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Conference on Lasers and Electro-Optics

Photon statistics of a two-level atom in a driven optical cavity: beyond the weak-field limit

Perry R. Rice, James Clemens

Published Nov 27, 2002• 0 citations
Publisher

Abstract

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.

DOI
10.1109/iqec.1998.680134

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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.
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 consider an optical cavity containing a single two-level atom driven on resonance by an external laser source.1 We focus on the limit of weak excitation where the dynamic response of this system is governed by just three parameters: the atom-field coupling constant g, spontaneous emission rate γ for the atom, and cavity decay rate κ. The statistics of the transmitted light are analyzed as a function of g, γ, and κ, in terms of the second-order correlation function g(2)(τ), and the quadrature variances measured in a homodyne detection scheme. Squeezing and photon antibunching exist over a wide range of parameters. For γ ~ κ, the system can exhibit an oscillatory response, even when the mean intracavity photon number is much less than unity.2 The oscillations can be understood in terms of the coupling between the free atom-field eigenstates |0,−>, |0,+>, and |1,−>. The oscillation frequency is determined by the energy level splitting produced between the degenerate one-quantum states |0,+> and |1,−> by the atom-field interaction. The second-order correlation function can exhibit a novel nonclassical effect, where, for g(2)(0) ≠ 0, at some finite delay τ0, the correlation function dips exactly to zero—g(2)(τ0) = 0.
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.
by Mambwe Mumba We examine a system comprised of a single two-level atom inside a driven optical cavity.We allow for cavity decay and atomic spontaneous emission out the side of the cavity.There is a spatial dependent coupling between the atom and the cavity mode, which we take into account, using explicit trapping potentials for the atom.Previous work has revolved around a harmonic oscillator potential, we also find here a solution for a realistic optical lattice potential when the lattice wavelength is half the driving laser wavelength.Atomic and cavity detunings are included, as well as effective Franck-Condon factors.Analytic results are obtained for various intensity-intensity and field-intensity correlation functions, using quantum trajectory theory in the weak driving field limit.Nonclassical effects are obtained, and we investigate the effect of a nonstationary atom on these effects.These result from violation of inequalities that must be satisfied if there is an underlying classical stochastic field; violations imply that there is no well defined electric field at all times, with some underlying positive definite probability distribution.The center of mass wave function is specified either by a list of probability amplitudes, or these amplitudes are calculated from an explicit wave function(typically a Gaussian).The correlation functions are quite sensitive to the center of mass wave function, and perhaps correlation functions can be used as probes of atomic motion.We also examine a new inequality between intensity-intensity and field intensity correlation functions, that is violated here.
We consider intensity-field correlation functions for a two-level atom in a degenerate optical parametric oscillator (OPO), which would result from a conditioned homodyne measurement. Analytic results are obtained in the limit of weak driving fields using quantum trajectory methods for both the transmitted and fluorescent fields. This system is unique in that after detection of a photon, it is known that one excitation is in the system, in either the atom or cavity mode. We find large violations of inequalities satisfied by classical fields, for both transmitted and fluorescent fields. This is in contrast to the usual cavity QED system of an atom in a driven cavity where we do not find nonclassical behavior in the intensity-field correlation function in fluorescence. This is understood in terms of a relationship between the intensity-field correlation function and the second-order intensity correlation function, as well as the different amount of field-atom entanglement in the two systems. We show that for weak-field cavity QED one must have photon bunching to have nonclassical behavior in the intensity-field correlation function. We compare our results to those of an ordinary OPO. Finally, we also consider cross correlations, where we examine the transmitted (fluorescent) field conditioned by detection of a fluorescent (transmitted) photon.