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IEEE Journal of Quantum Electronics

Bistability in the radiation pressure on two-level atoms in a ring cavity

R. Bonifacio, A. Caligiore, Federico Casagrande

Published Jul 1, 1988• 0 citations
Publisher

Abstract

A simple model for the interaction of a beam of two-level atoms with a running radiation model in a ring cavity is formulated. The occurrence of optical bistability significantly affects the radiation pressure force on atoms. Hysteresis effects are predicted for the transverse component of atomic velocity which couples with the electric field.>

DOI
10.1109/3.978

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A simple model for the interaction of a beam of two-level atoms with a running radiation model in a ring cavity is formulated. The occurrence of optical bistability significantly affects the radiation pressure force on atoms. Hysteresis effects are predicted for the transverse component of atomic velocity which couples with the electric field.>
We present an analysis of absorptive optical bistability in a system of cold atoms enclosed in a bidirectional ring cavity. This analysis is carried out using a system of equations that extends the so-called Maxwell-Bloch model to self-consistently include atomic center-of-mass motion. The analysis predicts an instability resulting in the simultaneous generation of an atomic density grating and a coherently backscattered radiation field. The formation of the density grating arises from a modulation of the radiation pressure forces exerted on the atoms. A consequence of this instability is that the lower transmission branch of the usual bistability curve, where atomic motion is neglected, can become unstable and the system switches to the upper transmission branch destroying the bistability.
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.
We study the optical bistability and dynamics in a hybrid optomechanical system, where the cavity mode is coupled to the mechanical resonator via radiation pressure and to a two-level atom via the Jaynes–Cummings coupling. The nonlinearity due to optomechanical coupling and the addition of an atom leads to bistable behaviors of the steady-state intracavity photon number and atomic population inversion. We show that the optical bistability can be effectively controlled by the Rabi frequency of the atomic driving field, the cavity–atom coupling strength, and the amplitude and frequency of the cavity pump field. Moreover, the effects of different initial conditions of the cavity field and the amplitude of the cavity pump field on the dynamics of the system also have been discussed.
The steady state behavior of a bistable system of a homogeneously or inhomogeneously broadened two sorts of two-level atoms placed in a ring cavity and driven by a coherent field is analyzed within the mean field limit where the transverse effect of the radiation field is taken into account within the single-transverse-mode model. Effects on the input–output relation, due to the transverse parameter and the Lorentzian and the Gaussian line widths which measure the inhomogeneous broadening of the atoms, are examined. The enlargement of the optical bistable (tristable) region according to the previously mentioned parameters is explained.
Optical bistable behavior for a system of inhomogeneously broadened two sorts of two-level atoms in a ring cavity is investigated outside the rotating wave approximation (RWA). The model Maxwell–Bloch equations are treated with Fourier decomposition up to first harmonic. The first harmonic output field component exhibits reversed or mushroom bistability simultaneously with bi- and double-bistability in the fundamental field component. Inhomogeneous broadening and transverse field effects are also considered.
The steady state behaviour of a bistable system of a homogeneously/inhomogeneously broadened two-level atomic medium in contact with a squeezed vacuum field and placed in a ring cavity driven by a coherent field is analysed within the mean field limit where the transverse effect of the radiation field is taken into account within the single-transverse-mode model. Effects on the input–output relation and the critical value of the cooperative parameter C crit are examined and compared with these results in the plane wave approximation. The 'cooperative switching effect' between the output states of the system due to variation of the cooperative parameter C is also investigated. Linear stability analysis for the model Maxwell–Bloch equations is presented in the homogeneously broadened case.