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arXiv:1807.05703

Cavity QED System with Optical Lattice: Photon Statistics and Conditioned Homodyne Detection

Mambwe Mumba, Dyan L. Jones, Perry R. Rice

Published Jul 16, 2018• 0 citations
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Abstract

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.

DOI
10.48550/arxiv.1807.05703

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•Jan 1, 2005•0 citations
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 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 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.
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 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.
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.
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.