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Journal of Physics A Mathematical and General

Decoherence of two entangled atoms in vacuum

Wei Guo

Published Apr 19, 2006• 2 citations
Publisher

Abstract

Decoherence of two atoms initially prepared in Bell states in free space is discussed theoretically through calculation of the probabilities for the atoms to remain respectively in these states. It is found that, due to quantum interference, the atoms never follow a purely exponential law to decohere from their initial states, even though spontaneous emission is illustrated to cause the decoherence.

DOI
10.1088/0305-4470/39/18/021

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Decoherence of two atoms initially prepared in Bell states in free space is discussed theoretically through calculation of the probabilities for the atoms to remain respectively in these states. It is found that, due to quantum interference, the atoms never follow a purely exponential law to decohere from their initial states, even though spontaneous emission is illustrated to cause the decoherence.
In this work, decoherence of a system from an entangled state is studied theoretically by computing the time-dependent probability amplitude with which the system remains in that state. The system is composed of, in addition to vacuum, identical two-level atoms that interact indirectly with each other through photons and have a uniform distribution in the vacuum. Under the assumption that in the initial entangled state only one atom is allowed to be in the excited state, a general expression for the probability amplitude is obtained and applied to two specific entangled states, one symmetric and one antisymmetric, to demonstrate that the system decoheres from these two states at the same rate under certain conditions.
Two four-level atoms resonantly interacting with a two-mode squeezed vacuum field through the intensity-dependent Jaynes–Cummings-like model are considered. It is shown that the atoms can evolve into pure entangled states at certain time. Moreover, the pure entangled states can probabilistically be projected onto extremely entangled states by quantum jump technique. It is shown that the success probability monotonously increases with increasing degree of squeezing without any decoherence processes. However, it is found that if decoherence processes such as atomic spontaneous emission and photon leakage out of the cavity take place, the total success probability first increases but then decreases with increasing degree of squeezing and finally approaches zero as the squeezing becomes stronger and stronger. Therefore, the high degree of squeezing in the initial state of the cavity field is not always helpful for a high probability of creating extremely entangled states when spontaneous emission and cavity decay exist. Given spontaneous emission and photon leakage rates, there is an optimal squeezing degree for which the total success probability becomes maximum.
We show that vacuum-induced coherence in three-level atomic systems can lead to preservation of bipartite entanglement when two such atoms are prepared as two initially entangled qubits, each independently interacting with their respective vacuum reservoirs. We explicitly calculate the time evolution of concurrence for two different Bell states and show that a large amount of entanglement can survive in the long time limit. The amount of entanglement left between the two qubits depends strongly on the ratio of the nonorthogonal transitions in each qubit and can be more than 5050%50. Moreover, we find that as a consequence of vacuum-induced coherence, sudden death of entanglement is prevented for an initial mixed entangled state of the qubits.
The dynamical evolution of entanglement between two polarizable two-level atoms in weak interaction with electromagnetic vacuum fluctuations is investigated. We find that, for initial Bell state ψ±\psi^{\pm}ψ±, the decay rate of entanglement between atoms is just the superradiant spontaneous emission rate, which depends not only on the spontaneous emission rate of atom but also on the modulation of the spontaneous emission rate due to the presence of another atom. It is shown that, with the presence of a boundary, the entanglement between transversely polarizable atoms can be protected for a very long time. It is pointed out that when the two atoms in initial Bell state ψ−\psi^{-}ψ− are put close enough , the entanglement between them can also be protected.
Abstract. We discuss the creation of entanglement between two two-level atoms in the dissipative process of spontaneous emission. It is shown that spontaneous emission can lead to a transient entanglement between the atoms even if the atoms were prepared initially in an unentangled state. The amount of entanglement created in the system is quantified by using two different measures: concurrence and negativity. We find analytical formulas for the evolution of concurrence and negativity in the system. We also find the analytical relation between the two measures of entanglement. The system consists of two two-level atoms which are separated by an arbitrary distance r12 and interact with each other via the dipole-dipole interaction, and the antisymmetric state of the system is included throughout, even for small inter-atomic separations, in contrast to the small sample model. It is shown that for sufficiently large values of the dipole-dipole interaction initially the entanglement exhibits oscillatory behaviour with considerable entanglement in the peaks. For longer times the amount of entanglement is directly related to the population of the slowly decaying antisymmetric state.