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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Observation of geometric phase in optical spectroscopy

H.-R. Xia, Stephen D. Swartz, J. L. Hall

Published Oct 28, 1992• 0 citations
Publisher

Abstract

We report the first observation of the geometric phase of a quantum system driven by laser fields. The observable geometric phase effects in optical FM spectroscopy, here distinguished from various known lineshape changes due to spectroscopic or technical causes, are characterized by the following aspects: (1) Dramatic lineshape variation of the optical heterodyne signal due to a monotonic signal phase change with increasing probe power; (2) The lineshape changes are associated with a nearly pure phase-change effect; and (3) The phase-change rate with probe power depends on rf sideband frequency, and less strongly on the rf modulation index.

DOI
10.1117/12.130462

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We report the first observation of the geometric phase of a quantum system driven by laser fields. The observable geometric phase effects in optical FM spectroscopy, here distinguished from various known lineshape changes due to spectroscopic or technical causes, are characterized by the following aspects: (1) Dramatic lineshape variation of the optical heterodyne signal due to a monotonic signal phase change with increasing probe power; (2) The lineshape changes are associated with a nearly pure phase-change effect; and (3) The phase-change rate with probe power depends on rf sideband frequency, and less strongly on the rf modulation index.
We discuss experimental observations of an induced phase shift of the rf signal produced in FM saturated absorption measurements under the conditions of large probe beam intensities. This phase shift can be understood in terms of the phase difference between the phase modulation of the optical driving field and the steady state macroscopic polarization of the medium. This phase difference is relatively insensitive to detuning of the laser from the atomic resonance, such that essentially the same spectrum can be observed by changing the rf detection phase. We also present theoretically calculated spectra which are based on the optical Bloch equations, and which are in excellent agreement with the experimental results.
We discuss experimental observations of an induced phase shift of the rf signal produced in frequency-modulated saturated-absorption measurements under the conditions of large probe-beam intensities. This phase shift can be understood in terms of the phase difference between the phase modulation of the optical driving field and the steady-state macroscopic polarization of the medium. We also present theoretically calculated spectra that are based on the optical Bloch equations and that are in excellent agreement with the experimental results.
A novel phase-modulation technique which permits subkilohertz-laser stability and new levels of precision in laser spectroscopy was reported recently. For spectroscopy, the basic arrangement consists of a combination of an optical pump and a probe field which is phase modulated. The pump prepares the atomic sample by burning a narrow hole within the atom's inhomogeneous line shape, and the probe beam samples the prepared hole when its modulation sidebands are swept into resonance. Off resonance, the probe is balanced as pairs of sidebands produce heterodyne beat signals of opposite phase which just cancel. On resonance, the balance is upset and yields a nonvanishing beat signal with a Lorentzian absorption or dispersion line shape and with residual noise approaching the shot noise limit. Here we investigate the theory of phase-modulation spectroscopy. We treat the nonlinear response of an atomic two-level quantum system subject to an intense pump and a weak copropagating or counterpropagating phase-modulated probe beam. The density-matrix equations of motion are solved by a Laplace-transform method and by the novel use of a translation operator which allows the infinite hierarchy of coupled equations to close. A solution equivalent to the rate-equation result is developed and coherence corrections are found which predict new resonances that have just been detected in this laboratory. The delayed pump-probe technique encountered in solid-state laser spectroscopy is analyzed in this context for two- and three-level quantum systems. The response of a Fabry-Perot cavity to a phase-modulated light wave is examined also and reveals an unexpected absorption feature.
We investigate the shift caused by asymmetry of spectroscopic lineshape in atomic interferometers, which has not previously been discussed in the scientific literature. This asymmetry arises because laser field is frequency-chirped not only during the free-evolution intervals of atoms, but also during the Ramsey pulses. As a result, the effective detuning from the working atomic transition during the pulses also depends on the chirping rate, which, in turn, leads to the lineshape-asymmetry-caused shift (LACS). It is shown that this shift has an inverse cubic dependence of ∝1/T3 \propto 1{\text{/}}{{T}^{3}}∝1/T3 on the duration of the interval between the Ramsey pulses T , which markedly contrasts with the ∝1/T2 \propto 1{\text{/}}{{T}^{2}}∝1/T2 dependence typical in atomic interferometry. Therefore, the metrological importance of this shift substantially increases for compact atomic interferometers with a short baseline. For example, for interferometers-gravimeters using two-photon transitions in rubidium atoms, at T∼1T \sim 1T∼1 ms we estimate the LACS shift and its variations at the level of 0.1–1 mGal, while for T∼100T \sim 100T∼100 μs this can reach a value of 0.1–1 Gal.
The paper presents a detailed analysis of FM laser oscillation which includes the effect of arbitrary atomic lineshape, saturation, and mode pulling. Such oscillation is achieved by means of an intracavity phase perturbation, and is a parametric oscillation wherein the laser modes oscillate with FM phases and nearly Bessel function amplitudes. One principal idea is that of the competition between different FM oscillations. The effect of the intracavity phase perturbation is to associate a set of sidebands with each of the previously free-running laser modes. While the free-running laser modes experienced their gain from essentially independent atomic populations, the competing FM oscillations to a large extent see the same atomic population; and in cases of interest the strongest of these oscillations is able to quench the competing weaker oscillations and establish the desired steady state condition. Results of the analysis include the following: threshold and power output, amplitudes and phases of all sidebands, frequency pulling of the entire oscillation, time domain behavior, distortion, super-mode conversion efficiency, and effect of mirror motion. Results of numerical application of the theory to a number of specific cases are given.