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arXiv:2101.08186 · Journal of High Energy Physics

Radiative process of two entangled uniformly accelerated atoms in a thermal bath: a possible case of anti-Unruh event

Subhajit Barman, Bibhas Ranjan Majhi

Published Mar 1, 2021• 32 citations
arXivHTMLPDF

Abstract

Abstract We study the radiative process of two entangled two-level atoms uniformly accelerated in a thermal bath, coupled to a massless scalar field. First, by using the positive frequency Wightman function from the Minkowski modes with a Rindler transformation we provide the transition probabilities for the transitions from maximally entangled symmetric and anti-symmetric Bell states to the collective excited or ground state in (1 + 1) and (1 + 3) dimensions. We observe a possible case of anti-Unruh-like event in these transition probabilities, though the (1+1) and (1+3) dimensional results are not completely equivalent. We infer that thermal bath plays a major role in the occurrence of the anti-Unruh-like effect, as it is also present in the transition probabilities corresponding to a single detector in this case. Second, we have considered the Green’s functions in terms of the Rindler modes with the vacuum of Unruh modes for estimating the same. Here the anti-Unruh effect appears only for the transition from the anti-symmetric state to the collective excited or ground state. It is noticed that here the (1 + 1) and (1 + 3) dimensional results are equivalent, and for a single detector, we do not observe any anti-Unruh effect. This suggests that the entanglement between the states of the atoms is the main cause for the observed anti-Unruh effect in this case. In going through the investigation, we find that the transition probability for a single detector case is symmetric under the interchange between the thermal bath’s temperature and the Unruh temperature for Rindler mode analysis; whereas this is not the case for Minkowski mode. We further comment on whether this observation may shed light on the analogy between an accelerated observer and a real thermal bath. An elaborate investigation for the classifications of our observed anti-Unruh effects, i.e., either weak or strong anti-Unruh effect, is also thoroughly demonstrated.

