Testing Optical Clock Calibration Procedures: Absolute Frequency Measurement of Rubidium 5S-7S Two-Photon Transitions Michał Zawada∗, Piotr Ablewski∗, Wojciech Gawlik† , Rafał Gartman∗ , Piotr Masłowski∗, Piotr Morzy´nski∗ , Bartłomiej Nag´orny∗, Filip Ozimek‡ , Czesław Radzewicz‡, Piotr Wcisło∗ , Marcin Witkowski∗§ and Roman Ciuryło∗ ∗ Institute
of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University Grudzia¸dzka 5, PL-87-100, Toru´n, Poland Email:
[email protected] † Institute of Physics, Jagiellonian University, Reymonta 4, PL-30-059 Krak´ow, Poland ‡ Institute of Experimental Physics, Faculty of Physics, University of Warsaw, Ho˙za 69, PL-00-681 Warsaw, Poland § Institute of Physics, University of Opole, Oleska 48, PL-45-052 Opole, Poland
Abstract—We report the absolute frequency measurements of rubidium 5S-7S two-photon transitions with an optical frequency comb. The digital lock to the transition, the procedures of evaluating the accuracy budget and measurements of the frequency with the optical frequency comb are tested with a simple setup for the sake of comparison of two optical lattice strontium clocks. The narrow, two-photon transition, 5S-7S (760 nm) is insensitive to a magnetic field and promising candidate for frequency standard. The preformed tests yield the transition frequency with accuracy better than reported previously.
I. I NTRODUCTION The International Committee for Weights and Measures recommended several radiations for applications including the practical realization of the metre. At the border of the visible and near-infrared ranges the BIPM recommends the 5S1/2 (F=3) - 5D5/2 (F=5) two-photon transition in 85 Rb with a standard uncertainty of 5 kHz (the relative standard uncertainty of 1.3 × 10−11 ) [1]. Recent development in phase-stabilized optical frequency combs based on mode-locked femtosecond lasers allowed determination of the absolute frequency of a similar transition in Rb, 5S1/2 -7S1/2 , which is 100 times weaker than 5S-5D, yet less sensitive to the stray magnetic fields. At the 5S-5D transition the rubidium atoms must be carefully shielded against the magnetic field to avoid any linear Zeeman shifts. On the other hand, the 5S and 7S levels have the same Land´e g factors which cancels the linear Zeeman shifts in the 5S-7S transition. The ac-Stark effect in the 5S-7S transition is also smaller than in the 5S-5D case. All previous measurements of the 5S-7S transition [2]–[5] gave worse estimations of the absolute frequency than the measurements of the 5S-5D transition [6]–[9]. In this work we report the measurement of the absolute frequency measurements of the 5S1/2 (F=2)-7S1/2(F=2) transition in 87 Rb with relative stan-
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Fig. 1.
Experimental setup.
dard uncertainty of 5.8 × 10−12 which is better than measured previously. II. E XPERIMENTAL ARRANGEMENT The experimental setup is shown in Fig.1. We have used a commercial ring-cavity titanium sapphire (TiSa) laser to study the two-photon 5S1/2 -7S1/2 transitions at 760 nm in a hot rubidium vapour cell at temperatures up to 140 Centigrades. The TiSa laser is pre-stabilised by a Fabry-P´erot cavity which narrows the laser linewidth to 300 kHz. The two-photon
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2013 Joint UFFC, EFTF and PFM Symposium
Fig. 2.
Fractional Allan deviation
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The scheme of the digital lock.
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Fig. 4. Allan variance of the beat frequency between the TiSa laser and optical frequency comb. TABLE I A CCURACY BUDGET. ( M - MEASURED , C - CALCULATED ) Effect Pressure shiftm Light shiftm Quadratic Zeeman Shiftm Line pullingc Beam alignment (residual Doppler shift)m Second order Doppler effectc DDS electronics & lockm Black Body Radiationc Rb frequency standard & GPSc Total:
Fig. 3. The line profile for different intensities of the probing light. The Lorentz profile is fitted to the measured data.
