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Journal of Experimental and Theoretical Physics

Removal of single-atom optical bistability by quantum fluctuations

A. V. Kozlovskiĭ, А. Н. Ораевский

Published Jun 1, 1999• 11 citations
Publisher

Abstract

The dynamics of the quantum-statistical properties of the radiation of an atom in a cavity interacting with an external coherent field is investigated. A high level of quantum fluctuations of the field in the cavity is shown to destroy optical bistability in the multiatom case. Photon-number fluctuations and the spectral dispersion of the canonically conjugate quadratures of the field inside and outside a cavity are calculated. It is found that in contrast to the multiatom case quadrature squeezing and squeezing of the radiation intensity of a single atom are negligible inside and outside the cavity.

DOI
10.1134/1.558897

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The dynamics of the quantum-statistical properties of the radiation of an atom in a cavity interacting with an external coherent field is investigated. A high level of quantum fluctuations of the field in the cavity is shown to destroy optical bistability in the multiatom case. Photon-number fluctuations and the spectral dispersion of the canonically conjugate quadratures of the field inside and outside a cavity are calculated. It is found that in contrast to the multiatom case quadrature squeezing and squeezing of the radiation intensity of a single atom are negligible inside and outside the cavity.
A quantum treatment of a coherently driven cavity with a medium of two-level atoms is given. The system displays both absorptive and dispersive bistability. Quantum fluctuations are included via a Fokker-Planck equation in a generalized PPP representation, after adiabatic elimination of the atomic variables. The transmitted spectrum and correlation function is calculated in a linearized (Gaussian) approximation. In the limit of large detuning and radiative damping, the quantum fluctuations are identical to those of a simple nonlinear polarizability theory. An analysis is given of the nonclassical statistical properties of the intensity-correlation spectrum.
A two-photon laser is modeled as NNN two-level atoms interacting via a two-photon transition with a single resonant-cavity field mode. The quadratic form of this interaction makes such a system a candidate to exhibit reduced quantum fluctuations (squeezing) in one quadrature of the output field. A Fokker-Planck equation containing all leading quantum noise terms is derived following the method of Haken. A linearized fluctuation analysis reveals that there is no squeezing in a two-photon laser with injected signal. A small amount of squeezing may be present in two-photon optical bistability. Our calculations confirm the results of Lugiato and Strini, who adopted a factorization of moment equations.
There is increasing interest in the photon statistics and spectroscopic properties of the radiation from atoms confined in an optical cavity. Effects such as the cavity enhancement and inhibition of spontaneous emission, which were first observed using microwave cavities, have recently been measured at optical frequencies.1 Recent measurements of squeezing and the dynamic effects of single-quantum-level splittings also demonstrate the possibilities for quantum-statistical studies of coupled atom-cavity systems at optical frequencies.2 We study a single two-level atom confined inside an optical cavity which is driven by coherent light in resonance with both cavity and atom. For weak driving field intensities we have calculated the spectrum of the light transmitted by the cavity and fluorescence out the sides of the cavity.
A Bose-Einstein condensate of ultracold atoms inside the field of a laser-driven optical cavity exhibits dispersive optical bistability. We describe this system by using mean-field approximation and by analyzing the correlation functions of the linearized quantum fluctuations around the mean-field solution. The entanglement and the statistics of the atom-field quadratures are given in the stationary state. It is shown that the mean-field solution, that is, the Bose-Einstein condensate, is robust against entanglement generation for most of the phase diagram.
The interaction of a quantized field with three-level atoms in $\ensuremath{\Lambda}$ configuration inside a two-mode cavity is analyzed in the small-noise approximation. The atoms are in a two-photon detuning with respect to the carriers of the field. We calculate the stationary quadrature noise spectrum of the field outside the cavity in the case where the input probe field is a squeezed state and the input pump field is a coherent state. The mean value of the field is unaltered in all the analysis: the atoms shows electromagnetically induced transparency. The effect of the atoms' base level decoherence in the cavity output field is also studied. It is found that the output field is very sensitive to two-photon detuning.
Absorptive optical bistability is shown to exist for a single two-level atom inside a resonant optical cavity. Solutions for the quantum-mechanical density operator are obtained numerically for a parameter regime at the interface between the quantum limit, in which quantum-mechanical noise invalidates the semiclassical prediction of bistability, and the classical limit, in which quantum noise is a negligible perturbation on semiclassical results. Bimodal photon number distributions and Q functions are obtained, and two-state transition rates are calculated.>