Measurement of the lifetime of the 7 s 2 S 1/2 state in atomic cesium using asynchronous gated detection
George Toh, Jose A. Jaramillo-Villegas, Nathan Glotzbach, Jonah Quirk, Ian C. Stevenson, J. Choi, Andrew M. Weiner, D. S. Elliott
MMeasurement of the lifetime of the s S / state in atomic cesium using asynchronousgated detection George Toh , , Jose A. Jaramillo-Villegas , , , Nathan Glotzbach , , Jonah Quirk , ,Ian C. Stevenson , , J. Choi , , Andrew M. Weiner , , and D. S. Elliott , , School of Electrical and Computer Engineering,Purdue University, West Lafayette, Indiana 47907, USA Purdue Quantum Center, Purdue University, West Lafayette, Indiana 47907, USA Facultad de Ingenier´ıas, Universidad Tecnol´ogica de Pereira, Pereira, Risaralda 660003, Colombia Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, USA Pott College of Science, Engineering and Education,University of Southern Indiana, Evansville, Indiana 47712, USA (Dated: January 18, 2019)We report a measurement of the lifetime of the cesium 7 s S / state using time-correlated single-photon counting spectroscopy in a vapor cell. We excite the atoms using a Doppler-free two-photontransition from the 6 s S / ground state, and detect the 1.47 µ m photons from the spontaneousdecay of the 7 s S / to the 6 p P / state. We use a gated single photon detector in an asynchronousmode, allowing us to capture the fluorescence profile for a window much larger than the detectorgate length. Analysis of the exponential decay of the photon count yields a 7 s S / lifetime of48.28 ± PACS numbers: 32.70.Cs
Precision laboratory measurements of electric dipole(E1) matrix elements are critical for the advancement ofatomic parity violation (PV) studies in several regards:Precise models of atomic structure are required to ex-tract the weak charge Q w from any measurement of thePV transition moment; E1 matrix elements are includedexplicitly in the perturbative expansion for the PV mo-ment; and measurements of the PV amplitude are alwayscarried out relative to a different optical transition am-plitude, such as a Stark-induced amplitude. Thus, werequire precise determinations of electric dipole matrixelements, through a variety of laboratory measurements,and detailed comparison with ab initio theoretical results.The most precise determination of a PV moment inany atomic system is that of the 6 s S / → s S / transition in cesium, carried out by Wood et al. in1997 [1]. In the past 30 years, several advances in mod-els of the atomic structure of the cesium atom [2–12],and measurements of key transition amplitudes [13–27]have been reported. The uncertainty in the E1 transi-tion moment (cid:104) s || r || p / (cid:105) is presently one of the pri-mary contributors, along with the (cid:104) p / || r || s (cid:105) matrixelement, to the uncertainty in the PV moment for the6 s S / → s S / transition [11, 23]. Similarly, theuncertainties in (cid:104) s || r || p / (cid:105) and (cid:104) s || r || p / (cid:105) are pri-mary contributors to the uncertainty of the scalar Starkpolarizability for the 6 s → s transition [20, 23].In this paper we present our measurement of the life-time of the cesium 7 s S / state using an asynchronoustime-correlated single-photon counting (TCSPC) tech-nique. By measuring the lifetime of the 7s state, we in-directly measure the matrix elements named above. Wefind a lifetime value of 48.28 ± et al. [13],but with much smaller uncertainty, and in agreementwith several theoretical determinations [3–6, 9, 11]. Thiswork paves the way to reducing the uncertainty of the PVtransition amplitude and Stark polarizability, and com-plements progress we are making toward a new atomicPV measurement in cesium [24, 28].Cesium atoms in the 7 s S / state can spontaneouslydecay through the 6 p P / or 6 p P / states, which sub-sequently decay to the 6 s S / ground state, as shownin Fig. 1. The total decay rate 1 /τ s of the excited state FIG. 1. Energy level diagram of atomic cesium, showing thestates relevant to this experiment. Atoms are excited fromthe 6 s S / ground state to the 7 s S / excited state by two-photon excitation. Fluorescence photons at 1.47 µ m from thedecay of atoms from the 7s state to the 6 p P / state arecollected and counted by the single photon detector. a r X i v : . [ phy s i c s . a t o m - ph ] J a n FIG. 2. Timing diagram of the experiment. The dashed linerepresents the start time for the TCSPC module, and t thearrival time of the first photon detected within the gate pulse. f = 1 .
