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Journal of Physics B Atomic Molecular and Optical Physics

Quantum inversion of cold atoms in a microcavity

Si-de Du, Zhou Lu-wei, Shangqing Gong, Zhizhan Xu, Jing Lu

Published Nov 30, 1999• 6 citations
Publisher

Abstract

We study quantum inversion of a cold atom in the Jaynes-Cummings model when its centre-of-mass (CM) motion is described quantum mechanically. The atom and the quantized cavity mode are initially prepared in the excited state and the coherent state, respectively. Many dramatic changes take place in atomic inversion when the atomic CM motion experiences a transition from the classical regime to the quantum regime. For ultra-cold atoms, in particular, fine resonances are found in the inversion. This novel effect, which originates from the de Broglie wave character of the atomic CM motion, is a direct manifestation of the `granularity' of the high-intensity cavity field. By means of the atom-field dressed-state picture, we explain the related phenomena in a qualitative way.

DOI
10.1088/0953-4075/32/24/302

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We study quantum inversion of a cold atom in the Jaynes-Cummings model when its centre-of-mass (CM) motion is described quantum mechanically. The atom and the quantized cavity mode are initially prepared in the excited state and the coherent state, respectively. Many dramatic changes take place in atomic inversion when the atomic CM motion experiences a transition from the classical regime to the quantum regime. For ultra-cold atoms, in particular, fine resonances are found in the inversion. This novel effect, which originates from the de Broglie wave character of the atomic CM motion, is a direct manifestation of the `granularity' of the high-intensity cavity field. By means of the atom-field dressed-state picture, we explain the related phenomena in a qualitative way.
The atomic inversion of cold atoms in a microcavity when its centre-of-mass (CM) motion is described quantum mechanically is presented, but is distinguished from other treatments by the inclusion of the spatial variation along the cavity axis. It is shown that the spatial dependence of the atomic inversion is very sensitive to changes of the atomic CM motion, as well as the cavity length. For ultracold atoms, different behaviours in the atomic inversion are demonstrated for the change in cavity length. The general conclusions reached are illustrated by numerical results.
A single two-level atom, with quantized centre-of-mass motion, is constrained to move in a one-dimensional harmonic potential, while interacting with a single-mode classical travelling light field. When the atom's centre-of-mass motion is in a coherent state, we show that the atomic inversion exhibits collapses and revivals. Whereas in the Jaynes-Cummings model this behaviour occurs due to the discrete nature of the light field, in our case the behaviour is due to the discrete nature of the vibrational trap states. The Q -function for the external motion is also calculated and shown to break into two peaks in the collapse region. Finally the parameter ranges under which the collapses and revivals can be observed are discussed, as well as the possibility of an experiment.
We extend the standard Jaynes-Cummings model to include transient effects due to a modulation of the atom-field coupling. The exact solution for such a generalized model is found in terms of Bessel functions for the atom-cavity mode interaction modulated by the exponential function. This function is incorporated into the basic Hamiltonian phenomenologically for modelling the processes of adiabatic switching on or switching off the interaction of a two-level atom (at rest) with a quantized mode. The dynamical behaviour of the atomic inversion for such processes is plotted and compared with the atomic dynamics for the standard model. If we take into account that, in micromaser experiments, Rydberg atoms move through a cavity with a spatially inhomogenous field, we deal with the Jaynes-Cummings model with a spatial modulation the form of which is defined by the mode-shape function depending, in turn, on the geometrical form of resonator. In the cases of a rectangular and a spherical cavity the analytical solutions for atomic inversion are found in the explicit form in the weak-coupling limit. We consider in detail the time evolution of the atomic inversion while the atom passes through a rectangular cavity. Contrary to the standard model the initial inversion can be exactly restored during the atomic transit depending on the relation between the detuning, the atomic velocity and the number of half-wavelengths of the chosen mode. The numerical solutions of the basic equations are also obtained and plotted for rectangular and spherical resonators.
Stability and instability of quantum evolution are studied in the interaction between a two-level atom with photon recoil and a quantized field mode in an ideal cavity, the basic model of cavity quantum electrodynamics. It is shown that the Jaynes-Cummings dynamics can be unstable in the regime of chaotic motion of the atomic center of mass in the quantized field of a standing wave in the absence of any kind of interaction with environment. This kind of quantum instability manifests itself in strong variations of reduced quantum purity and entropy, correlating with the respective classical Lyapunov exponent, and in exponential sensitivity of fidelity of quantum states to small variations in the atom-field detuning. The connection between quantum entanglement and fidelity and the center-of-mass motion is clarified analytically and numerically for a few regimes of that motion. The results are illustrated with two specific initial field states: the Fock and coherent ones. Numerical experiments demonstrate various manifestations of the quantum-classical correspondence, including dynamical chaos and fractals, which can be, in principle, observed in real experiments with atoms and photons in high-finesse cavities.
The emission probability of a cold atom in a microcavity when its center-of-mass motion is described quantum mechanically is presented, but is distinguished from other treatments by the inclusion of the spatial variation along the cavity axis. In particular, the mesa mode cavity profile is considered. The quantum theory of the one-photon mazer is constructed in the framework of the dressed-state coordinate formalism. Simple expressions for the atomic populations, the cavity photon statistics, and the reflection and transmission probabilities are given for any initial state of the atom-field system. The general conclusions reached are illustrated by numerical results.