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arXiv:quant-ph/0205042 · Physical Review A

Dressed-state approach to quantum systems

G. Flores-Hidalgo, Adolfo P. C. Malbouisson

Published Oct 25, 2002• 21 citations
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Abstract

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.

DOI
10.1103/physreva.66.042118

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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 {\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 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 a particle in the harmonic approximation, having frequency ωˉ\barωωˉ, coupled to a scalar field inside a spherical reflecting cavity of diameter LLL. 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\barωωˉ of the order ωˉ∼4.00×1014/s\barω\sim 4.00\times 10^{14}/sωˉ∼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∼1.0×10−6mL\sim 1.0\times 10^{-6}mL∼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 λλλ. We obtain for a large cavity an explicit λλλ-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 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
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.