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Journal de Physique II

Quantum effects in atomic reflection

Sze Meng Tan, Daniel F. Walls

Published Nov 1, 1994• 3 citations
Publisher

Abstract

In this paper we consider the effects of spontaneous emission on the problem of atomic reflection from an optical evanescent travelling wave. The atoms are assumed to be travelling so slowly that the external degrees of freedom of the atom need to be treated quantum mechanically. Spontaneous emission is modelled using a fully quantum mechanical model based on the quantum Monte Carlo technique which includes the effects of atomic recoil. The results of the simulation are compared with a semi-classical Monte Carlo simulation in which the atomic motion is treated classically and the internal state of the atom is assumed to follow the light-induced quasipotentials adiabatically between spontaneous emission events. The spontaneous emission leads to a broadening of the momentum distribution of the outgoing wave packet and mechanisms for this broadening are discussed.

DOI
10.1051/jp2:1994238

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Teubner-Texte zur Physik•Jan 1, 1996•0 citations
In this paper we consider the effects of spontaneous emission on the problem of atomic reflection from an optical evanescent travelling wave. The atoms are assumed to be travelling so slowly that the external degrees of freedom of the atom need to be treated quantum mechanically. Spontaneous emission is modelled using a fully quantum mechanical model based on the quantum Monte Carlo technique which includes the effects of atomic recoil. The results of the simulation are compared with a semi-classical Monte Carlo simulation in which the atomic motion is treated classically and the internal state of the atom is assumed to follow the light-induced quasipotentials adiabatically between spontaneous emission events. The spontaneous emission leads to a broadening of the momentum distribution of the outgoing wave packet and mechanisms for this broadening are discussed.
A Monte Carlo simulation of the atomic master equation for spontaneous emission in terms of atomic wave functions is developed. Realizations of the time evolution of atomic wave functions are constructed that correspond to an ensemble of atoms driven by laser light undergoing a sequence of spontaneous emissions. The atomic decay times are drawn according to the photon count distribution of the driven atom. Each quantum jump of the atomic electron projects the atomic wave function to the ground state of the atom. Our theory is based on a stochastic interpretation and generalization of Mollow's pure-state analysis of resonant light scattering, and the Srinivas-Davies theory of continuous measurements in photodetection. An extension of the theory to include mechanical light effects and a generalization to atomic systems with Zeeman substructure are given. We illustrate the method by simulating the solutions of the optical Bloch equations for two-level systems, and laser cooling of a two-level atom in an ion trap where the center-of-mass motion of the atom is described quantum mechanically.
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.
The motion of atoms and nanoparticles in a trap formed by sequences of counter-propagating light pulses has been analyzed. The atomic state is described by a wave function constructed with the use of the Monte Carlo method, whereas the atomic motion is considered in the framework of classical mechanics. The effects of the momentum diffusion associated with the spontaneous radiation emission by excited atoms and the pulsed character of the atom-to-field interaction on the motion of a trapped atom or nanoparticle are estimated. The motion of a trapped atom is shown to be slowed down for properly chosen parameters of the atom-to-field interaction, so that the atom oscillates around the antinodes of a non-stationary standing wave formed by counter-propagating light pulses at the point where they “collide”.
We calculate the modes in a stable gravitational cavity where the atomic mirror at the bottom of the bounce is caused by an internally reflected intense Gaussian-mode laser beam. In contrast to Wallis, Dalibard, and Cohen-Tannoudji [Appl. Phys. B 54, 407 (1992)], who treated the bottom bouncing mechanism as due to an infinite potential, we include the effect of the exponentially decaying potential caused by the evanescent wave. Nevertheless, we find that above this evanescent wave potential the mode structure corresponds exactly to that obtained using an infinite potential. The allowed energies differ slightly due to the phase change through the evanescent wave. The broadening of the modes due to the damping effects of spontaneous emission was calculated and because of the intrinsic transverse width of the modes was found to depend strongly on energy and transverse excitation, which differs from a simple one-dimensional classical calculation. The finesse and QQQ of the cavity due to the damping effects of spontaneous emission were also calculated and in contrast to an optical Fabry-P\'erot cavity were found to depend strongly on energy.
Spontaneous emission of a photon by an atom is described theoretically in three dimensions with the initial wave function of a finite-mass atom taken in the form of a finite-size wave packet. Recoil and wave-packet spreading are taken into account. The total atom-photon wave function is found in the momentum and coordinate representations as the solution of an initial-value problem. The atom-photon entanglement arising in such a process is shown to be closely related to the structure of atom and photon wave packets which can be measured in the coincidence and single-particle schemes of measurements. Two predicted effects, arising under the conditions of high entanglement, are anomalous narrowing of the coincidence wave packets and, under different conditions, anomalous broadening of the single-particle wave packets. Fundamental symmetry relations between the photon and atom single-particle and coincidence wave-packet widths are established. The relationship with the famous scenario of Einstein-Podolsky-Rosen is discussed.
Spontaneous emission of photons by an atom placed near the dielectric waveguide is analyzed using global free electromagnetic modes, satisfying necessary continuity conditions at the waveguide boundaries 1. These modes include modes extended over the whole space (travelling) and modes trapped to the waveguide. To describe angular properties of the spontaneous emission, a parameterization of the travelling modes by the outgoing waves has been proposed. Otherwise, using a more common parameterization of these modes by the incoming waves, one has to take into account the interference of different reflected and transmitted waves accompanying photons incoming from both sides of the waveguide 2, what was overlooked in 3. Angular characteristics of the travelling photon emission (a), distributions of the trapped photon emission (b), as well as global decay rates (c), have been calculated using the quantum approach and standard perturbation theory. Enhancement and suppression of radiative decay rates in various configurations have been shown. A certain calculational error, in the treatment of the density of trapped states, in an earlier paper by Khosravi and Loudon 4, affecting emission rates for thin waveguides, has been corrected.