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Communications in Theoretical Physics

Entanglement generation and protection for two atoms in the presence of two parallel mirrors

Yuhong 玉洪 Ye 叶, Hongwei Yu, Jiawei Hu

Published Mar 19, 2021• 3 citations
Publisher

Abstract

Abstract We study, in the framework of open quantum systems, the entanglement generation of two atoms in between two parallel mirrors in a thermal bath of quantum scalar fields. We find that the presence of mirrors plays an important role in entanglement generation and protection. The entanglement dynamics is crucially dependent on the geometric configurations of the two-atom system with respect to the mirrors, and the ranges of temperature and interatomic separation within which entanglement can be generated are significantly changed compared with those in a free space. In particular, when the atomic transition wavelength is larger than twice the distance between the two mirrors, the atoms behave as if they were isolated from the environment and the entanglement can persist in the steady state if the atoms are initially entangled and no entanglement can be created if they are initially separable, no matter how the atoms are placed with respect to the mirrors and to each other. This is in sharp contrast to the fact that in a free space, steady-state entanglement is possible only when the two atoms are placed extremely close to each other, while in the presence of one mirror, it is possible when the two atoms placed extremely close to the mirror.

DOI
10.1088/1572-9494/abf03d

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Abstract We study, in the framework of open quantum systems, the entanglement generation of two atoms in between two parallel mirrors in a thermal bath of quantum scalar fields. We find that the presence of mirrors plays an important role in entanglement generation and protection. The entanglement dynamics is crucially dependent on the geometric configurations of the two-atom system with respect to the mirrors, and the ranges of temperature and interatomic separation within which entanglement can be generated are significantly changed compared with those in a free space. In particular, when the atomic transition wavelength is larger than twice the distance between the two mirrors, the atoms behave as if they were isolated from the environment and the entanglement can persist in the steady state if the atoms are initially entangled and no entanglement can be created if they are initially separable, no matter how the atoms are placed with respect to the mirrors and to each other. This is in sharp contrast to the fact that in a free space, steady-state entanglement is possible only when the two atoms are placed extremely close to each other, while in the presence of one mirror, it is possible when the two atoms placed extremely close to the mirror.
We examine the entanglement creation between two mutually independent two-level atoms immersed in a thermal bath of quantum scalar fields in the presence of a perfectly reflecting plane boundary. With the help of the master equation that describes the evolution in time of the atom subsystem obtained, in the weak-coupling limit, by tracing over environment (scalar fields) degrees of freedom, we find that the presence of the boundary may play a significant role in the entanglement creation in some circumstances and the new parameter, the distance of the atoms from the boundary, besides the bath temperature and the separation between the atoms, gives us more freedom in manipulating entanglement generation. Remarkably, the final remaining entanglement in the equilibrium state is independent of the presence of the boundary.
We study the entanglement dynamics for two uniformly accelerated two-level atoms in interaction with a bath of fluctuating electromagnetic fields in vacuum in the presence of a reflecting boundary. We consider two different alignments of atoms, i.e., parallel and vertical alignments with respect to the boundary. In particular, we focus on the effects of the boundary, and acceleration on the entanglement dynamics, which are closely related to the orientations of polarization. For the parallel case, the initial entanglement of two transversely polarizable atoms very close to the boundary can be preserved as if it were a closed system, while for two vertically polarizable atoms, the concurrence evolves two times as fast as that in the free space. In the presence of a boundary, entanglement revival is possible for two atoms initially in the symmetric state depending on the orientations of the atomic polarizations, which is in sharp contrast to the fact that the concurrence always decays monotonically in the free space. Interestingly, two initially separable atoms, for which entanglement generation can never happen in the free space with any given acceleration and separation, can get entangled in the presence of a boundary if they are aligned parallel to the boundary. The birth time of entanglement can be noticeably advanced or postponed for the parallel two-atom system placed close to the boundary, while the maximal concurrence during evolution can be significantly enhanced when the atoms are vertically aligned. Moreover, two inertial atoms with different polarizations remain separable all the time, while as the acceleration increases, the delayed birth of entanglement happens, and the nonzero concurrence can be enhanced.
A model of entanglement generation of two initially disentangled qubits, each coupled to a separate cavity with the cavities connected by a fiber, is considered. The creation and evolution of the atomic entanglement are studied in the framework of the microscopic master equation capable of describing an open quantum system. The cavities and fiber are coupled to their own thermal environment. In these conditions, we compute the concurrence as a measure of the atomic entanglement and study the contribution of the environments at finite temperature to the dynamics of entanglement. As a result, one finds interesting effects where the thermal baths stimulate the generation of the entanglement in a given range of temperatures and the effect could be seen especially at some stage of the entanglement evolution. The range of temperatures at which entanglement increases is limited by some optimal values, depending on the physical characteristics of the system, such as operating cavity/fiber frequencies, atom–field detuning and couplings, and loss rates.
We study, in the framework of open quantum systems, the entanglement generation between two mutually independent static two-level atoms in de Sitter spacetime. We treat the two-atom system as an open system in interaction with a bath of fluctuating conformally coupled massless scalar fields in the de Sitter invariant vacuum and derive the master equation that governs its evolution. With the help of the partial transposition criterion, we analyze entanglement generation between the two initially separable atoms and find that static atoms in de Sitter spacetime exhibit distinct characteristics from those in a thermal bath in flat spacetime in terms of entanglement generation. So, in principle, one can tell whether he is in a thermal bath or in de Sitter space by checking the entanglement creation between two initially separable static atoms in certain circumstances.
Abstract We study the entanglement dynamics of two static atoms coupled with a bath of fluctuating scalar fields in vacuum in the cosmic string spacetime. Three different alignments of atoms, i.e. parallel, vertical, and symmetric alignments with respect to the cosmic string are considered. We focus on how entanglement degradation and generation are influenced by the cosmic string, and find that they are crucially dependent on the atom-string distance r, the interatomic separation L, and the parameter ν\nu ν ν that characterizes the nontrivial topology of the cosmic string. For two atoms initially in a maximally entangled state, the destroyed entanglement can be revived when the atoms are aligned vertically to the string, which cannot happen in the Minkowski spacetime. When the symmetrically aligned two-atom system is initially in the antisymmetric state, the lifetime of entanglement can be significantly enhanced as ν\nu ν ν increases. For two atoms which are initially in the excited state, when the interatomic separation is large compared to the transition wavelength, entanglement generation cannot happen in the Minkowski spacetime, while it can be achieved in the cosmic string spacetime when the position of the two atoms is appropriate with respect to the cosmic string and ν\nu ν ν is large enough.
We study two two-level atomic quantum systems (qubits) placed close to a body held at a temperature different from that of the surrounding walls. While at thermal equilibrium the two-qubit dynamics is characterized by non-entangled steady thermal states, we show that the absence of thermal equilibrium may bring to the generation of entangled steady states. Remarkably, this entanglement emerges from the two-qubit dissipative dynamic itself, without any further external action on the two qubits, suggesting a new protocol to create and protect entanglement which is intrinsically robust to environmental effects.