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EFFECTS OF COUPLING BETWEEN CENTER OF MASS MOTION OF AN ATOM AND A CAVITY MODE: PHOTON STATISTICS AND WAVE-PARTICLE CORRELATIONS

Mambwe Mumba

Published Jan 1, 2005• 0 citations

Abstract

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.

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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 investigate the quantum fluctuations of a single atom in a weakly driven cavity, where the center of mass motion of the atom is quantized in one dimension. We present analytic results for the second order intensity correlation function g((2))(tau) and the intensity-field correlation function h(theta)(tau), for transmitted light in the weak driving field limit. We find that the coupling of the center of mass motion to the intracavity field mode can be deleterious to nonclassical effects in photon statistics and field-intensity correlations, and compare the use of trapped atoms in a cavity to atomic beams.

We investigate the quantum fluctuations of a single atom in a weakly driven cavity, with an intracavity optical lattice. The weak driving field is on resonance with the atoms and the cavity, and is the second-harmonic of the lattice beam. In this special case we can find eigenstates of the Hamiltonian in terms of Mathieu functions.We present analytic results for the second order intensity correlation function

g^{(2)}(τ)

and the intensity-field correlation function

h_θ(τ)

, for both transmitted and fluorescent light for weak driving fields. We find that the coupling of the center of mass motion to the intracavity field mode can be deleterious to nonclassical effects in photon statistics; less so for the intensity-field correlations, and compare the use of trapped atoms in a cavity to atomic beams.

In this work, we will look at the dynamics of a two-level atom in a damped, driven optical cavity in which atomic center-of-mass motion (CMM) is quantized.Of particular interest is the addition of an external potential (not related to the cavity field) in the cavity that effects the atom.Specifically, we are introducing to the system Hamiltonian a harmonic potential that effectively represents the presence of an optical lattice within the cavity.Thus, we are interested in the interplay of cold atoms and cavity QED.The form of our investigation of the system's dynamics will be in the study of the photon statistics and field-intensity correlation of the transmitted and fluoresced fields.

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 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.

We investigate intensity cross-correlation functions for two cavity QED systems. These are a driven optical cavity containing a single two-level atom interacting with a single mode of the cavity field with quantized centre of mass motion, and a two-level atom in an optical parametric oscillator. We find analytic results in the weak driving field limit using quantum trajectory theory. We find large violations of inequalities that must be satisfied by classical fields. One of these inequalities is well known, g (2) ij (τ) ≤ √g (2) jj (0)g (2) jj (0), where i and j denote two modes of the field. We also derive a new inequality that cross-correlations must satisfy, |g (2) ij (τ) - 1| 2 ≤ |(g (2) ii (0) - 1)(g (2) jj (0) - 1)|. Large violations of classical inequalities and asymmetrical behaviour in delay time τ are found in complimentary regimes for the cavity QED system with quantized centre of mass motion. They always exist for the two-level atom inside an optical parametric oscillator.