Stability of excited atoms in small cavities

Abstract

We consider a system consisting of an atom in the approximation of a harmonic oscillator of frequency $\bar{\omega}$, coupled to the scalar potential inside a spherical reflecting cavity of radius R. We use {\it dressed} states introduced in a previous publication [Andion, Malbouisson and Matos Neto, J. Phys. A34, 3735 (2001)], which allow a non-perturbative 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 $\bar{\omega}$ of the order $\bar{\omega}\sim 4.00\times 10^{14}/s$ (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 $2R\sim 1.0\times 10^{-6}m$, the probability that the atom be at any time still in the first excited level, will be of the order of 97%. For a typical microwave frequency $\bar{\omega}\sim 2,00\times 10^{10}/s$ we find stability in the first excited state also of the order of 97% for a cavity radius $R\sim 1.4\times 10^{-2}m$.Comment: 7 pages, no figures, RevTe

Dressed-state approach to quantum systems

“…We are able to give formulas for the probability of an atom to remain excited for an infinitely long time, provided it is placed in a cavity of appropriate size. For an emission frequency in the visible red, the size of such cavity is in good agreement with experimental observations ( [10], [11]). The generalization of the work presented in this paper to the case of a generic (supraohmic or subohmic) environment and finite temperature is in progress and will be presented elsewhere.…”

“…(4.9) we obtain after some straightforward calculations, From Refs. [9][10][11] we recognize the function f 00 (t) as the probability amplitude that at time t the dressed particle still be excited, if it was initially (at t = 0) in the first excited level. We see that underlying to our dressed states formalism there is an unified way to study two physically different situations, the radiation process and the Brownian motion.…”

“…In recent publications [9][10][11] a method (dressed coordinates and dressed states) has been introduced that allows a non-perturbative approach to situations of the type described above, provided they can be approximated by a linear coupling. More precisely, the method applies for all systems that can be described by an Hamiltonian of the form,…”

“…When applied to the Brownian motion, we give explicit non-perturbative formulas for the classical path of the particle in the weak and strong coupling regimes. When applied to study atomic behaviours in cavities, the method accounts very precisely for experimentally observed inhibition of atomic decay in small cavities [10,11]. …”

Time evolution of a superposition of dressed oscillator states in a cavity

“…(22), in this case. However, if the cavity is sufficiently small, the frequencies Ω r can be determined as follows [8]. In terms of the small dimensionless parameter…”