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Journal of the Physical Society of Japan

Population Inversion between Uncoupled Atomic States through Cavity Modes

Takashi Taneichi, Takayoshi Kobayashi

Published May 15, 1998• 6 citations
Publisher

Abstract

A theory for the position-dependent dynamics of an atom confined in a cavity with a movable-boundary mirror is developed. The mirror motion induces substantial transition between two optically uncoupled atomic states.
DOI
10.1143/jpsj.67.1594

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Summary form only given.C.K Law et al. (1995) directed attention to the interaction between a field inside a cavity with a movable boundary and an atom inside the cavity and calculated the effect of the oscillatory motion of a boundary on the spontaneous spectrum in the adiabatic regime. In the present paper we show that fascinating features of such an interaction appear even in the case where the adiabatic approximation is satisfied. The dynamics of a three-state atom interacting with a cavity field is considered. Two states out of the three do not couple with each other directly but via the cavity modes, whose eigenfrequencies determined by the cavity length change with time. It is shown that the transition in the cavity can be enhanced through the indirect coupling. In the present analysis, the formulation based on the mode expansion of the cavity field is used. Since the mode functions contain a cavity length explicitly, the moving-boundary condition is taken into account in the population dynamics. This formulation also allows us to calculate the position-dependent behavior of the system. Here the discussion is restricted to the case where the atom exists at the center of the cavity. Initially the atom is assumed to be prepared in its first excited state. Coupling between the two states is enhanced under some conditions and it results in a population inversion between the two excited states. Furthermore, an interaction between two two-state atoms located in a cavity is studied and the dependence of the energy shift and interatomic energy transfer on the cavity length are analyzed. We found a resonance effect in the cavity length-dependent transition dipole.
We consider the dynamics of a movable mirror (cantilever) of a cavity coupled through radiation pressure to the light scattered from ultracold atoms in an optical lattice. Scattering from different atomic quantum states creates different quantum states of the scattered light, which can be distinguished by measurements of the displacement spectrum of the cantilever. We show that for large pump intensities the steady-state displacement of the cantilever shows bistable behavior. Due to atomic back action, the displacement spectrum of the cantilever is modified and depends on the position of the condensate in the Brillouin zone. We further analyze the occurrence of splitting of the normal mode into three modes due to mixing of the mechanical motion with the fluctuations of the cavity field and the fluctuations of the condensate with finite atomic two-body interaction.
Abstract We consider a two-level atom interacting with a quantized field in an optomechanical cavity and study the population inversion of the atom in this hybrid optomechanical system. Analytical solutions of the excited state population in the hybrid system are derived for various initial states of the cavity field and the mechanical mirror in the limit of weak single-photon coupling regime. Due to the mechanical mirror, the population inversion exhibits anomalous behavior, compared to the results predicted by the Jaynes–Cummings (JC) model. For an initial Fock state cavity field, we show that the atomic population inversion can undergo collapses and revivals induced by the mechanical mirror which is in a Fock state for the resonant atom-field interaction. When the cavity field is far-detuned from the atomic transition, the atom can couple to the mechanical mirror effectively via the JC interaction. In this case, the atomic population inversion can display either full Rabi oscillations or the collapse and revival behavior induced by a Fock state or a coherent state of the mechanical mirror, respectively. We also explore an experimentally more relevant situation when the mechanical mirror is initially in a mixed state. We derive an analytical expression of the excited state population via the unitary evolution for the density operator of the whole system. We find that the population inversion in this case exhibits slower collapse and smaller revival amplitude due to the initial mixture of the mechanical state. For an initial coherent state cavity field, we show that the predicted collapse regime in the original JC model can display nonzero oscillating values. Our analytical predications are further confirmed with numerical calculations in which the dissipation mechanism from the system is included.