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Annual Meeting Optical Society of America

Photon antibunching in the single-atom limit of absorptive bistability

H. J. Carmichael

Published Jan 1, 1985• 0 citations
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Abstract

Photon antibunching has been predicted at weak intensities along the lower branch in optical bistability. Existing theories assume large atomic numbers to justify their linearized analysis. From such a theory photon antibunching in absorptive bistability is given for weak intensities by where C is the bistability parameter, μ is the ratio of atomic and cavity decay times, and N is the number of atoms. Clearly this result becomes invalid as the system size is reduced to the limit of a single atom; then g(2) (0) is negative for moderate values of C. I calculate g(2) (0) for the transmitted light from an optical cavity containing a single atom, where the injected field, the atom, and the cavity are all resonant.

DOI
10.1364/oam.1985.fu1

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Photon antibunching has been predicted at weak intensities along the lower branch in optical bistability. Existing theories assume large atomic numbers to justify their linearized analysis. From such a theory photon antibunching in absorptive bistability is given for weak intensities by where C is the bistability parameter, μ is the ratio of atomic and cavity decay times, and N is the number of atoms. Clearly this result becomes invalid as the system size is reduced to the limit of a single atom; then g(2) (0) is negative for moderate values of C. I calculate g(2) (0) for the transmitted light from an optical cavity containing a single atom, where the injected field, the atom, and the cavity are all resonant.
While the problem of photon antibunching in optical bistability has been the subject of numerous theoretical investigations, there appears to be no general result in the literature that includes a complete specification of the dependence of antibunching on the system parameters. Motivated by the importance of such a result to experimental observation of this effect, we present a treatment that includes the parametric dependences on cavity and atomic detunings, cooperativity parameter, nonradiative (collisional) damping, and the ratio of cavity and atomic damping rates. We also attempt to analyze the contribution of fourth-order correlations of the fluctuating fields, which have been neglected in previous treatments. Although the antibunching initially increases with decreasing system size due to the approximate scaling of quantum fluctuations as the inverse of the saturation photon number ns, higher-order fluctuations begin playing an increasingly important role at values of ns ⪝ 1. We show that the linearized theory itself does not necessarily break down for arbitrarily small values of ns (as previously suggested), but that photon antibunching is lost in this limit, thus placing restrictions on the design of an experiment.
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.
Photon antibunching in intracavity second-harmonic generation and intracavity atomic absorption inside a high-Q optical cavity is discussed. A linearized description of quantum dynamics in the weak-field limit is used because the system size, as characterized by the number of photons n0{\mathit{n}}_{0}n0​ needed to probe the nonlinearity of the system, is often quite large for realistic parameters. In both cases standard results are recalled that demonstrate that antibunching is a small effect given by g(2){\mathit{g}}^{(2)}g(2)(0)-1\ensuremath{\approxeq}-1/n0{\mathit{n}}_{0}n0​ for large values of n0{\mathit{n}}_{0}n0​. We show that when higher-order terms that are usually ignored in linearized treatments are retained, g(2){\mathit{g}}^{(2)}g(2)(0) satisfies the lower bound g(2){\mathit{g}}^{(2)}g(2)(0)\ensuremath{\ge}0 even for small values of n0{\mathit{n}}_{0}n0​. It is further shown that by employing a high-Q cavity to suppress the coherent part of the spectrum of field fluctuations, perfect antibunching can be achieved even for large systems. Conditions under which this is possible are derived and curves are presented to illustrate the behavior.
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.
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.>