We study the time evolution of superposition of product states of two dressed atoms in a spherical cavity in the extreme situations of an arbitrarily large cavity (free space) and of a small one. In the large-cavity case, the system dissipates, whereas, for the small finite cavity, the system evolves in an oscillating way and never completely decays. We also compute the von Neumann entropy for such a system, a measurement of the degree of entanglement of the two atoms, as the superposed state evolves in time. We find that this entropy does not depend on time, nor on the size of the cavity.
We study the time evolution of entangled states of a pair of identical atoms, considered in the harmonic approximation, coupled to an environment represented by an infinite set of free oscillators, with the whole system confined within a spherical cavity of radius
R. Taking the center-of-mass and the relative-position coordinates, and using the dressed-state approach, we present the time evolution of some quantities measuring the entanglement for both limits of a very large and a small cavity; the chosen examples are simple and illustrate these very distinct behaviors.
We consider a system modeled by a harmonic oscillator of frequency , coupled to the scalar potential inside a reflecting sphere of radius R. We use dressed states introduced originally in [1] and recently employed in [2] to present a non-perturbative unified description of the decay process of the system, in free space and in the case of the system being confined in a finite cavity. In the situation that we start from the initial condition that the system is in the first excited state, we give exact formulas to describe its time evolution for a cavity of arbitrary size. In the particular case of a very large cavity (free space), we recover the behaviour expected from perturbation theory in the limit of the small coupling constant. In the case of a very small cavity, our results are in good agreement with experimental observations
Using the formalism of renormalized coordinates and dressed states introduced in previous publications, we perform a nonperturbative study of the time evolution of a superposition of two states, the ground state and the first excited level of a harmonic oscillator, the system being confined in a perfectly reflecting cavity of radius R . For R → ∞ , we find dissipation with dominance of the interference terms of the density matrix, in both weak- and strong-coupling regimes. For small values of R all elements of the density matrix present an oscillatory behavior as time goes on and the system is not dissipative. In both cases, we obtain improved theoretical results with respect to those coming from perturbation theory.
An atom, coupled linearly to an environment, is considered in a harmonic approximation in thermal equilibrium inside a cavity. The environment is modeled by an infinite set of harmonic oscillators. We employ the notion of dressed states to investigate the time evolution of the atom initially in the first excited level. In a very large cavity (free space) for a long elapsed time, the atom decays and the value of its occupation number is the physically expected one at a given temperature. For a small cavity the excited atom never completely decays and the stability rate depends on temperature.
We consider a complete study of the influence of the cavity size on the spontaneous decay of an atom excited state, roughly approximated by a harmonic oscillator. We confine the oscillator-field system in a spherical cavity of radius
R, perfectly reflective, and work in the formalism of dressed coordinates and states, which allows to perform non-perturbative calculations for the probability of the atom to decay spontaneously from the first excited state to the ground state. In free space,
R→∞, we obtain known exact results an for sufficiently small
R we have developed a power expansion calculation in this parameter. Furthermore, for arbitrary cavity size radius, we developed numerical computations and showed complete agreement with the exact one for
R→∞ and the power expansion results for small cavities, in this way showing the robustness of our results. We have found that in general the spontaneous decay of an excited state of the atom increases with the cavity size radius and vice versa. For sufficiently small cavities the atom practically does not suffers spontaneous decay, whereas for large cavities the spontaneous decay approaches the free-space
R→∞ value. On the other hand, for some particular values of the cavity radius, in which the cavity is in resonance with the natural frequency of the atom, the spontaneous decay transition probability is increased compared to the free-space case. Finally, we showed how the probability spontaneous decay go from an oscillatory time behaviour, for finite cavity radius, to an almost exponential decay, for free space.