25 MHz is the laser repetition rate and f is the SPDgate repetition rate. The difference in frequencies ( f (cid:54) = f )causes the SPD to gate during a different part of the measure-ment window every cycle. This gate-free method of capturingdata allows us to utilize the SPD with a 40 ns gate, while cap-turing a 800 ns measurement window of photon fluorescence. is written as the sum of transition rates to these twointermediate states1 τ s = (cid:88) J =1 / , / ω J c α |(cid:104) s || r || p J (cid:105)| J (cid:48) + 1 , (1)where τ s is the lifetime of the 7 s S / state, ω / and ω / are the transition frequencies of the 7 s S / → p P / and 7 s S / → p P / transitions, respec-tively, J (cid:48) = is the angular momentum of the 7 s S / upper state, α is the fine-structure constant, and c is the speed of light. Once the lifetime of the 7 s state is measured, only the ratio of matrix elements, (cid:104) s || r || p / (cid:105) / (cid:104) s || r || p / (cid:105) , is needed to extract the indi-vidual matrix elements. This ratio is reliably calculatedby theory and very consistent across different theoreticalcalculations [3–6].TCSPC has been used to accurately measure atomicexcited state lifetimes in Cs [15–17], Fr [29–31] andRb [32, 33]. A train of laser pulses repeatedly excitesthe atoms, and a detector records the exponential de-cay of fluorescence photons from the excited atoms. Weintroduce an asynchronous detection scheme in order tocollect the fluorescence for a measurement window muchlonger than the gate duration of our gated single photondetector (SPD), and to reduce the impact of any possi-ble temporal variations of the detector efficiency over themeasurement window. The key to the asynchronous de-tection scheme is to cycle the laser excitation pulses andgated-SPD at different frequencies, f and f , respec-tively, as illustrated in Fig. 2. This causes varying delaytimes between the beginning of the measurement window(of duration 1 /f ) and the SPD gate, which effectivelycauses the SPD gate pulse to repetitively scan across thefull measurement window. When repeated over many cy- cles, the result is a flat response of the detector in time,comparable to using a free-running detector [34].We show a schematic of our experimental setup inFig. 3. The excitation laser is a home-made 1079 nmexternal cavity diode laser (ECDL), coupled into a fiberamplifier to amplify the optical power to 4 W, and splitalong two paths using a polarizing beam splitter (PBS)cube. We use the first of these beams to lock thelaser frequency to the two-photon resonance frequency,and the second to carry out the lifetime measurements.The first beam passes through an acousto-optic modu-lator (AOM) driven by a constant-amplitude 90 MHzsignal. We direct the first-order diffracted beam to aheated vapor cell (VC1), where a photomultiplier tube(PMT) picks up atomic fluorescence at 852 nm. Thissignal is processed and fed back to the laser frequencycontrol to stabilize the laser frequency to the cesium6 s S / , F = 4 → s S / , F = 4 transition ( F isthe total angular momentum, electron spin plus nuclearspin). We direct the second beam from the PBS to asecond AOM, which is also driven at 90 MHz. The rfpower driving AOM2 is pulsed on for 250 ns at a repe-tition rate of f = 1 .
