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European Quantum Electronics Conference (EQEC)

Atomic Wave-Packet in a Ring Cavity

Hubert Stoop, Paweł Masiak, Kazimierz Rza̧żewski

Published Jan 1, 1996• 0 citations
Publisher

Abstract

We solve the spontaneous and induced emission problem for an atom coupled to a ring cavity, taking into account the center-of-mass motion. We solve analytically the non-Hermitian Schrodinger equation Tor the spontaneous emission. Then we use this solution to test our quantum Monte Carlo solution for the induced processes. The coherence of atomic center-of-mass wave function combined with a well-defined phase of the field produces noteworthy interference phenomena. They may be understood with the help of the semiclassical solution.

DOI
10.1109/eqec.1996.561869

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We solve the spontaneous and induced emission problem for an atom coupled to a ring cavity, taking into account the center-of-mass motion. We solve analytically the non-Hermitian Schrodinger equation Tor the spontaneous emission. Then we use this solution to test our quantum Monte Carlo solution for the induced processes. The coherence of atomic center-of-mass wave function combined with a well-defined phase of the field produces noteworthy interference phenomena. They may be understood with the help of the semiclassical solution.
We solve the spontaneous and induced emission problem for an atom coupled to a ring cavity, taking into account the center-of-mass motion. We solve analytically the non-Hermitian Schr\"odinger equation for the spontaneous emission. Then we use this solution to test our quantum Monte Carlo solution for the induced processes. The coherence of atomic center-of-mass wave function combined with a well-defined phase of the field produces noteworthy interference phenomena. They may be understood with the help of the semiclassical solution.
We solve the spontaneous-emission problem for an atom coupled to a standing-wave cavity mode. The interaction between the atom and the cavity mode is treated nonperturbatively with the quantized motion of the atom along the cavity axis included. Results are presented for the spontaneous-emission spectrum and the final momentum distribution of the atom. For equal atomic and cavity linewidths analytical results are obtained using a Bloch-state basis (eigenstates of the coupled atom and cavity mode); these are compared with results calculated in the Raman-Nath approximation. The case of unequal linewidths may be solved numerically using the eigenstates of the uncoupled atom and cavity mode as a basis, or analytically by making a secular approximation in the Bloch-state basis. The distribution of final atomic momentum shows that under strong-coupling conditions the atom is diffracted by its radiation reaction field. We compare the spontaneous emission spectra with spectra calculated by treating the motion of the atom classically. Generally there is good agreement when the classical results are averaged over the quantum-mechanical uncertainty in the initial position of the atom. The agreement is lost for sufficiently strong dipole coupling or sufficiently light atoms. Then, spectra that are symmetric in the classical treatment are asymmetric in the quantum treatment due to energy exchange between the internal degrees of freedom and center-of-mass degrees of freedom of the atom.
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 present a nonperturbative result for the spectrum of spontaneous photons emitted by an atom coupled on resonance to a standing-wave cavity mode. Motion of the atom through the standing-wave mode function is included in a classical way. We discuss the form of the spectrum as a function of the velocity of the atom in the limit of strong dipole coupling. For slow atoms the normal-mode doublet (``vacuum'' Rabi spectrum) survives with small changes. The motion of a fast atom through the standing wave averages the coupling constant to zero, and the spectrum reverts to a single peak. At intermediate velocities the spectrum has a complicated multipeaked structure that can be understood in terms of interfering probability amplitudes for different quantum-mechanical emission paths or as a frequency-modulation spectrum for radiating coupled oscillators.
We use a basis of Bloch wave functions to solve the problem of spontaneous emission from an atom inside a standing-wave cavity. In this way we incorporate the effects of the atom’s quantized center-mass-motion in the periodic light-force potential of the one-quantum dressed states during the spontaneous emission process. We calculate emission spectra and the momentum distribution of the atom. Under strong-coupling conditions, “vacuum” Rabi spectra become asymmetric, with an increased relative weight given to the red side of the spectrum because of the transfer of energy to the center-of-mass motion of the atom. Because of the nonperturbative interaction between the atom and the cavity mode, many momentum quanta are transferred to the atom from the cavity mirrors during the irreversible emission of just one photon. Thus, the atom is diffracted by its own radiation reaction field. We analyze these effects using the Bloch-state basis. Use of the secular approximation provides a simple rate equation description of transitions from the Bloch states excited in the initial state to the atom-cavity ground state. We compare this approach with other ways of doing the calculations and discuss the accuracy of the secular approximation. We consider the extension of these calculations to treat the effects of photon statistics on the momentum distribution of atoms traversing a standing-wave cavity.
Utilizing a recently found solution to the problem of a spontaneously radiating atom with an extended center-of-mass wave function [K. Rza\ifmmode \mbox{\c{}}\else \c{}\fi{}\ifmmode \dot{z}\else \.{z}\fi{}ewski and W. \ifmmode \dot{Z}\else \.{Z}\fi{}akowicz, J. Phys. B 25, L319 (1992)] it is shown, for nonrelativistic atomic velocities, that the field density matrix is a statistical mixture of parts corresponding to emission from different positions within the wave packet. \textcopyright{} 1996 The American Physical Society.