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Physical Review A

Optical bistability in the mixed absorptive-dispersive regime with two-state atoms

Luis A. Orozco, Albert T. Rosenberger, Harry J. Kimble

Published Oct 1, 1987• 9 citations
Publisher

Abstract

Quantitative comparisons between experiment and theory for the steady-state characteristics in optical bistability with two-state atoms are reported. Nonresonant conditions for both the cavity and the atomic medium are investigated in two different cavity geometries (ring and standing wave). The experiment fulfills to a very good degree the conditions that have been widely employed in theoretical models that consider a collection of two-state atoms interacting with a single mode of the electromagnetic field in a cavity.

DOI
10.1103/physreva.36.3248

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Quantitative comparisons between experiment and theory for the steady-state characteristics in optical bistability with two-state atoms are reported. Nonresonant conditions for both the cavity and the atomic medium are investigated in two different cavity geometries (ring and standing wave). The experiment fulfills to a very good degree the conditions that have been widely employed in theoretical models that consider a collection of two-state atoms interacting with a single mode of the electromagnetic field in a cavity.
Absolute quantitative comparisons between experiment and theory are reported for the steady-state characteristics of optical bistability with two-state atoms in ring and in standing-wave resonators. The case treated here is the absorptive one, with both atoms and cavity resonant with the field. The experiment is designed to realize as closely as possible a standard theoretical model of two-state atoms interacting with a single mode of the electromagnetic field in a resonator and is described in detail. A detailed explanation is also given of the extensions to the standard theory that are needed to account for unavoidable experimental limitations such as transit broadening and the nonideal nature of the resonator. The good agreement observed between experiment and theory provides a foundation for quantitative investigation of nonlinear dynamics and quantum phenomena in this nonequilibrium optical system.
Observations of steady-state hysteresis in absorptive bistability are reported for well-collimated atomic beams of sodium within a traveling-wave interferometer. The atomic medium approximates a system of homogeneously broadened "two-level" atoms, and effects due to standing waves are eliminated. The experiment thus represents the first demonstration of optical bistability under conditions that have been widely employed in theoretical models. Absolute measurements of switching intensities versus atomic cooperativity CCC are reported, and a preliminary comparison with Gaussian-beam theory is made.
Beams of homogeneously broadened two-state sodium atoms in a confocal ring resonator have been employed to investigate the steady-state characteristics of absorptive [1] and dispersive optical bistability. Also studied in the same system is the dynamical behavior due to the intrinsic single-longitudinal-mode instability [2] originating in the alteration of the atomic absorption profile by a strong field as in the Lorenz-type instability in the homogeneously broadened laser. All experimental parameters are carefully measured and corrected for transit broadening, finite absorption, and residual Doppler broadening in order to be able to make an absolute comparison with the single-Gaussian-transverse-mode theory [3-6]. Despite the frequency degeneracy of the transverse modes of the resonator, the agreement with this theory for absorptive bistability is remarkably good. The dispersive bistability data are more difficult to interpret, but they seem to be in reasonable agreement with the theory; the same can be said of the results for the domain and oscillation frequency of the instability, at least within a certain region of parameter space. Outside this region, multiple unstable states appear for various intracavity intensities; recent observations suggest that these may be due in part to instabilities involving higher-order transverse modes of the resonator.
We analyze instabilities in mixed absorptive and dispersive optical bistability in the rate-equation approximation and the mean-field and good-cavity limits. Our starting point is a set of multimode equations derived from the Maxwell-Bloch equations for ring-cavity boundary conditions. We obtain analytic expressions for the instability conditions. In a plane-wave analysis, we find that a portion of the lower transmission branch can be unstable in addition to the upper-branch instability found in purely absorptive bistability. Also, a new disconnected region of instability can exist on the upper branch. Our analysis becomes particularly simple for equal and opposite cavity detunings and we explore this case in detail. We extend our treatment to include a Gaussian transverse intensity profile and show that the instabilities remain in the presence of Gaussian averaging. We also show that many of the results obtained in the rate-equation approximation hold when the atomic linewidth and atomic decay rate are of the same order.
The control of light transmission through a standing-wave Fabry-P\'erot cavity containing atoms is theoretically and numerically investigated, when the cavity mode beam and an intersecting control beam are both close to specific atomic resonances. A four-level atomic system is considered and its interaction with the cavity mode is studied by solving for the cavity field and atomic state populations. The conditions for optical bistability of the atom-cavity system are obtained. The response of the intracavity intensity to an intersecting beam on atomic resonance is understood in the presence of stationary atoms (closed system) and nonstatic atoms (open system) in the cavity. The nonstatic system of atoms is modelled by adjusting the atomic state populations to represent the exchange of atoms in the cavity mode, which corresponds to a thermal environment where atoms are moving in and out of the cavity mode volume. The control behavior with three- and two-level atomic systems is also studied, and the rich physics arising out of these systems for closed and open atomic systems is discussed. The solutions to the models are used to interpret the steady-state and transient behavior observed by Sharma et al. [Phys. Rev. A 91, 043824 (2015)].
Observations of optical bistability are reported for a system composed of multiple atomic beams passing through a high-finesse optical cavity. Both the transmitted power and the intracavity fluorescent intensity have been recorded as functions of incident laser power for zero cavity and atomic detunings. A quantitative study has been made of the evolution of the steady-state switching intensities from well below the critical onset of bistability to well above this point. The results show reasonable agreement with a Gaussian-beam theory of optical bistability, but systematic departures are noted.