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International Journal of Quantum Information

ENTANGLEMENT DEATH AND PURITY LOSS FOREVER IN THE DISPERSIVE INTERACTION OF A TRAPPED ION AND LIGHT WITHOUT ENERGY RELAXATION

Abdel‐Baset A. Mohamed

Published Feb 1, 2011• 2 citations
Publisher

Abstract

Death of entanglement between light and the vibrational motion of a single trapped ion in the dispersive regime with a reservoir is investigated. It is found that with phase-damped cavity, the purity of the light-motional states is lost forever, unlike the purity of the ion's internal states which have regular patterns and they do not decay. The asymptotic behavior of the states of the light, the ion-motional and the total system fall into a mixed state. The entanglement and purity have strong sensitivity to the phase damping and the ionic distribution angle. The entanglement sudden death has been treated as it arises from the effect of phase damping on mixed as well as pure states.

DOI
10.1142/s0219749911007605

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Death of entanglement between light and the vibrational motion of a single trapped ion in the dispersive regime with a reservoir is investigated. It is found that with phase-damped cavity, the purity of the light-motional states is lost forever, unlike the purity of the ion's internal states which have regular patterns and they do not decay. The asymptotic behavior of the states of the light, the ion-motional and the total system fall into a mixed state. The entanglement and purity have strong sensitivity to the phase damping and the ionic distribution angle. The entanglement sudden death has been treated as it arises from the effect of phase damping on mixed as well as pure states.
In this paper, we consider the entanglement dynamics of two cavities interacting with independent reservoirs. When the cavity entanglement suddenly disappeared, the reservoir entanglement suddenly and necessarily appears. We study the effect of purity of initial entangled state of two cavities on the entanglement evolution, and acquire that the purity of initial entangled state of two cavities can control the apparition time of the entanglement sudden death and the entanglement sudden birth. Also, we find that the conditions on the apparition of the entanglement sudden death and the entanglement sudden birth can be generalized when the initial entangled state of cavities is not pure, which is a complement to the result in the paper [Phys. Rev. Lett.101 (2008) 080503] for the pure case.
The entanglement in a system of a single two-level trapped ion and a single-mode quantized field in a coherent state inside a phase-damped cavity is investigated. Analytic results under certain parametric conditions are obtained, by means of which we analyze the influence of dissipation on the atomic Fisher information and its marginal distribution. An interesting relation between the temporal entanglement sudden birth, sudden death, atomic Fisher information and the dissipation effect is observed.
In this paper, we study the effect of atom decay on the atomic tunneling and entanglement dynamics in an atom-cavity system. This system consists of an atom trapped in a double-well potential and a cavity that couples to the atom. The population of the atom in the left/right well and the dynamics of entanglement are calculated and discussed. We find that the tunneling behaves as a damping-oscillating function of time, and the entanglement between the internal and external degree of freedom of the atom exhibits entanglement sudden death (ESD).
We investigate the phenomenon of sudden death of entanglement in a bipartite system subjected to dissipative environments with arbitrary initial pure entangled state between two atoms. We find that in a vacuum reservoir the presence of the state where both atoms are in excited states is a necessary condition for the sudden death of entanglement. Otherwise entanglement remains for an infinite time and decays asymptotically with the decay of individual qubits. For pure 2-qubit entangled states in a thermal environment, we observe that the sudden death of entanglement always happens. The sudden death time of the entangled states is related to the temperature of the reservoir and the initial preparation of the entangled states.
We investigate the phenomenon of sudden death of entanglement in a high-dimensional bipartite system subjected to dissipative environments with an arbitrary initial pure entangled state between two fields in the cavities. We find that in a vacuum reservoir, the presence of the state where one or more than one (two) photons in each cavity are present is a necessary condition for the sudden death of entanglement. Otherwise entanglement remains for infinite time and decays asymptotically with the decay of individual qubits. For pure two-qubit entangled states in a thermal environment, we observe that sudden death of entanglement always occurs. The sudden death time of the entangled states is related to the number of photons in the cavities, the temperature of the reservoir and the initial preparation of the entangled states.
The dynamical behavior of the entanglement and the squeezing in the system of two ions trapped in a lossy optical cavity is discussed, in which the vibrational mode of the first ion is coupled to the cavity field via a linear-mixing interaction and the vibrational mode of the second ion is coupled to the cavity field via an effective parametric interaction, respectively. It is found that when the effective strength r1{r}_{1}r1​ of the coupling between the first ion and the cavity field is stronger than the strength r2{r}_{2}r2​ of the coupling between the second ion and the cavity field, the motional state of the two ions develops into a robust two-mode mixed Gaussian entangled state and the two-mode squeezing of phonons appears. But the entanglement between the cavity mode and the vibrational mode of the second ion can only happen periodically in a small time range. When r1<r2{r}_{1}<{r}_{2}r1​<r2​, only the entanglement between the two vibrational modes appears but the two-mode squeezing does not exist. And the entanglement between the cavity mode and the motional mode of the second ion can also take place in a small time range.