25 MHz. This pulsed beam is fo-cused into a second heated cesium vapor cell (VC2) ina nearly-counter-propagating geometry for Doppler-freetwo-photon excitation (for enhancement of the signal) ofthe 7 s S / stateWe filter the fluorescence at 1.47 µ m from this cellusing a long-pass filter to reduce unwanted background(scattered laser light, other fluorescence components, androom lights, for example), and use a commercial fibercollimator to couple the fluorescence light into a 10 µ msingle-mode fiber. We choose to detect this fluorescenceline for its reduced susceptibility to radiation trappingeffects, its time dependence as a simple single exponen-tial (in contrast to the double exponential of [16, 31–33])and its large branching ratio, compared to the 1.36 µ m FIG. 3. Experimental setup. Abbreviations in this fig-ure are: (PBS) polarizing beam splitter cube; (AOM1) and(AOM2) acousto-optic modulators; (VC1) and (VC2) cesiumvapor cells; (PMT) photomultiplier; (FC) fiber coupling op-tics; (AWG) arbitrary waveform generator; (SPD) single pho-ton detector; and (TCSPC) time-correlated single photoncounter. line. The collection optics allows us to image decayingatoms within an area of ∼ µ m diameter. This de-tection volume is much greater than the region excitedby the laser, and much larger than the ∼ µ m distancetraveled by an average velocity atom within one lifetime τ s . The fiber transmits the fluorescence light to an Au-rea Technology InGaAs gated avalanche single photondetector.For accurate timing of photon arrivals, we use a Hy-draHarp 400 TCSPC module with a specified timing un-certainty of <
12 ps. An arbitrary waveform generator(AWG) produces the start pulse for the TCSPC module,indicating the start of the 1 /f = 800 ns long measure-ment window. The AWG also generates the 90 MHz rfmodulation pulse for driving AOM2, which generates thetrain of optical excitation pulses sent to VC2. We gatethe SPD on for T gate = 40 ns at a slightly different fre-quency f (where f ≈ f + 20 Hz). The TCSPC moduleregisters the arrival time t of a SPD pulse generated bythe 1.47 µ m fluorescence photon arriving within a gatepulse. The precision of the lifetime measurement relieson the accuracy of the TCSPC timing module, but noton that of the frequency sources.We show an example of the histogram of photon countsvs. t in Fig. 4. In this figure, the ordinate represents thenumber of fluorescence photons N i detected in the i -thbin over the course of a 1 hour data run, where each bin isof duration T bin = 256 ps. The laser turns on at t ∼ ∼ ,
000 counts per bin over thecourse of a few excited state lifetimes. This corresponds
Time (ns) P ho t on C oun t s
350 400 450 500 55010 FIG. 4. Decay curve of the Cs 7 s level. The main figureconsists of 1 hour of recorded data and shows the excitationof atoms and exponential decay of fluorescence. Inset:
Thesame data for 350 −
550 ns with the background deducted,shown on a logarithmic scale in red and the best-fit line inblack. to a photon incidence rate (without gating) of 2 × persecond, or the probability of detecting a photon withina 40 ns window of 0.8%. The laser then turns off at ∼
320 ns, and the signal drops, approaching a baselinevalue which primarily represents the detector dark noisecounts. The noise level of our signal is consistent withthe shot noise limit.We apply two corrections to the raw data before de-termining the lifetime τ s . The first is for pile-up error,in which we account for the probability that a secondphoton arrives within the 40 ns gated detection window.The correction that we apply in the asynchronous mea-surement scheme differs from the typical pile-up errorcorrections described, for example, in [30, 32, 33]. Theprobability of detecting a photon within the 40 ns windowcentered on the i -th bin of the data set is approximately: P i = N i N E × T gate T bin × (cid:18) T gate f (cid:19) = N i N E T bin f , (2)where N E is the total number of laser pulse repetitions(typically f × . × ), and T gate f is theduty cycle of the SPD gate. We make sure that P i < P i / P i / µ s) is longer than the timing window (0.8 µ s),after a photon is detected, the gated-SPD is not readyto detect any photons during the next laser pulse cy-cle. We chose the frequency f as a compromise betweenrapid data collection rates and long duration measure-ment windows, 1 /f (cid:29) τ s ≈