spectroscopy signal is observed by a photomultiplier tube in the 7S-6P-5S radiative cascade, with the 6P-5S decay blue fluorescence around 421 nm. The idea of the digital lock is depicted in Fig.2. An acoustooptic modulator (AOM) driven by a direct digital synthesizer (DDS) square-wave modulates the light frequency with the step 2∆f equal to the half-width of the line. The AOM carrier frequency fAOM is chosen such that the AOM efficiency with f+ =fAOM + ∆f and f− =fAOM − ∆f is the same. The microcontroller (Atmel AT91SAM7S), which controls the DDS, counts the photomultiplier pulses. The error signal for the laser lock is calculated from the difference of the counts for f+ and f− . The software PI regulator in the microcontroller calculates the correction ∆fL and applies it to the TiSa laser. The power of the light sent to the rubidium cell is stabilised by the software PI regulator on the embedded PC (FOX Board G20) with a half-wave plate mounted on a piezo-driven mount and a polariser. To exclude the residual Doppler shift, the counter-propagating beams in the two-photon spectroscopy are not focused and their relative position is controlled by a CCD beam profiler camera. By changing ∆f in the digital lock we can measure the line profile. Since the counter-propagating beams are not focused we can measure the line-shape of the transition broadened only by the 300 kHz laser linewidth and the light power (Fig. 3). Part of the TiSa light is sent directly to the Er-dopped fiber optical frequency comb (Menlo FC1500-250-WG). The comb, the DDS synthesizers and counters in the experiment are locked to a microwave Rb frequency standard (SRS FS725), disciplined by the GPS (Connor Winfield FTS 375). The
Shift [kHz] -24.14 0.4 0.055 0 0 -0.168 -4.44 -0.666 0 -29.0
Uncert. [kHz] 1.1 1.6 0.034 0.01 0.3 0.001 0.48 0.004 0.4 2.0
fractional Allan variance of the beat frequency between the locked TiSa laser and the optical frequency comb is presented in Fig. 4. After 1000 s our Rb frequency standard reaches its final stability, and our system is further disciplined by the GPS which improves the stability, as seen in the plot, after 104 s integration time. III. R ESULTS Several systematic effects should be taken into account to deduce the transition frequency. The measurements are dominated by a systematic pressure shift. By measuring the absolute frequencies at different temperatures (accuracy of 0.2K), we determined the pressures [10], estimated the pressure shift coefficient in our cell as -17.82(81) kHz/mTorr (Fig. 5) and extrapolated it to zero pressure. In the same way we measured and calibrated the ac-Stark and quadratic Zeeman shifts. By measuring the absolute frequency while misaligning the probe beams we estimated the uncertainty due to the residual Doppler shift. Varying the ∆f value in the DDS lock and the AOM diffraction order (+fAOM or -fAOM ) to cancel any residual efficiency imbalance between f+ and f− , we also estimated the shift of the digital lock. The black body radiation and second order Doppler shifts were calculated for a given stabilised cell temperature in the cell. The accuracy budget for typical experimental conditions, i.e. laser intensity of 8 W/cm2 and temperature of 128.5◦C, is presented in Table I.
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2013 Joint UFFC, EFTF and PFM Symposium
[2] Ming-Sheng Ko and Yi-Wei Liu, Opt. Lett., 29, 1799 (2004) [3] A. Marian et al., Phys. Rev. Lett. 95, 023001 (2005) [4] K. Pandey et al., Opt. Lett., 33, 1675 (2008) [5] I. Barmes et al., Phys. Rev. Lett., 111, 023007 (2013) [6] D. Touahri et al., Opt. Commun. 133, 471 (1997) [7] D. J. Jones et al., Science 288, 635 (2000) [8] J. E. Bernard et al., Opt. Commun. 173, 357 (2000) [9] C. S. Edwards et al., Metrologia 42, 464 (2005) [10] D. A. Steck Rubidium 87 D Line Data, C. B. Alcock, et al., Canadian Metallurgical Quarterly 23, 309 (1984)
Pressure shift. Frequency is relative to the best previously known
Rb87 F=2-2 frequency relative to 394397384000 [kHz]
Fig. 5. value.
500 490 480 470 460 450 440 430 420 410 [2]
Fig. 6.
[3]
[4]
[5]
Our measurement
Comparison with previously known values.
The absolute optical frequency for the 87 Rb F=2F’=2 two-photon transition is determined to be 394397384444.3(2.3) kHz Its comparison with previously measured values is depicted in Fig. 6. IV. C ONCLUSION We performed a series of measurements of the absolute frequency of the 5S-7S two-photon transitions in rubidium vapour with an optical frequency comb. The digital lock to the transition, the procedures of evaluation the accuracy budget and measurements of the frequency with the optical frequency comb, prepared for a future system of two optical lattice clocks with strontium atoms, were tested with a simple setup. Thanks to a very good long-term stability of our experimental system, we obtained higher accuracy of the 5S-7S transition frequency than any previously reported [2]–[5]. ACKNOWLEDGMENT This work has been performed in the National Laboratory FAMO in Toru´n and supported by the TEAM Project of the FNP, co-financed by the EU within the European Regional Development Fund. R EFERENCES [1] Bureau International des Poids et Mesures (BIPM), in Report of the 86th Meeting of the Comit´e International des Poids et Mesures (CIPM), (BIPM, S`evres, France, 1997)
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