laer cooled clock without mechanical hutter, Proc. Freq. Contr. Symp., New Orlean, pp , 00. [] We believe the group of K. Gibble ha operated a Rb fountain without hutter and with low light hift, private communication. [3] D. G. Enzer and W. M. Kliptein. Performance of the PARCS tetbed Ceium fountain frequency tandard, Proc. 004 IEEE Int. Freq. Contr. Symp. and Expoition, Montreal, pp , 004. [4] H. J. Metcalf and P. van der Staten, Laer Cooling and Trapping, New York: Springer, 1999, ch. 8. [5] J. Dalibard and C. Cohen-Tannoudji, Laer cooling below the doppler limit by polarization gradient: imple theoretical model, J. Opt. Soc. Am. B, vol. 6, no. 11, pp , Nov [6] W. M. Kliptein, G. J. Dick, S. R. Jeffert, F. L. Wall Phae modulation with independent cavity-phae control in laer cooled clock in pace, Proc. Freq. Contr. Symp., Seattle, pp. 5-3, 001. [7] S. R. Jeffert et al., Accuracy evaluation of NIST-F1, Metrologia, vol. 39, pp , 00. [8] C. Cohen-Tannoudji, J. Dupont-Roc, G. Grynberg, Atom-Photon Interaction, New York: Wiley, 199, ch. 6. [9] H. J. Metcalf and P. van der Staten, Laer Cooling and Trapping, New York: Springer, 1999, pp [] M. Calhoun, private communication. VII. CONCLUSION We have demontrated that it i poible to mitigate the light hift in laer cooled frequency tandard without the ue of mechanical hutter. Two different attenuation technique, one uing SP AOM to attenuate the laer light (AT mode), and one uing DP AOM to detune it (FR mode), independently reduce the light hift by >~ 4. When both technique are ued together, the light hift i confirmed to be < -15 and expected to be < -19. Thi reult hould have important implication for building fountain clock that can operate for longer period without human intervention. 84