50 ns. This necessitates anadditional correction to the raw data of 1 + P i . In total,these two corrections alter the fitted lifetime by 0 . N i = A s exp (cid:18) − tτ s (cid:19) + y o (3)to the falling edge of the data to extract the lifetime ofthe 7s state, τ s . Here, A s is the amplitude of the ex-ponential and y is the background photon count. Weshow an example of data and the fitted function on asemi-log plot in the inset of Fig. 4. The laser pulse hasfinite turn-off time, which we measured to be ∼
20 ns(90% to 10%). This produces some ambiguity regardingthe appropriate range of data to include in the fits, as thefluorescence decay follows an exponential only when thelaser has completely turned off. We run fits to the datafor a range of starting truncation points t = 360 − t = 800 ns.For each individual dataset, we determine the lifetime Experiment Data Set F itt e d L i f e ti m e ( n s ) FIG. 5. A plot showing the 16 individual measurement re-sults used to calculate the final value. Data sets 9 and 10were 10 hours long, while the rest were for 1 hour. The to-tal of 34 hours of data was captured over a period of threedays. The final data point T and the red horizontal line is theweighted mean of the 16 data sets, with error bars inclusiveof truncation and systematic uncertainties. from the mean of these fitted lifetimes. The statisticaluncertainties of these fits do not vary much across this 20ns range, so we use the statistical uncertainty of the mid-dle value, which we add in quadrature to the standarddeviation over this range of lifetimes (the truncation er-ror) to determine the uncertainty for each dataset. Thiseffectively adds truncation error into our statistical un-certainty value. For most of the data sets, the truncationerror is ∼
50% of the statistical uncertainty.We show a plot of the 16 different measurement resultsused to calculate the final value of the 7 s lifetime in Fig. 5.Fourteen 1 hour long data sets and two overnight datasets of 10 hours (labeled 9 and 10 in Fig. 5) were used todetermine the final lifetime. The weighted mean of these16 lifetimes is 48.28 ± χ ν of theresulting fit was 2.98, suggesting that our uncertaintieswere not sufficiently conservative. We observed that thelaser lost lock several times during runs 11 −
16, whichcould be the cause of the larger variability of the results.For lack of a clear link however, we chose to increase ourstatistical uncertainty by √ . Error % uncertaintyStatistical and truncation 0.12Detection sensitivity 0.05Radiation trapping 0.03Time calibration 0.03Pile-up correction 0.02SPD detector jitter 0.01Total uncertainty 0.14TABLE I. Sources of error and the percentage uncertaintyresulting from each source. The error is dominated primarilyby statistical error. Group τ s (ns) Experimental
Marek, time-resolved fluorescence, 1977 [35] 49 ± et al. , Hanle effect, 1981 [36] 53 . ± . et al. , Hanle effect, 1984 [13] 48 . ± . . ± . Theoretical
C. Bouchiat et al. , semi-empirical [37] 48.35Dzuba et al. , ∗ et al. , ∗ et al. , ∗ et al. , ∗ et al. , † et al. , † τ s of the cesium 7 s S / state. We derived theoryvalues marked with an asterisk ( ∗ ) from matrix elements (cid:104) s || r || p / (cid:105) and (cid:104) s || r || p / (cid:105) reported here. In the theo-retical works marked with a dagger ( † ), the authors only re-ported values of (cid:104) s || r || p / (cid:105) , so we estimated (cid:104) s || r || p / (cid:105) from 1 . × (cid:104) s || r || p / (cid:105) in order to derive τ s . no effect from radiation trapping, collisions, or Zeemanquantum beats. (Data sets 6 through 9 of Fig. 5 weretaken at a temperature of ∼ ◦ C, with the rest takenat ∼ ◦ C. In data sets 3 through 5, a 3 G magnetic fieldwas applied to the vapor cell in each of three orthogonaldirections.) Additionally, we quantified the effect of thedetector jitter, included a correction for pile-up error andaddressed truncation effects. We summarize the mag-nitudes of these effects on our error budget in Table I.Adding statistical and systematic errors in quadrature,our final result is τ s = 48.28 ± et al. [13] which was based on the Hanle effect. The theoryvalues shown in the table are calculated from the E1matrix elements reported in these works and the mea-sured transition energies. Our result agrees within ouruncertainty with the two most recent theoretical worksby Dzuba [9] and Porsev [11]. These works only re-port values of (cid:104) s || r || p / (cid:105) , so we estimate the ratio (cid:104) s || r || p / (cid:105) / (cid:104) s || r || p / (cid:105) = 1 .
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