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Physical Review A

Entanglement properties of an ultracold atom interacting with a cavity quantized electromagnetic field

Octavio Castaños, Rocío Jáuregui

Published Nov 15, 2010• 3 citations
Publisher

Abstract

We study the temporal evolution of the properties of a two-level atom coupled to a single-mode cavity field without dissipation with its center-of-mass motion quantized in one dimension. It is shown that, starting with a separable state, genuine tripartite entangled states can be generated under resonance conditions of the light frequency and atom transition frequency in the cold regime. The onset of Rabi oscillations is analyzed and explicit predictions for properties like emission probability and dispersions for the center-of-mass position and momenta are given for resonance and detuned conditions. Transmission-resonance effects on entanglement and other properties are also analyzed. Comparisons with the semiclassical adiabatic approximation predictions are also made.

DOI
10.1103/physreva.82.053815

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We study the temporal evolution of the properties of a two-level atom coupled to a single-mode cavity field without dissipation with its center-of-mass motion quantized in one dimension. It is shown that, starting with a separable state, genuine tripartite entangled states can be generated under resonance conditions of the light frequency and atom transition frequency in the cold regime. The onset of Rabi oscillations is analyzed and explicit predictions for properties like emission probability and dispersions for the center-of-mass position and momenta are given for resonance and detuned conditions. Transmission-resonance effects on entanglement and other properties are also analyzed. Comparisons with the semiclassical adiabatic approximation predictions are also made.
We propose an experimental setup, feasible with present day technology, involving two highquality- factor cavities, one Ramsey zone and a two-level atom which interacts with them. The dynamics in the cavities is modeled by a dissipative dispersive Jaynes-Cummings model. Analytical expresions for the evolution superoperator in each part of the proposed setup and for the concurrence between the atom and the first cavity are given, and the pairwise entanglement of the subsystems is calculated numerically. We consider initial separable states given by the tensor product of a superposition of the two atomic relevant states and coherent states for the fields. We show that for realistic model parameters (including dissipation), when the dissipation rates are smaller than the dispersive frequencies (the ratio between the squared vacuum Rabi frequencies and the detunings), the final state of the cavity fields remains entangled.
We consider that an ultracold two-level atom passes through multi spatially separated single-mode cavity fields and investigate the influence of the center-of-mass motion of the atom, the length of the cavity and the separation between two cavities on the transmission and photon emission probabilities of the atom. We find that both the transmission and photon emission probabilities as functions of the cavity length have multi-resonance peaks when the separation between two cavities is equal to an integer multiple of half the de Broglie wavelength of the atomic center-of-mass motion. The present work shows that the wave function of the atomic center-of-mass motion may be modulated in a macroscopic level by arranging the cavities.
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.
An two-level atom is considered passes through double spatially separated single-mode cavity fields and the influence of the center-of-mass motion of the atom is investigated,the length of the cavity and the separation between two cavities on entanglement between the cavity fields because of interaction between the atom and the cavity fields.It is found that in the case of ultra-cold atom,when k / k0 1,the probility that the atom passes through double cavity fields is small,and the entanglement is generated is small too.And when k / k0 1,the result is contraty.
The center-of-mass motion of two two-level atoms coupled to a single damped mode of an electromagnetic resonator is investigated. For the case of one atom being initially excited and the cavity mode in the vacuum state, it is shown that the atomic time evolution is dominated by the appearance of dark states. These states, in which the initial excitation is stored in the internal atomic degrees of freedom and the atoms become quantum mechanically entangled, are almost immune against photon loss from the cavity. Various properties of the dark states within and beyond the Raman-Nath approximation of atom optics are worked out.
The entanglement dynamics of a two-level atom with center-of-mass motion in a single-mode quantized field is investigated.The behavior of the entropy changes of the subsystems,as well as the concurrence of the coupled atom-field system is explored.These results show that when the atom is initially prepared in ground state anti-correlation behavior occurs,but a positively correlated behavior appears gradually as the increasing of the probability of the atom initially in excited state.Also,the amplitude of the concurrence increases with the increasing of the probability of the atom initially in excited state.In addition,with increasing of the atomic center-of-mass motion,both the amplitudes of the partial entropy changes and the concurrence are reduced.