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Physical Review A

Modifications to the chaotic dynamics of laser-cooled atoms due to spontaneous emission

Sigurd Dyrting

Published Apr 1, 1996• 10 citations
Publisher

Abstract

We study the dynamics of laser-cooled two-level atoms in a time-dependent standing wave. In the absence of spontaneous emission, our model reduces to the much studied quantum standard mapping. For a sample of atoms initially cooled to the Doppler limit, the momentum variance increases linearly with interaction time. A sample of atoms initially cooled to the recoil limit will display momentum diffusion at a rate that is determined by two numbers: the classical chaos parameter and a dimensionless Planck parameter. This diffusion ceases after the quantum-mechanical break time. Spontaneous emission will modify the diffusion rate of both Doppler- and recoil-cooled atoms. We show that one component of the new diffusion constant is due to spontaneous recoil and that there is a correction to the deterministic diffusion rate due to the destruction of correlations in the stroboscopic position. Spontaneous emission will destroy the dynamic localization of atoms cooled to the recoil limit. The new momentum diffusion constant can be related to the quasistationary state-decoherence rate. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physreva.53.2522

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We study the dynamics of laser-cooled two-level atoms in a time-dependent standing wave. In the absence of spontaneous emission, our model reduces to the much studied quantum standard mapping. For a sample of atoms initially cooled to the Doppler limit, the momentum variance increases linearly with interaction time. A sample of atoms initially cooled to the recoil limit will display momentum diffusion at a rate that is determined by two numbers: the classical chaos parameter and a dimensionless Planck parameter. This diffusion ceases after the quantum-mechanical break time. Spontaneous emission will modify the diffusion rate of both Doppler- and recoil-cooled atoms. We show that one component of the new diffusion constant is due to spontaneous recoil and that there is a correction to the deterministic diffusion rate due to the destruction of correlations in the stroboscopic position. Spontaneous emission will destroy the dynamic localization of atoms cooled to the recoil limit. The new momentum diffusion constant can be related to the quasistationary state-decoherence rate. \textcopyright{} 1996 The American Physical Society.
The quantized center-of-mass dynamics of two-level atoms in a periodically modulated standing-wave laser field is analyzed, including the decohering effect of spontaneous emission. Under conditions appropriate for the occurrence of dynamical localization as determined in previous work, we predict a random diffusive motion of dynamically localized de Broglie waves due to spontaneous emission and calculate the diffusion constant and the diffusing distribution of wave packets. \textcopyright{} 1996 The American Physical Society.
We simulate atomic ballistic transport in a standing-wave laser field in the framework of a Monte Carlo stochastic wavefunction approach in which the coherent Hamiltonian evolution is interrupted at random times by spontaneous emission events. It is shown in numerical experiments and confirmed analytically that the character of spatial and momentum diffusion of spontaneously emitting atoms changes abruptly in the atom-laser detuning regime where the deterministic Hamiltonian dynamics has been shown to be chaotic. Thus, we find a manifestation of underlying Hamiltonian chaos in the diffusive-like center-of-mass motion which can be observed in real experiments.
The phenomenon of localization manifests itself in many quantum mechanical systems ranging from the localization of light in a random medium via Anderson localization of an electronic wave to the motion of atoms in time-dependent laser fields. In all these cases the underlying classical system is chaotic and shows diffusion as a function of time. In contrast, the quantum mechanical counterpart has a localized wave function whose width is governed by the classical diffusion and Planck’s constant. In this paper we show that there exists an additional quantum parameter that controls the localization length. In the system of a two-level ion stored in a Paul trap and interacting with a standing wave it is the detuning between the transition frequency and the laser field. We also discuss the effect of decoherence in form of spontaneous emission. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
The influence of spontaneous emission on the dynamical localization in atomic momentum transfer observed in recent experiments is investigated. Our numerical and analytical results indicate that contrary to previous expectation quantum diffusion due to decoherence by spontaneous emission is non-negligible in the experimental regime and may actually be visible in the measured data. Modifications of the experiments to strengthen this point are proposed. \textcopyright{} 1996 The American Physical Society.
Summary form only given. Recent advances in laser cooling and trapping have led to a growing interest in laser spectroscopy in cold atomic samples. Examples include the work of Guo et al. and Courtois et al. about the recoil-induced resonance, and Bonifacio et al. and Moore et al. about the collective-atomic-recoil lasers (CARL). At the heart of these applications is the atomic recoil by photon absorption and emission. In the work, we explore a recoil-related phenomenon: hole burning resulting from the momentum redistribution of atoms by spontaneous emission, and its possible application in the precision spectroscopy. In the traditional saturation spectroscopy, the hole in the Doppler profile is created by laser excitation of atoms from the ground to the excited level. By contrast, the hole, is produced by removing the atoms in the velocity group, where the hole is burned, into the neighboring velocity groups of the same ground level. This process is accomplished through optical pumping and momentum redistribution by spontaneous emission. As a result, the requirement on the intensities of the driving laser fields is low, limited only by the interaction time. This is in contrast to the traditional saturation spectroscopy where the driving laser intensity has to be comparable to the saturation intensity determined by the decay rate of the excited level.
We study dissipative transport of spontaneously emitting atoms in a one-dimensional (1D) standing-wave laser field in the regimes where the underlying deterministic Hamiltonian dynamics is regular and chaotic. A Monte Carlo stochastic wave-function method is applied to simulate semiclassically the atomic dynamics with coupled internal and translational degrees of freedom. It is shown in numerical experiments and confirmed analytically that chaotic atomic transport can take the form either of ballistic motion or a random walking with specific statistical properties. The character of spatial and momentum diffusion in the ballistic atomic transport is shown to change abruptly in the atom-laser detuning regime where the Hamiltonian dynamics is irregular in the sense of dynamical chaos. We find a clear correlation between the behavior of the momentum diffusion coefficient and Hamiltonian chaos probability which is a manifestation of chaoticity of the fundamental atom-light interaction in the diffusivelike dissipative atomic transport. We propose to measure a linear extent of atomic clouds in a 1D optical lattice and predict that, beginning with those values of the mean cloud's momentum for which the probability of Hamiltonian chaos is close to 1, the linear extent of the corresponding clouds should increase sharply. A sensitive dependence of statistical characteristics of dissipative transport on the values of the detuning allows us to manipulate the atomic transport by changing the laser frequency.