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Physical Review Letters

Atomic Stabilization of Electromagnetic Field Strength Using Rabi Resonances

James C. Camparo

Published Jan 12, 1998• 74 citations
Publisher

Abstract

For nearly fifty years, atomic resonances have been employed to stabilize electromagnetic field frequency. Here, a dynamical Rabi resonance, associated with an alkali atom's ground state hyperfine transition, is used to stabilize electromagnetic field strength: A 7% sinusoidal variation was superimposed on a microwave field's strength, and through atomic stabilization this variation was reduced to 0.1%. Although the method is demonstrated with microwave fields, the technique could also be employed to stabilize optical fields via Rabi resonances associated with electronic transitions in atoms or molecules.

DOI
10.1103/physrevlett.80.222

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Physical Review A•Jan 1, 1989•23 citations
For nearly fifty years, atomic resonances have been employed to stabilize electromagnetic field frequency. Here, a dynamical Rabi resonance, associated with an alkali atom's ground state hyperfine transition, is used to stabilize electromagnetic field strength: A 7% sinusoidal variation was superimposed on a microwave field's strength, and through atomic stabilization this variation was reduced to 0.1%. Although the method is demonstrated with microwave fields, the technique could also be employed to stabilize optical fields via Rabi resonances associated with electronic transitions in atoms or molecules.
Just as it is possible to stabilize the frequency of an electromagnetic field to an atomic resonance between energy eigenstates, it is possible to stabilize the intensity or brightness of a field to an atomic Rabi resonance. For ease of reference, such a stabilized field is termed an ``atomic candle.'' Here, we describe a microwave atomic candle based on the (F=2,(F=2,(F=2, mF=0){m}_{F}=0)mF​=0)--(F=1,(F=1,(F=1, mF=0){m}_{F}=0)mF​=0) ground-state hyperfine transition of 87Rb{}^{87}\mathrm{Rb}87Rb (6834.7 MHz) as observed in an optically pumped vapor. We discuss the atomic candle's operation and the intensity stability of the field it produces (relative to the Rabi-resonance peak). We then discuss our use of the candle to investigate Rabi-resonance shifts. Specifically, we find that the Rabi resonance depends on the ac Stark shift of the hyperfine transition, the microwave field-atom detuning, and the alkali-metal vapor temperature.
Just as it is possible to stabilize the frequency of an electromagnetic field to an atomic resonance between energy eigenstates, so it is possible to stabilize the intensity or brightness of a field to an atomic Rabi-resonance. We term such a device an "atomic candle." We describe the operation of a microwave atomic candle based on the 0-0 ground state hyperfine transition in /sup 87/Rb, and our experiments examining its stability and sensitivity to various experimental parameters. Specifically, we have measured the microwave power stability of our candle, relative to the peak of the Rabi-resonance, and obtained /spl sigma//sub /spl Delta/P/P/(/spl tau/)=9/spl times/10/sup -7/+10/sup -7//spl radic//spl tau/. Additionally, we examined the Rabi-resonance shift as a function of various experimental parameters including microwave detuning from the 0-0 resonance and resonance-cell temperature. The paper concludes with a discussion of a novel application of the atomic candle: the precision measurement of a material's complex dielectric constant.
The present Rabi resonance microwave sensing technique cannot fully describe the microwave magnetic field strength distribution due to the signal detection method. Here, we propose an alternative Rabi resonance-based microwave imaging technique using a digital micromirror device and an alkali atomic cell. The experimental results well describe the distribution of the microwave field quantitatively and agree with the absorption imaging results. This technique can also be used as a method to analyze and measure the relaxation rate in an atomic vapor cell and offers a SI-traceable imaging approach for the microwave magnetic field. Its simple architecture holds great potential for the development of compact/miniature microwave field sensors.
The coupling between microwave fields and atoms (or atomlike systems) is inherently weaker than for optical fields, making microwave signal manipulation for applications like quantum information processing technically challenging. In order to better understand this coupling and to develop tools for measuring it, we explore the microwave coupling to atoms using the ``atomic candle'' technique, and push it beyond the bounds of the small-signal regime in order to deliver a larger signal. In familiar two-level systems, responses beyond the usual Rabi oscillations can arise when a single-tone drive is phase modulated, causing the steady-state populations to oscillate at integer harmonics of the modulation frequency. Resonant behavior of the first two harmonics for frequencies near the Rabi frequency, known as $\ensuremath{\alpha}$ and $\ensuremath{\beta}$ Rabi resonances, is widely used for microwave-field magnetometry and as a power standard known as the atomic candle. Here, we explore Rabi resonances beyond the small-signal approximation and report upon experimental observations of higher-order-harmonic population response for microwave hyperfine transitions in cold 87Rb^{87}\mathrm{Rb}87Rb atoms, which we compare to numerical simulations.
We have studied the transient response of undamped two-level atoms to excitation by a classical bichromatic field consisting of a strong resonant component and a moderate-strength, tunable, ``perturber'' component. It is found that the strong field tends to stabilize the atom against the influence of the perturber field. Exceptions to this general result occur when the perturber is detuned from the strong field by the Rabi frequency of the latter or its subharmonics. We believe this stabilization phenomenon is a semiclassical analog of the effect that leads to the dynamical modification of spontaneous emission [M. Lewenstein and T. W. Mossberg, Phys. Rev. Lett. 59, 775 (1987)], and the presence of detunings at which the stabilization fails provides a simple motivation for the Rabi subharmonic resonances found in certain cw bichromatic spectra. Interestingly, when the perturber field is relatively weak, detuned from the atomic resonance by the strong-field Rabi frequency, and turned on with a specific initial phase relative to the strong field, one finds that the bichromatic field can be employed to dressed-state polarize initially ground-state atoms. In a related vein, we find that perturbations at the subharmonic detunings lead to interesting phase-dependent atomic dynamics. Results were obtained using both numerical and approximate analytical techniques entirely within the context of the rotating-wave approximation. The validity of the latter is ensured by demanding that all detunings and Rabi frequencies are vanishingly small compared to the atomic transition frequency.