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Physical Review A

N two-level atoms in a driven optical cavity: Quantum dynamics of forward photon scattering for weak incident fields

Robert J. Brecha, Perry R. Rice, Min Xiao

Published Mar 1, 1999• 116 citations
Publisher

Abstract

We investigate the photon statistics of the light transmitted from a driven optical cavity containing N two-level atoms, with emphasis on the weak driving field limit. This limit is of most interest from the point of view of quantum fluctuations. We find that various types of nonclassical behavior are possible, even with large numbers of atoms in the cavity, under conditions of strong atom-field coupling, which we refer to as the cavity quantum electrodynamics limit. We describe the system with a pure-state formalism valid for weak fields, and also use a Fokker-Planck equation obtained by a small fluctuation linearization. We examine the conditions under which the linearized theory is appropriate, and explore the sensitivity of nonclassical effects in the system to atom number, transit-time broadening, and detunings.

DOI
10.1103/physreva.59.2392

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We investigate the photon statistics of the light transmitted from a driven optical cavity containing N two-level atoms, with emphasis on the weak driving field limit. This limit is of most interest from the point of view of quantum fluctuations. We find that various types of nonclassical behavior are possible, even with large numbers of atoms in the cavity, under conditions of strong atom-field coupling, which we refer to as the cavity quantum electrodynamics limit. We describe the system with a pure-state formalism valid for weak fields, and also use a Fokker-Planck equation obtained by a small fluctuation linearization. We examine the conditions under which the linearized theory is appropriate, and explore the sensitivity of nonclassical effects in the system to atom number, transit-time broadening, and detunings.
We present analytic results for the photon statistics of a weakly driven optical cavity containing N two-level atoms. The second-order intensity correlation function g(2)() is calculated in the weak field limit for arbitrary atomic and cavity loss rates, and cavity and atomic detunings are included. The transmitted light field may exhibit photon antibunching, sub-Poissonian photon statistics, and other novel nonclassical effects.1,2 The size of these effects depends principally on the single-atom coupling constant C1 = g2/κγ, so these effects persist with many atoms in the cavity. Our results can be interpreted via the collapse of the wave function and quantum interference of probability amplitudes. These phenomena can also be understood in terms of the self-homodyning of the driving field with squeezed polarization fluctuations.2
We investigate the photon statistics of light transmitted from a driven optical cavity containing one or two atoms interacting with a single mode of the cavity field. We treat arbitrary driving fields with emphasis on departure from previous weak field results. In addition effects of dephasing due to atomic transit through the cavity mode are included using two different models. We find that both models show the nonclassical correlations are quite sensitive to dephasing. The effect of multiple atoms on the system dynamics is investigated by placing two atoms in the cavity mode at different positions, therefore having different coupling strengths.
The photon statistics of the transmitted light from a driven cavity containing a single resonant two-level atom are studied in the bad-cavity limit. For weak driving fields, the second-order intensity correlation function shows novel nonclassical behavior due to the interference of the driving field and forward reradiation from the atom. This behavior is related to squeezing in the cavity transmission. A physical interpretation is given in terms of the reduced quantum state of the coupled atom-field system following photodetection.>
We consider a single two-level atom in an optical cavity, in which the system is driven by a coherent driving field. In the bad-cavity limit, when the cavity loss rate is taken to be large compared to the atomic decay rate and atom-field coupling, the cavity field can be adiabatically eliminated from the equations of motion for the atomic operators. The main effect of the cavity in this limit is the enhancement of spontaneous emission into the cavity mode. For this model, the second-order intensity correlation function g(2)() has been shown to exhibit photon antibunching, sub-Poissonian photon number distributions, and other nonclassical effects.1 In this paper, analytic results are presented for g(2)() for both the transmitted and fluorescent light fields when broadband squeezed light is injected into the cavity. Effects of the squeezing on nonclassical behavior is examined.
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.
Summary form only given.We consider a single two-level atom in a driven optical cavity, and calculate the second-order intensity correlation function g/sup (2)/(/spl tau/) and the waiting-time distribution W(t). Previous results have dealt primarily with the weak driving field limit, and the presence of nonclassical effects. These could be interpreted in several ways, using quantum interference between detection probability amplitudes, or as due to intracavity squeezing. In this paper we extend these results outside the weak-field limit, to determine the robustness of these nonclassical effects, and to compare with recent experimental results of Mielke et al. We include transit-time broadening and decoherence explicitly using quantum trajectory methods. Two methods are used, first a simple resetting of the atom to the ground state every transit time, simulating the leaving of one atom and arrival of another. Secondly we use a Poisson distribution of atom arrival times, simulating an atomic beam. In the latter case we consider traditional oven beams and atoms dropped from a magneto-optical trap. We make comparisons between the trajectory method and traditional density matrix methods. Further, we examine the relationship between the waiting-time distribution and g/sup (2)/(/spl tau/), which are the same for small delay times, in the context of recent experiments.