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IEEE Journal of Quantum Electronics

Single atom optical bistability

Craig M. Savage, H. J. Carmichael

Published Aug 1, 1988• 134 citations
Publisher

Abstract

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.>

DOI
10.1109/3.7075

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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.

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Annual Meeting Optical Society of America•Jan 1, 1991•0 citations
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 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.
The quantum mechanical master equation for a single two-level atom in a single-mode optical cavity is numerically solved in both the quantum and the semiclassical limits. The quantum limit of few cavity photons shows semiclassically forbidden behaviour such as steady state two-level population inversion. Qualitatively new fluorescent spectra, having sidebands broadened by the cavity interaction, also occur. The quantum theory of the single-atom laser with injected signal is presented. At the interface between its quantum and semiclassical dynamics we elucidate the signature of semiclassical limit cycles.
We consider an optomechanical system composed of a trapped ion dispersively coupled to a single mode of a pumped optical cavity. We focus on a parameter range for which the semiclassical description predicts two clearly distinct equilibrium configurations in the limits of small and large photon pumping, while a bistable regime is found for intermediate pumping. This semiclassical description, however, is not valid in close proximity to the system transitions or when the mean photon number is low. Here, we provide a numerical analysis of the fully quantum state in the few-photon regime, exploring the features of the asymptotic state across the transition and analyzing possible markers of semiclassical bistability. We find an increase in the entropy of the system and of the entanglement in the transition region but no clear signatures of metastability in the spectrum of the evolution.
We give a microscopic description of the optical bistability, where the transmission coefficient has two different values as a function of input light intensity, and the system exhibits a discontinuous jump with a hysteresis loop. We developed an efficient numerical algorithm to treat the quantum master equation for hybridized systems of many photons and a large number of two-level atoms. By using this method, we characterize the bistability from the viewpoint of eigenmodes and eigenvalues of the time-evolution operator of the quantum master equation. We classify types of optical bistability according to the photon number density in the cavity. In contrast to previous studies of optical bistability in the high-photon-density regime where the photons can be treated as a classical electromagnetic field and the resonance spectrum has a single-peak structure, we study the nature of optical bistability in the low-photon-density regime where the hybridization of photon and atom degrees of freedom occurs and the resonance spectrum has a double-peak structure. Unraveling the nature of the optical bistability in the latter regime may be important for the manipulation of quantum systems. Concretely, we discuss the steady-state properties of the optical bistability: dependencies of the photon number density on the intensity and the double-peak structure of the photon number distribution inside the bistable region. As for the dynamical properties, we find that the relaxation timescale shows an exponential growth with the system size and reveal how the hysteresis loop of the optical bistability depends on the size of the system and the sweeping rate of the driving amplitude. Finally, by investigating the effects of detuning frequency of the input field, we clarify the characteristic properties of the present optical bistability within the low-photon-density regime, which are qualitatively different from the standard optical bistable phenomena.
The radiative properties of atoms inside an optical cavity can be dramatically changed with respect to those in free space. In the strong-coupling limit, the reversible dipole interaction between an atom and the cavity field dominates the irreversible decay resulting from spontaneous emission and cavity damping. In this limit the atom and field can no longer be regarded as separate quantities but instead form a composite dynamic system. To enhance the dipole coupling constant and increase the photon storage time, our experiments are performed with a small cavity 1 mm long, with a finesse of 8 × 104. On average, 0.4 photons are sufficient to saturate the resonance transition at 852 nm for the cesium atoms used, while the cooperativity parameter for a single atom is 2. Optical bistability is studied in this system over the range 3 < N < 65 atoms inside the cavity, with the semiclassical theory predicting bistability for N > 5. We report observations of manifestly quantum effects in this regime, including photon antibunching and sub-Poissonian photon statistics, with the magnitude of these nonclassical effects observed to be largely independent of the number of intracavity atoms.