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arXiv:quant-ph/0209117

Storage of energy in confined quantum systems

Adolfo P. C. Malbouisson

Published Sep 22, 2002• 0 citations
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Abstract

Using the non-perturbative method of {\it dressed} states introduced in previous publications [N.P.Andion, A.P.C. Malbouisson and A. Mattos Neto, J.Phys.{\bf A34}, 3735, (2001); G. Flores-Hidalgo, A.P.C. Malbouisson, Y.W. Milla, Phys. Rev. A, {\bf 65}, 063314 (2002)], we study the evolution of a confined quantum mechanical system embedded in a {\it ohmic} environment. Our approach furnishes a theoretical mechanism to control inhibition of the decay of excited quantum systems in cavities, in both weak and strong coupling regimes.

DOI
10.48550/arxiv.quant-ph/0209117

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Using the non-perturbative method of {\it dressed} states introduced in previous publications [N.P.Andion, A.P.C. Malbouisson and A. Mattos Neto, J.Phys.{\bf A34}, 3735, (2001); G. Flores-Hidalgo, A.P.C. Malbouisson, Y.W. Milla, Phys. Rev. A, {\bf 65}, 063314 (2002)], we study the evolution of a confined quantum mechanical system embedded in a {\it ohmic} environment. Our approach furnishes a theoretical mechanism to control inhibition of the decay of excited quantum systems in cavities, in both weak and strong coupling regimes.
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.
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 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.