Abstract We study the average rate of change of energy of two accelerated entangled atoms coupled to electromagnetic fields in the presence of a reflecting boundary, which according to the Dalibard, Dupont–Roc and Cohen-Tannoudji formalism is only attributed to the contribution of the radiative reaction of atoms. When the boundary is present, this result can be expressed as the sum of the free-space result and the boundary-induced modifications, and it generally depends on the two-atom initial state, the orientations of atomic dipole moments, as well as the relative scales among atom-boundary distance, interatomic separation and the inverse of atomic acceleration. When the two atoms are vertically aligned and one atom is very close to the boundary, we find that the terms only related to the closer atom are zero for the symmetric state but double the free-space counterpart for the antisymmetric state, if the atom is polarizable parallel to the boundary. However, for the atom polarizable vertically to the boundary, these terms vanish for the antisymmetric state but are twice the free-space counterpart for the symmetric state. Moreover, the terms related to the farther atom exhibit obviously oscillatory behavior, and the terms related to both atoms are vanishing unless the dipole moments of two atoms both have their components vertical to the boundary. When the two atoms are aligned parallel to and very close to the boundary, the terms related to one atom are interatomic-separation-independent and only influenced by the atomic dipole moments. The terms related to both atoms are actually consistent with the counterpart in the vertical-alignment case. In addition, when the two atoms are polarizable along the direction parallel to the boundary, the average rate of change of energy of two parallel-aligned and symmetric entangled atoms vanishes as if the two atoms were a closed system.
Abstract We study the average rate of change of energy of two accelerated entangled atoms coupled to electromagnetic fields in the presence of a reflecting boundary, which according to the Dalibard, Dupont–Roc and Cohen-Tannoudji formalism is only attributed to the contribution of the radiative reaction of atoms. When the boundary is present, this result can be expressed as the sum of the free-space result and the boundary-induced modifications, and it generally depends on the two-atom initial state, the orientations of atomic dipole moments, as well as the relative scales among atom-boundary distance, interatomic separation and the inverse of atomic acceleration. When the two atoms are vertically aligned and one atom is very close to the boundary, we find that the terms only related to the closer atom are zero for the symmetric state but double the free-space counterpart for the antisymmetric state, if the atom is polarizable parallel to the boundary. However, for the atom polarizable vertically to the boundary, these terms vanish for the antisymmetric state but are twice the free-space counterpart for the symmetric state. Moreover, the terms related to the farther atom exhibit obviously oscillatory behavior, and the terms related to both atoms are vanishing unless the dipole moments of two atoms both have their components vertical to the boundary. When the two atoms are aligned parallel to and very close to the boundary, the terms related to one atom are interatomic-separation-independent and only influenced by the atomic dipole moments. The terms related to both atoms are actually consistent with the counterpart in the vertical-alignment case. In addition, when the two atoms are polarizable along the direction parallel to the boundary, the average rate of change of energy of two parallel-aligned and symmetric entangled atoms vanishes as if the two atoms were a closed system.
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.
We apply the DDC formalism [proposed by Dalibard, Dupont-Roc and Cohen-Tannoudji] to study the average rate of change of energy of two identical two-level atoms interacting with the vacuum massless scalar field in synchronized motion along stationary trajectories. By separating the contributions of vacuum fluctuations and atomic radiation reaction, we first show that for the two-atom system initially prepared in the factorizable eigenstates ∣gAgB⟩ and ∣eAeB⟩, where g and e represent the ground state and the excited state of a single atom, respectively, both vacuum fluctuations and atomic radiation reaction contribute to the average rate of change of energy of the two-atom system, and the contribution of vacuum fluctuations is independent of the interatomic separation while that of atomic radiation reaction is dependent on it. This is contrary to the existing results in the literature where vacuum fluctuations are interatomic-separation dependent. However, if the two-atom system is initially prepared in the unfactorizable symmetric/antisymmetric entangled state, the average rate of change of energy of the two-atom system is never perturbed by the vacuum fluctuations, but is totally a result of the atomic radiation reaction. We then consider two special cases of motion of the two-atom system, which is initially prepared in the symmetric/antisymmetric entangled state, i.e., synchronized inertial motion and synchronized uniform acceleration. In contrast to the average rate of change of energy of a single uniformly accelerated atom, the average rate of change of energy of the uniformly accelerated two-atom system is nonthermal-like. The effects of noninertial motion on the transitions of states of the two correlated atoms are also discussed.
