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arXiv:0912.0461 · Physical Review A

Quantum fluctuations in a cavity-QED system with quantized center-of-mass motion

Joseph Leach, Mambwe Mumba, Perry R. Rice

Published Jun 29, 2011• 0 citations
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Abstract

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 ${g}^{(2)}(\ensuremath{\tau})$ and the intensity-field correlation function ${h}_{\ensuremath{\theta}}(\ensuremath{\tau})$ 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, but less so for the intensity-field correlations.

DOI
10.1103/physreva.83.063844

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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)(\ensuremathτ){g}^{(2)}(\ensuremath{\tau})g(2)(\ensuremathτ) and the intensity-field correlation function h\ensuremathθ(\ensuremathτ){h}_{\ensuremath{\theta}}(\ensuremath{\tau})h\ensuremathθ​(\ensuremathτ) 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, but less so for the intensity-field correlations.
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)g^{(2)}(τ)g(2)(τ) and the intensity-field correlation function hθ(τ)h_θ(τ)hθ​(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.
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.
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
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.
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.