DOI
10.1007/jhep03(2021)245

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Abstract We study the radiative process of two entangled two-level atoms uniformly accelerated in a thermal bath, coupled to a massless scalar field. First, by using the positive frequency Wightman function from the Minkowski modes with a Rindler transformation we provide the transition probabilities for the transitions from maximally entangled symmetric and anti-symmetric Bell states to the collective excited or ground state in (1 + 1) and (1 + 3) dimensions. We observe a possible case of anti-Unruh-like event in these transition probabilities, though the (1+1) and (1+3) dimensional results are not completely equivalent. We infer that thermal bath plays a major role in the occurrence of the anti-Unruh-like effect, as it is also present in the transition probabilities corresponding to a single detector in this case. Second, we have considered the Green’s functions in terms of the Rindler modes with the vacuum of Unruh modes for estimating the same. Here the anti-Unruh effect appears only for the transition from the anti-symmetric state to the collective excited or ground state. It is noticed that here the (1 + 1) and (1 + 3) dimensional results are equivalent, and for a single detector, we do not observe any anti-Unruh effect. This suggests that the entanglement between the states of the atoms is the main cause for the observed anti-Unruh effect in this case. In going through the investigation, we find that the transition probability for a single detector case is symmetric under the interchange between the thermal bath’s temperature and the Unruh temperature for Rindler mode analysis; whereas this is not the case for Minkowski mode. We further comment on whether this observation may shed light on the analogy between an accelerated observer and a real thermal bath. An elaborate investigation for the classifications of our observed anti-Unruh effects, i.e., either weak or strong anti-Unruh effect, is also thoroughly demonstrated.
We investigate the transition rates of uniformly accelerated two-level single and entangled atomic systems in empty space as well as inside a cavity. We take into account the interaction between the systems and a massless scalar field from the viewpoint of an instantaneously inertial observer and a coaccelerated observer, respectively. The upward transition occurs only due to the acceleration of the atom. For the two-atom system, we consider that the system is initially prepared in a generic pure entangled state. In the presence of a cavity, we observe that for both the single and the two-atom cases, the upward and downward transitions are occurred due to the acceleration of the atomic systems. The transition rate manifests subtle features depending upon the cavity and system parameters, as well as the initial entanglement. It is shown that no transition occurs for a maximally entangled superradiant initial state, signifying that such entanglement in the accelerated two-atom system can be preserved for quantum information processing applications. Our analysis comprehensively validates the equivalence between the effect of uniform acceleration for an inertial observer and the effect of a thermal bath for a coaccelerated observer, in free space as well as inside a cavity, if the temperature of the thermal bath is equal to the Unruh temperature.
We calculate respectively, from the viewpoints of an instantaneously/locally inertial observer and a coaccelerated observer, the transition rates of the two-atom system in the symmetric/antisymmetric entangled state [$|{\ensuremath{\psi}}_{\ifmmode\pm\else\textpm\fi{}}⟩$]. The scalar fields to which the atoms are coupled are respectively assumed to be in the vacuum state and a thermal state in the instantaneously inertial frame and in the coaccelerated frame. We show that both the upward transition $|{\ensuremath{\psi}}_{\ifmmode\pm\else\textpm\fi{}}⟩\ensuremath{\rightarrow}|{e}_{A}{e}_{B}⟩$ and the downward transition $|{\ensuremath{\psi}}_{\ifmmode\pm\else\textpm\fi{}}⟩\ensuremath{\rightarrow}|{g}_{A}{g}_{B}⟩$ take place, where ∣gAgB⟩|{g}_{A}{g}_{B}⟩∣gA​gB​⟩ and ∣eAeB⟩|{e}_{A}{e}_{B}⟩∣eA​eB​⟩ represent two collective eigenstates of the two-atom system with both atoms in their ground state and excited state respectively, and the transition rates observed in the two frames are identical only if there exists a thermal bath at the Fulling-Davies-Unruh temperature in the coaccelerated frame. Though both the downward and upward transition rates are characterized by the Plankian factor, this factor does not show up in the average variation rate of energy of the two-atom system, as a result of the perfect cancellation of the terms in the transition rates in the instantaneously inertial frame multiplied by the Plankian factor which corresponds to the Unruh thermal bath, and the cancellation of the temperature-dependent terms in the transition rates observed in the coaccelerated frame. A comparison of the transition rates of a static two-atom system in interaction with the massless scalar field in a thermal state at an arbitrary temperature with those of a uniformly accelerated two-atom system in interaction with the vacuum massless scalar field shows that the equivalence between the thermal bath and the uniform acceleration, which is well known to be valid for the single atom case, no longer holds for the two-atom system in the symmetric/antisymmetric entangled state. The effect of atomic uniform acceleration in the transition rates of the two-atom system, and the roles of both the downward and the upward transitions in the disentanglement of the two-atom system are also discussed.
Abstract We study, in the framework of open quantum systems, the entanglement dynamics for a quantum system composed of two uniformly accelerated Unruh-Dewitt detectors interacting with a bath of massive scalar fields in the Minkowski vacuum. We find that the entanglement evolution for the quantum system coupled with massive fields is always slower compared with that of the one coupled with massless fields, and this time-delay effect brought about by the field being massive can however be counteracted by a large enough acceleration, in contrast to the case of a static quantum system in a thermal bath, where this time delay is not affected by the temperature. Remarkably, the maximal concurrence of the quantum system generated during evolution may increase with acceleration for any inter-detector separation while that for static ones in a thermal bath decreases monotonically with temperature, and this can be considered as an anti-Unruh effect in terms of the entanglement generated.
Abstract Transition rates of a uniformly accelerated atom coupled to a vacuum scalar field are identical with those of one being static in a thermal bath at a temperature proportional to the proper acceleration a, i.e., TU=a2πT_U=\frac{a}{2\pi }TU​=2πa​ T U = a 2 π . We discuss in this paper whether there exists such an equivalence in the electromagnetic field case if more atoms are involved. To be specific, we explore the similarities and distinctions between effects of a thermal bath and those of the uniformly accelerated motion by comparing the transition rates of a two-atom system initially in the symmetric or antisymmetric entangled state [ ∣ψ±⟩|\psi _{\pm }\rangle ∣ψ±​⟩ | ψ ± ⟩ ] in two cases, i.e., two static atoms in a thermal bath [the thermal case] and two atoms uniformly accelerated in vacuum [the acceleration case]. We discover that, for some particular orientations of atomic dipole moments, coherent radiation which happens in the acceleration case never occurs in the thermal case. The rates in the acceleration case with a low acceleration which means a low TUT_UTU​ T U can be smaller or larger and even equal to their counterparts in the thermal case; while the rates in the acceleration case with a high acceleration which means a high TUT_UTU​ T U are always much larger than their counterparts in the thermal case. Our results suggest that effects of a thermal bath and those of the uniformly accelerated motion on transition properties of a two-atom system in ∣ψ±⟩|\psi _{\pm }\rangle ∣ψ±​⟩ | ψ ± ⟩ are not necessarily distinctive, but can be equivalent if the acceleration is relatively low, depending on the value of the interatomic separation.
The entanglement generated for a uniformly accelerated two-atom system in vacuum during its evolution may increase with acceleration, while that for a static one in a thermal bath always decreases monotonically with temperature. This phenomenon is named as the anti-Unruh effect in terms of the entanglement generated. In this paper, we study the effects of the interatomic interaction induced by the electromagnetic vacuum fluctuations on the entanglement dynamics of two uniformly accelerated atoms. We show that the anti-Unruh phenomenon may exist or disappear depending critically on the configuration of the orientation of the atomic polarization and the directions of the uniform acceleration and the interatomic separation. This is in sharp contrast to the scalar-field case, in which the anti-Unruh phenomenon is always lost when the environment-induced interatomic interaction is considered.
A uniformly accelerated observer perceives the Minkowski vacuum as a thermal bath, so acceleration acts as a noise channel on correlations shared with an inertial partner. For a Dirac field in the standard treatment, the resulting map is a one-sided amplitude-damping channel, and entanglement and quantum discord survive at infinite acceleration. We introduce a symmetric Unruh-like map in which the vacuum and the one-particle state both exchange amplitude with the inaccessible Rindler region; for a Bell state it yields a bit-flip channel whose flip probability is the Fermi-Dirac occupation at the Unruh temperature. Using negativity, mutual information, and all six pairwise quantum discords, we find that the entanglement and discord between the inertial observer and the accessible mode vanish together at infinite acceleration, leaving only one bit of classical correlation. These results show that the fate of quantum correlations in noninertial frames depends on the structure of the Minkowski-Rindler map.