We investigate the rate of change of the mean atomic energy for centripetally accelerated atoms interacting with electromagnetic vacuum fluctuations near a reflecting boundary, using the Dalibard-Dupont-Roc-Cohen-Tannoudji formalism. The distinct contributions from vacuum fluctuations and radiation reaction are analyzed separately. Our results reveal that, when the centripetal acceleration significantly exceeds the characteristic acceleration set by the atomic transition frequency, vacuum fluctuations dominates over radiation reaction, irrespective of the atom-boundary distance and the atomic polarization. In the near-zone regime, where the atom-boundary distance is much smaller than both the characteristic length associated with the acceleration and the transition wavelength of the atom, the boundary introduces substantial corrections to the rate of change of the mean atomic energy. These corrections are comparable in magnitude to those in free space and exhibit strong dependence on the atomic polarization. Remarkably, in the intermediate and far regions, contributions stemming from the combined effects of the boundary and acceleration can become the leading and subleading terms, respectively. An acceleration-independent term also arises from their interplay. These findings highlight the significant interplay between acceleration and the presence of a boundary in shaping atomic radiative properties and may have potential implications for experimentally probing the circular Unruh effect.
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=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±⟩ | 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 TU 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 TU 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±⟩ | ψ ± ⟩ are not necessarily distinctive, but can be equivalent if the acceleration is relatively low, depending on the value of the interatomic separation.
We explore, respectively, from the viewpoints of a locally inertial observer and a coaccelerated observer, the transition rates of a two-atom system in the symmetric or antisymmetric entangled state, [Formula: see text] or [Formula: see text], and coupled to the electromagnetic fields. The interatomic separation is assumed to be constant and perpendicular to the acceleration; the fields to which the atoms are coupled are assumed to be in the vacuum state in the locally inertial frame and in a thermal state in the coaccelerated frame. We find that, in the viewpoints of the two observers, both the downward transition [Formula: see text] and the upward transition [Formula: see text] can take place, where [Formula: see text] and [Formula: see text] denote two eigenstates of the two-atom system with both atoms in their ground states and excited states, respectively. With an appropriate choice of the orientations of the atomic dipole moments, coherent radiation can happen for a system in acceleration but not for one in inertial motion. By comparing the transition rates viewed by the two observers, we show that the transition rates of the accelerated two-atom system viewed by a locally inertial observer can only be recovered in the coaccelerated frame by assuming a thermal bath at the Fulling–Davies–Unruh temperature. The effects of these collective transitions on the evolution of energy of the two-atom system are also analyzed.
We study the resonant dipole–dipole interaction energy between two non-inertial identical atoms, one excited and the other in the ground state, prepared in a correlated Bell-type state, and interacting with the scalar field or the electromagnetic field nearby a perfectly reflecting plate. We suppose the two atoms move with the same uniform acceleration, parallel to the plane boundary, and that their separation is constant during the motion. By separating the contributions of radiation reaction field and vacuum fluctuations to the resonance energy shift of the two-atom system, we show that Unruh thermal fluctuations do not affect the resonance interaction, which is exclusively related to the radiation reaction field. However, non-thermal effects of acceleration in the radiation-reaction contribution, beyond the Unruh acceleration–temperature equivalence, affect the resonance interaction energy. By considering specific geometric configurations of the two-atom system relative to the plate, we show that the presence of the mirror significantly modifies the resonance interaction energy between the two accelerated atoms. In particular, we find that new and different features appear with respect to the case of atoms in the free-space, related to the presence of the boundary and to the peculiar structure of the quantum electromagnetic field vacuum in the locally inertial frame. Our results suggest the possibility to exploit the resonance interaction between accelerated atoms as a probe for detecting the elusive effects of atomic acceleration on radiative processes.