Addendum to “Behavior of a bipartite system in a cavity”

Abstract

This note is an Addendum to our previous article [Phys. Rev. A 81, 053820 (2010)]. We show that under the assumption of a Bose-Einstein distribution for the thermal reservoir, zero-temperature properties of the entangled states considered there are not changed by heating, for temperatures up to the order of room temperatures. In this case, the system is dissipative in free space and presents stability for a small cavity, both for T = 0 and for finite temperature.In this note we consider how heating could affect the properties of the bipartite system studied in [1]. This bipartite system consists of two dressed atoms inside a reflecting cavity that do not interact with each other, only with an environmental field. Our approach to this problem makes use of the notion of dressed thermal states [2], in the context of a model already employed in the literature, of atoms-or, more generally, material particles-in the harmonic approximation, coupled to an environment modeled by an infinite set of pointlike harmonic oscillators (the field modes). The dressed thermal state approach is an extension of the dressed (zerotemperature) formalism that was introduced earlier. The reader is referred to [1] and [2] for details of our formalism.Here we consider entanglement as a pure quantum effect, a characteristic of quantum mechanics, which is also nonlocal, in the sense that distant and noninteracting systems may be entangled. This is due to the physical meaning attributed to superposed states, a concept with no correspondence in classical physics, and not to the interaction between the (in our case, dressed) atoms. Indeed, such properties of entanglement of noninteracting systems have been used in the realm of teleportation and quantum information theory and to conceive quantum communication devices. We think that investigation the measure to which the properties of such systems are affected by heating is important, particularly in the case of room temperatures. The possibility of constructing such devices at temperatures of everyday life would be an interesting matter.In this note we remain on theoretical grounds and perform a study of thermal effects on our bipartite system, assuming that the dressing fields of the atoms obey a Bose-Einstein distribution and that the first-level excited dressed atomic states evolve in the same way as in [1]. Under these assumptions, it results that the reduced density matrix does not depend on temperature. In contrast, employing methods and relying on results obtained in [2] and [3], one finds that the individual dressed atoms in the bipartite system are very little affected by heating for temperatures of about 300 K. The overall conclusion is that the methods and results from [1] are valid if we consider the system at room temperatures. * adolfo@cbpf.br Our bipartite system is composed of two subsystems, A and B; the subsystems consist of dressed atoms A and B, respectively, and the whole system is contained in a perfectly reflecting sphere of radius R in thermal equilibrium with an environme...

Spontaneous Decay of a Dressed Harmonic Oscillator Inside a Spherical Cavity

“…[19] as a method to account, in a nonperturbative way, for the oscillator radiation process in free space. In subsequent works, the concept was used to study the spontaneous emission of atoms inside small cavities [20], the quantum Brownian motion [21,22], the thermalization process [23][24][25], the time evolution of bipartite systems [26][27][28], the entanglement of biatomic systems [29][30][31], and other related issues [32][33][34][35][36]. For a clear explanation, see reference [33].…”