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Physical Review A

Observation of absorptive bistability with two-level atoms in a ring cavity

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

Published Oct 1, 1983• 143 citations
Publisher

Abstract

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 $C$ are reported, and a preliminary comparison with Gaussian-beam theory is made.

DOI
10.1103/physreva.28.2569

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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.

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In nonlinear optical interactions, one expects the transverse spatial intensity dependence to be modified. Nonlinear interactions within an optical resonator, in the absence of a mode-selective element such as an aperture, will thus in general couple the energy into various transverse modes of the resonator. One attractive analytical model incorporating transverse effects into optical bistability assumes, in spite of the observations above, that the transverse intensity profile remains a single-Gaussian (TEM00) mode. This model seems to be supported by experimental results for bistability with two-level sodium atoms in a confocal ring resonator. To test the generality of the single-Gaussian mode model, we have performed bistability experiments with two-level atoms in standing-wave resonators. Two resonators, differing only in length, were used. The confocal resonator is transverse-mode-degenerate and will support a combination of modes, as would the ring; the slightly longer resonator will allow only a single-transverse mode to be excited. Preliminary results indicate that there may be a difference in the two cases; although the behavior near the critical onset of bistability seems to be the same in the two cases, there seems to be a difference in the evolution of hysteresis with increasing cooperativity parameter. Further results, including a quantitative comparison with the single-Gaussian mode theory for standing-wave resonators, are presented.

Annual Meeting Optical Society of America•Jan 1, 1985•0 citations

Aspects of optical bistability in atomic sodium

Werner E Schulz

Experiments were performed on a bistable system consisting of a low finesse cavity and sodium atoms as the nonlinear medium. The atoms were excited by a dye laser system tuned to the D lines. Both ring and Fabry-Perot configurations were employed, and steady-state as well as transient behaviour was investigated. Flat mirrors of approximately 93% reflectivity were used in all experiments. With sodium vapour as the medium, experiments were performed in steady state, and a marked difference was observed in the behaviour of the Fabry-Perot cavity as compared to the ring set-up. This discrepancy could be explained when the sodium transition was modelled as a three - level lambda -type system, where the Doppler width is of the same order of magnitude as the ground state splitting. In this case the atoms with a Doppler shift close to half the ground state splitting have a major influence on the macroscopic refractive index. Extensive computer simulations were performed using this three -level model, and good qualitative agreement between experiment and theory was obtained for both types of cavity. A vacuum system containing a multiple atomic beam apparatus was constructed in order to reduce the Doppler width. Both the ring and the Fabry-Perot configuration could be set up inside the vacuum chamber.. The steady-state experiments displayed bistability when the laser intensity, laser frequency or cavity frequency were cycled. At higher atomic densities the system showed instabilities and multiple switching.

•Jan 1, 1985•0 citations
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.
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.
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.
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.
In nonlinear optical interactions, one expects the transverse spatial intensity dependence to be modified. Nonlinear interactions within an optical resonator, in the absence of a mode-selective element such as an aperture, will thus in general couple the energy into various transverse modes of the resonator. One attractive analytical model incorporating transverse effects into optical bistability assumes, in spite of the observations above, that the transverse intensity profile remains a single-Gaussian (TEM00) mode. This model seems to be supported by experimental results for bistability with two-level sodium atoms in a confocal ring resonator. To test the generality of the single-Gaussian mode model, we have performed bistability experiments with two-level atoms in standing-wave resonators. Two resonators, differing only in length, were used. The confocal resonator is transverse-mode-degenerate and will support a combination of modes, as would the ring; the slightly longer resonator will allow only a single-transverse mode to be excited. Preliminary results indicate that there may be a difference in the two cases; although the behavior near the critical onset of bistability seems to be the same in the two cases, there seems to be a difference in the evolution of hysteresis with increasing cooperativity parameter. Further results, including a quantitative comparison with the single-Gaussian mode theory for standing-wave resonators, are presented.
Experiments were performed on a bistable system consisting of a low finesse cavity and sodium atoms as the nonlinear medium. The atoms were excited by a dye laser system tuned to the D lines. Both ring and Fabry-Perot configurations were employed, and steady-state as well as transient behaviour was investigated. Flat mirrors of approximately 93% reflectivity were used in all experiments. With sodium vapour as the medium, experiments were performed in steady state, and a marked difference was observed in the behaviour of the Fabry-Perot cavity as compared to the ring set-up. This discrepancy could be explained when the sodium transition was modelled as a three - level lambda -type system, where the Doppler width is of the same order of magnitude as the ground state splitting. In this case the atoms with a Doppler shift close to half the ground state splitting have a major influence on the macroscopic refractive index. Extensive computer simulations were performed using this three -level model, and good qualitative agreement between experiment and theory was obtained for both types of cavity. A vacuum system containing a multiple atomic beam apparatus was constructed in order to reduce the Doppler width. Both the ring and the Fabry-Perot configuration could be set up inside the vacuum chamber.. The steady-state experiments displayed bistability when the laser intensity, laser frequency or cavity frequency were cycled. At higher atomic densities the system showed instabilities and multiple switching.