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arXiv:2105.14712

Can a pure state remain pure in the Unruh effect?

Saptarshi Saha, Arpan Chatterjee, Chiranjeeb Singha

Published May 31, 2021• 0 citations
arXivHTMLPDF

Abstract

A uniformly accelerated detector in an inertial vacuum undergoes an unavoidable dissipation, and the final steady-state becomes thermal. However, to attain such a mixed state, there is no bound for the acceleration of the single atomic detector. Here we show that the scenario is entirely different for two atoms with the same energy levels. There exists a critical limit of the acceleration for two atomic detectors, below which the purity of a particular initial state can be preserved. We observe that the generator of the dissipative dynamics (Lindbladian) is invariant under a weak symmetry transformation at this limit. Hence one of the eigenstates of the symmetry operator is unchanged during the evolution. This kind of state is called a quantum dark state, which is essentially a decoherence-free subspace. As a consequence, the system becomes localized, and it can skip the Unruh thermalization. Beyond the critical limit, the symmetry is explicitly broken. Therefore our results suggest that the system goes through a first-order dissipative phase transition from a localized to a thermal phase.

DOI
10.48550/arxiv.2105.14712

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A uniformly accelerated detector in an inertial vacuum undergoes an unavoidable dissipation, and the final steady-state becomes thermal. However, to attain such a mixed state, there is no bound for the acceleration of the single atomic detector. Here we show that the scenario is entirely different for two atoms with the same energy levels. There exists a critical limit of the acceleration for two atomic detectors, below which the purity of a particular initial state can be preserved. We observe that the generator of the dissipative dynamics (Lindbladian) is invariant under a weak symmetry transformation at this limit. Hence one of the eigenstates of the symmetry operator is unchanged during the evolution. This kind of state is called a quantum dark state, which is essentially a decoherence-free subspace. As a consequence, the system becomes localized, and it can skip the Unruh thermalization. Beyond the critical limit, the symmetry is explicitly broken. Therefore our results suggest that the system goes through a first-order dissipative phase transition from a localized to a thermal phase.
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.
The master equation describing the completely positive time evolution of a uniformly accelerated two-level system in weak interaction with a scalar field in the Minkowski vacuum is derived and explicitly solved. The moving system is found to be subjected to dissipation that drives its density matrix to a purely thermal equilibrium state, exhibiting a nonvanishing probability of spontaneous excitation, this phenomenon being usually referred to as the Unruh effect. Remarkably, when the uniformly accelerating system is composed by two, independent two-level atoms, the corresponding asymptotic, equilibrium state turns out to be entangled.
A uniformly accelerated atom in an inertial vacuum generally thermalizes to a Gibbs state, which is known as the Unruh effect. In contrast, for a noninteracting many-body system coupled to a common massless scalar field, we find that thermalization proceeds in multiple stages: the system first attains a prethermal generalized Gibbs state, before eventual relaxation to the thermal Gibbs state. The prethermal state is protected by emergent conserved quantities; hence, the system behaves like a nearly integrable one, which shows a sharp distinction from the Unruh effect. We coin the term “Unruh prethermalization” to characterize this phenomenon. The measure of entanglement is a good estimation of the lifetime of the prethermal state and is consistent with previous studies. Finally, we show that in such a regime, the dynamics show a Dicke superradiance-type radiation burst before reaching the prethermal state. In contrast, only a monoexponential decay is observed for Unruh thermalization. In addition, to highlight the significance of our results, we compare them with existing experimental observations.
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.
Uniform acceleration induces a thermal response to the Minkowski vacuum and can thereby modify quantum correlations. For measurement-induced nonlocality (MIN), a form of nonclassical correlation distinct from entanglement, previous field-mode analyses of bosonic fields found that it decreases with increasing acceleration and vanishes in the infinite-acceleration limit. This raises the question of whether the disappearance of MIN is a generic consequence of the Unruh effect or depends on the physical description of the accelerated quantum system. To address this question, we study two uniformly accelerating Unruh-DeWitt detectors interacting with a massless scalar field. We find that the response of MIN to the Unruh temperature depends sensitively on the initial detector state: it can decrease monotonically, vanish at an intermediate temperature and subsequently recover, or increase monotonically. Moreover, for a broad class of initial states, MIN approaches a nonzero value in the high-temperature limit. These results show that the suppression of MIN under strong acceleration is not universal. Instead, Unruh-induced detector dynamics gives rise to a state-dependent response in which measurement-induced nonlocality can be suppressed, restored, or enhanced.