We recently reported that the transmitted light from a driven optical cavity containing a single-atom absorber shows strong nonclassical features.1 Also, Savage and Carmichael2 have shown that this single-atom system can be operated in a regime in which the transmitted light has a bimodal photon-counting distribution; as the saturation photon number is increased this bimodality develops into a single-atom version of absorptive optical bistability. We present results for the degree of second-order coherence and the spectrum of the transmitted light in the operating regime at the onset of bimodality. In this regime we can study the onset of low frequency behavior associated with transitions between the local states defined by the peaks of the bimodal distribution. Our results are calculated numerically, using a supercomputer to solve matrix element equations derived in the Fock-state basis. Our numerical approach also allows us to extend our analytical study of nonclassical effects in single-atom cavity-enhanced absorption. Our analytical results are restricted either to the bad-cavity limit1 or to weak driving fields outside this limit. We can now study how the nonclassical effects identified in these analytical calculations are changed by using finite driving fields outside the bad-cavity limit.
We recently reported that the transmitted light from a driven optical cavity containing a single-atom absorber shows strong nonclassical features.1 Also, Savage and Carmichael2 have shown that this single-atom system can be operated in a regime in which the transmitted light has a bimodal photon-counting distribution; as the saturation photon number is increased this bimodality develops into a single-atom version of absorptive optical bistability. We present results for the degree of second-order coherence and the spectrum of the transmitted light in the operating regime at the onset of bimodality. In this regime we can study the onset of low frequency behavior associated with transitions between the local states defined by the peaks of the bimodal distribution. Our results are calculated numerically, using a supercomputer to solve matrix element equations derived in the Fock-state basis. Our numerical approach also allows us to extend our analytical study of nonclassical effects in single-atom cavity-enhanced absorption. Our analytical results are restricted either to the bad-cavity limit1 or to weak driving fields outside this limit. We can now study how the nonclassical effects identified in these analytical calculations are changed by using finite driving fields outside the bad-cavity limit.
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.
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 study a single two-level atom interacting on resonance with a weakly driven optical cavity mode. In earlier work on this system we calculated the degree of second-order coherence, the optical spectrum, and the spectrum of squeezing for both the transmitted light and fluorescence out the sides of the cavity.1,2 We present results for the cross-correlation functions that determine joint probabilities for a photodetection in transmission (fluorescence) followed by a photodetection in fluorescence (transmission). We compute these correlation functions numerically for arbitrary values of the three rates that govern the system dynamics: the atomic decay rate γ to modes other than the cavity mode, the photon escape rate from the cavity 2K, and the atom-field coupling constant g. Analytical results provide insight for the following limits of the parameters: (1) the bad-cavity limit, κ/γ→∞,κ/g→∞,g2/κγ constant; (2) the atomic-loss limit, κ/γ→0,κ/g→0,γ/g constant; (3) the cavity-loss limit, γ/κ→0,γ/g→0,g/κ constant; and (4) the good-cavity limit, k/γ→0,k/g→0,g2/κγ constant. In the bad-cavity limit the cross-correlation functions are symmetric with respect to the order of detection in transmission and fluorescence; in general they are not symmetric.
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.
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.>
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.