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.
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.
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
We consider a system consisting of a particle in the harmonic approximation, having frequency ωˉ, coupled to a scalar field inside a spherical reflecting cavity of diameter L. By introducing {\it dressed} coordinates we define {\it dressed} states which allow a non-perturbative unified description of the radiation process, for weak and strong coupling regimes. We perform a study of the energy distribution in a small cavity, with the initial condition that the particle is in the first excited state. In the {\it weak} coupling regime, we conclude for the quasi-stability of the excited particle. For instance, for a frequency ωˉ of the order ωˉ∼4.00×1014/s (in the visible red), starting from the initial condition that the particle is in the first excited level, we find that for a cavity with diameter L∼1.0×10−6m, the probability that the particle be at any time still in the first excited level, will be of the order of 97%. For appropriate cavity dimensions, which are of the same order of those ensuring stability for weak coupling, we ensure for strong coupling the complete decay of the particle to the ground state in a small ellapsed time. Also we consider briefly the effects of a quartic interaction up to first order in the interaction parameter λ. We obtain for a large cavity an explicit λ-dependent expression for the particle radiation process. This formula is obtained in terms of the corresponding exact expression for the linear case and we conclude for the enhancement of the particle decay induced by the quartic interaction.
Using the non-perturbative method of dressed states introduced in previous publications, we study effects of the electromagnetic field on an atom, in the case the field is described by an ensemble of non interacting harmonic oscillators.This method allows to separate the whole system into the dressed atom and the dressed field, in terms of which a non-perturbative approach is possible.When applied to study atomic behaviours in cavities, the method accounts for experimentally observed inhibition of atomic decay in small cavities.
We consider a system consisting of an atom in the approximation of a harmonic oscillator of frequency $\overline{\ensuremath{\omega}},$ coupled to the scalar potential inside a spherical reflecting cavity of radius R. We use dressed states introduced in a previous publication [Andion, Malbouisson, and Mattos Neto, J. Phys. A 34, 3735 (2001)], which allow a nonperturbative unified description of the atom radiation process, in both cases, of a finite or an arbitrarily large cavity. We perform a study of the energy distribution in a small cavity, with the initial condition that the atom is in the first excited state and we conclude for the quasi-stability of the excited atom. For instance, for a frequency $\overline{\ensuremath{\omega}}$ of the order $\overline{\ensuremath{\omega}}\ensuremath{\sim}4.00\ifmmode\times\else\texttimes\fi{}{10}^{14}/\mathrm{s}$ (in the visible red), starting from the initial condition that the atom is in the first excited level, we find that for a cavity with diameter $2R\ensuremath{\sim}1.0\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6} \mathrm{m},$ the probability of the atom being at any time still in the first excited level, will be of the order of 97%. For a typical microwave frequency $\overline{\ensuremath{\omega}}\ensuremath{\sim}2.00\ifmmode\times\else\texttimes\fi{}{10}^{10}/\mathrm{s}$ we find stability in the first excited state also of the order of 97% for a cavity radius $R\ensuremath{\sim}1.4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2} \mathrm{m}.$
Using the nonperturbative method of dressed states introduced in a previous publication [N. P. Andion, A. P. C. Malbouisson, and A. Mattos Neto, J. Phys. A 34, 3735 (2001)], we study effects of the environment on a quantum-mechanical system, in the case in which the environment is modeled by an ensemble of noninteracting harmonic oscillators. This method makes it possible to separate the whole system into the dressed mechanical system and the dressed environment, in terms of which a nonperturbative approach is possible. When applied to the Brownian motion, we give explicit nonperturbative formulas for the classical path of the particle in the weak and strong coupling regimes. When applied to studying atomic behaviors in cavities, the method accounts for experimentally observed inhibition of atomic decay in small cavities.
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.