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arXiv:0810.2071 · American Journal of Physics

Atomic clocks and coherent population trapping: Experiments for undergraduate laboratories

Nathan Belcher, Eugeniy E. Mikhailov, Irina V. Novikova

Published Oct 12, 2009• 21 citations
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Abstract

We demonstrate how to construct and operate a simple and affordable apparatus for producing coherent effects in atomic vapor and for investigating their applications in time-keeping and magnetometry. The apparatus consists of a vertical cavity surface emitting diode laser directly current-modulated using a tunable microwave oscillator to produce multiple optical fields needed for the observation of coherent population trapping. This effect allows very accurate measurement of the transition frequency between two ground state hyperfine sublevels, which can be used to construct a coherent population trapping-based atomic clock.

DOI
10.1119/1.3120262

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We demonstrate how to construct and operate a simple and affordable apparatus for producing coherent effects in atomic vapor and for investigating their applications in time-keeping and magnetometry. The apparatus consists of a vertical cavity surface emitting diode laser directly current-modulated using a tunable microwave oscillator to produce multiple optical fields needed for the observation of coherent population trapping. This effect allows very accurate measurement of the transition frequency between two ground state hyperfine sublevels, which can be used to construct a coherent population trapping-based atomic clock.
The spectroscopic technique of coherent population trapping (CPT) enables an all-optical interrogation of the groundstate hyperfine splitting of cesium (or rubidium), compared to the optical-microwave double resonance technique conventionally employed in atomic frequency standards. All-optical interrogation enables the reduction of the size and power consumption of an atomic clock by two orders of magnitude, and vertical-cavity surface-emitting lasers (VCSELs) are preferred optical sources due to their low power consumption and circular output beam. Several research teams are currently using VCSELs for DARPA's chip-scale atomic clock (CSAC) program with the goal of producing an atomic clock having a volume < 1 cm^3, a power consumption < 30 mW, and an instability (Allan deviation) < 1x10^-11 during a 1-hour averaging interval. This paper describes the VCSEL requirements for CPT-based atomic clocks, which include single mode operation, single polarization operation, modulation bandwidth > 4 GHz, low power consumption (for the CSAC), narrow linewidth, and low relative intensity noise (RIN). A significant manufacturing challenge is to reproducibly obtain the required wavelength at the specified VCSEL operating temperature and drive current. Data are presented that show the advantage of operating at the D1 (rather than D2) resonance of the alkali atoms. Measurements of VCSEL linewidth will be discussed in particular, since atomic clock performance is especially sensitive to this parameter.
We report on the performance of the first table-top prototype atomic clock based on coherent population trapping (CPT) resonances with parallel linearly polarized optical fields (lin‖lin configuration). Our apparatus uses a vertical-cavity surface-emitting laser (VCSEL) tuned to the D1 line of 87Rb with the current modulation at the 87Rb hyperfine frequency. We demonstrate cancellation of the first-order light shift by the proper choice of rf modulation power and further improve our prototype clock stability by optimizing the parameters of the microwave lock loop. Operating in these optimal conditions, we measured a short-term fractional frequency stability (Allan deviation) 2×10−11τ−1/2 for observation times 1 s ≤ τ ≤ 20 s. This value is limited by large VCSEL phase noise and environmental temperature fluctuation. Further improvements in frequency stability should be possible with an apparatus designed as a dedicated lin‖lin CPT resonance clock with environmental impacts minimized.
A scheme for a Ramsey-coherent population trapping (CPT) atomic clock that eliminates the acousto-optic modulator (AOM) is proposed and experimentally studied. Driven by a periodically microwave modulated current, the vertical-cavity surface-emitting laser emits a continuous beam that switches between monochromatic and multichromatic modes. Ramsey-CPT interference has been studied with this mode-switching beam. In eliminating the AOM, which is used to generate pulsed laser in conventional Ramsey-CPT atomic clock, the physics package of the proposed scheme is virtually the same as that of a conventional compact CPT atomic clock, although the resource budget for the electronics will slightly increase as a microwave switch should be added. By evaluating and comparing experimentally recorded signals from the two Ramsey-CPT schemes, the short-term frequency stability of the proposed scheme was found to be 46% better than the scheme with AOM. The experimental results suggest that the implementation of a compact Ramsey-CPT atomic clock promises better frequency stability.
We have performed a series of experiments demonstrating the use of a vertical-cavity surface-emitting laser for nonlinear spectroscopy on the cesium D2 transition at 852 nm wavelength. Due to the high modulation efficiency of the VCSEL sufficiently strong modulation sidebands at 9.2 GHz frequency can be produced by direct modulation of the laser injection current. Using, the carrier and one of the modulation sidebands coherent population trapping (CPT) resonances in a buffered cesium vapor can be prepared with linewidths of only 60 Hz. For application of these narrow resonances to precision magnetometry we find a sensitivity of 10 pT in 0.3 s integration time. For the use of our setup as a frequency reference a relative stability of 1 • 10 − 11 / τ is predicted. In both applications of CPT resonances the use of VCSELs as light sources helps to build compact and reliable devices.
Observation of CPT for the ground hyperfine interval in 133^{133}133Cs
We use the technique of coherent population trapping (CPT) to access the ground hyperfine interval (clock transition) in 133^{133}133Cs. The probe and control beams required for CPT are obtained from a single compact diode laser system. The phase coherence between the beams, whose frequency difference is the clock frequency, is obtained by frequency modulating the laser with an electro-optic modulator (EOM). The EOM is fiber coupled and hence does not require alignment, and the atoms are contained in a vapor cell. Both of these should prove advantageous for potential use as atomic clocks in satellites.
An all-optical microwave frequency standard based on coherent population trapping (CPT) in 85Rb is developed. The CPT resonances are detected by an ordinary edge-emitting diode laser in a simple optical setup. A buffer-gas mixture is carefully optimized to yield a narrow linewidth and a reduced temperature dependence of the resonance frequency. With the developed system we are able to measure ultranarrow optically induced hyperfine CPT resonances at <20 Hz, which is in good agreement with the linewidth calculated from experimental parameters. The frequency of an RF-signal generator has been stabilized to the CPT resonance between the two mF=0 magnetic sublevels. The relative frequency stability (square root of Allan variance) follows a slope of 3.5×10-11 τ-1/2(1 s<τ<2000 s). The best stability of 6.4×10-13 is reached at an integration time of τ=2000 s. This stability is sufficient for many high-precision applications. Frequency-shift measurements were made to evaluate the frequency dependencies on the operation parameters.