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Journal of Physics B Atomic Molecular and Optical Physics

Production and protection of entanglement via vacuum induced coherences

Anjali N. Nair, R. Arun

Published Feb 27, 2024• 2 citations
Publisher

Abstract

Abstract The entanglement dynamics of a pair of three-level V-type atoms decaying spontaneously in a common vacuum reservoir is investigated. Under the condition that the decaying transitions in the atoms have parallel dipole moments, the effect of coherences induced by spontaneous emission is considered in the atomic dynamics. We show that vacuum-induced coherence (VIC) and collective effects in atomic decay play a significant role in the creation of entanglement. By using negativity as a measure of entanglement, we study the time evolution of entanglement for initial separable and generalized Dicke states as well as maximally entangled qutrit states. We show that the effects of VIC enhance the production of entanglement from initial separable states of the atoms. We also show that the entanglement can be protected in steady-state for atoms evolving from initial entangled states. The amount of entanglement that can be preserved is more in the presence of VIC than in its absence.

DOI
10.1088/1361-6455/ad2d5d

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Abstract The entanglement dynamics of a pair of three-level V-type atoms decaying spontaneously in a common vacuum reservoir is investigated. Under the condition that the decaying transitions in the atoms have parallel dipole moments, the effect of coherences induced by spontaneous emission is considered in the atomic dynamics. We show that vacuum-induced coherence (VIC) and collective effects in atomic decay play a significant role in the creation of entanglement. By using negativity as a measure of entanglement, we study the time evolution of entanglement for initial separable and generalized Dicke states as well as maximally entangled qutrit states. We show that the effects of VIC enhance the production of entanglement from initial separable states of the atoms. We also show that the entanglement can be protected in steady-state for atoms evolving from initial entangled states. The amount of entanglement that can be preserved is more in the presence of VIC than in its absence.
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.
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.
We study an extended velocity-selective coherent population trapping (VSCPT) model where vacuum-induced coherence (VIC) is considered. This effect takes place when two nonorthogonal electric dipole moments of a $\ensuremath{\Lambda}$-type three-level atom couple with a common continuous vacuum. First, we introduce the main results of a conventional VSCPT model in the nondegenerate and unsymmetrically driven situation. Then, we work out the dynamic equation of the system in the presence of VIC expressed in both internal and external degrees of freedom. We report on the generation of atomic external coherences due to VIC, which counteract the feeding action of spontaneous emission to the trapping state and indicate its limited function negative to the formation of the trapping state if the atomic center-of-mass motion is considered.
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.
The role of the collective antisymmetric state in entanglement creation by spontaneous emission in a system of two non-overlapping two-level atoms has been investigated. Populations of the collective atomic states and the Wootters entanglement measure (concurrence) for two sets of initial atomic conditions are calculated and illustrated graphically. Calculations include the dipole-dipole interaction and a spatial separation between the atoms that the antisymmetric state of the system is included throughout even for small interatomic separations. 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. It is found that the ability of spontaneous emission to create transient entanglement relies on the absence of population in the collective symmetric state of the system. For the initial state of only one atom excited, entanglement builds up rapidly in time and reaches a maximum for parameter values corresponding roughly to zero population in the symmetric state. On the other hand, for the initial condition of both atoms excited, the atoms remain unentangled until the symmetric state is depopulated. A simple physical interpretation of these results is given in terms of the diagonal states of the density matrix of the system. We also study entanglement creation in a system of two non-identical atoms of different transition frequencies. It is found that the entanglement between the atoms can be enhanced compared to that for identical atoms, and can decay with two different time scales resulting from the coherent transfer of the population from the symmetric to the antisymmetric state. In addition, it was found that a decaying initial entanglement between the atoms can display a revival behaviour.