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Physical Review A

Nonclassical photon statistics in cavity QED with an inhomogeneous medium

Hayato Goto, Kouichi Ichimura

Published Jan 8, 2008• 1 citation
Publisher

Abstract

A theoretical method for the calculation of the second-order intensity correlation function for the light transmitted from a weakly driven optical cavity containing an inhomogeneous medium is presented. This method is based on the expectation-value approach [H. Goto and K. Ichimura, Phys. Rev. A 70, 023815 (2004)]. This method allows one to calculate the second-order intensity correlation function in the case where there are many atoms whose transition frequencies and coupling rates have various values. We discuss the effects of the inhomogeneities of the atomic transition frequency and the coupling rate.

DOI
10.1103/physreva.77.015804

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A theoretical method for the calculation of the second-order intensity correlation function for the light transmitted from a weakly driven optical cavity containing an inhomogeneous medium is presented. This method is based on the expectation-value approach [H. Goto and K. Ichimura, Phys. Rev. A 70, 023815 (2004)]. This method allows one to calculate the second-order intensity correlation function in the case where there are many atoms whose transition frequencies and coupling rates have various values. We discuss the effects of the inhomogeneities of the atomic transition frequency and the coupling rate.
The second-order intensity correlation function for the light transmitted from a driven optical cavity containing identical two-level atoms is calculated in the weak-field limit by using the equations for expectation values of operators. Atomic nonradiative dephasing is taken into account in addition to cavity-field damping and atomic radiative decay. The correlation function including the atomic nonradiative dephasing rate is numerically calculated. An analytic expression for the correlation function is also derived in the case of purely radiative atomic decay.
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 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 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.>