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Conference on Lasers and Electro-Optics

Population transfer between uncoupled atomic states through cavity modes

T. Kobayashi, Takashi Taneichi

Published Nov 27, 2002• 0 citations

Abstract

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.

DOI: 10.1109/iqec.1998.680255

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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.

The interaction between an ultracold cascade three-level atom and a two-mode cavity field has been studied. The effects of the centre-of-mass motion, the cavity length, the coupling constants, the initial field states and the initial field intensity on the atomic dynamics have been examined. We have found that the population probabilities show dependence on the interaction time in the fast-atom region while they show dependence on the interaction length in the slow-atom region. The variations of the probabilities versus the cavity length show resonant peaks, and the peaks become sharper as the atom moves more slowly. The coupling constants, the initial field states and the initial field intensity also influence the atomic dynamics significantly. The two transitions are competitive for the atomic probability in the middle state, while they are cooperative for that in the lower state.

The transferred energy between two (three) radiators localized in two (three) cavities in interaction through an evanescent field is investigated. In the good-cavity limit the exact solution of the Schrödinger equation for this system is obtained. An interesting problem appears when the located excitation in one atom from one distinguished cavity is transferred to a second atom from another cavity. We analyze analytically and numerically the dynamics of the transferred energy as a function of the coupling constant between the cavities. Another interesting problem is the trapping condition for two atoms flying through different coupled cavities. For subsystems consisting of two atomic levels, we know that, only a dynamic trapping condition can be found. In this paper, we show that due to the coupling of the cavities, the trapping condition for two atoms flying through different cavities becomes possible. This effect depends on the coupling constants between the cavities and the dipole interaction between the radiators and cavity modes. A similar problem is studied in the bad-cavity limit, when the lifetime of photons in the cavity is smaller than the decay time of excited atoms. In this case, we write the analytical solution of the master equation and show its entanglement. We obtain that entangled states arise from non-entangled initial states of the atoms. The exact description of such a system opens up new possibilities for the processing of quantum information with two optical cavities.

We study the dynamics of a ∨-type three-level atom in the cavity employing the dressed state of the system. We consider a ∨-type three-level atom initially in a different state that interacts with two mode photons in a closed cavity. The initial state of the atom and Rabi frequency have a significant effect on the population exchange between excited and ground levels. The numerical results show that the atom-field coupling strength determines the fast and slow periodic oscillation of the probability between the upper and ground states. The highest probability of finding it in the upper and ground states is determined by the initial state conditions of the atom. In general, the initial state conditions of the atom and the atom-field coupling strength have a significant effect on population transfer between the upper and ground states of a ∨-type three-level atom.

In this paper, the non-resonant interaction of two two-level atoms with two quantized cavity fields is studied by considering the dipole–dipole interaction between the two atoms. The correlation between the fields has been taken into account and the parametric down conversion is considered. Under certain initial conditions which is determined for the atoms and the fields, the analytical solution for the time-dependent Schrödinger equation is obtained. Employing this solution, we are able to discuss about some physical properties such as atomic population inversion and entanglement between various subsystems, i.e. “atoms–fields” and “atom–atom” by using respectively von Neumann entropy and negativity. It is deduced from the numerical results that, the mentioned quantities can be controlled by the atomic dipole–dipole interaction and detuning parameter, appropriately. The results show that the degree of entanglement between the two atoms is increased due to the presence of dipole–dipole coupling of the atoms at the beginning of atom–field interaction. Furthermore, it is found that, in the non-resonance condition, the so-called entanglement sudden death occurs in the presence of dipole–dipole interaction.

In quantum information processing, quantum cavities play an important role by providing the mechanisms to transfer information between atom qubits and photon qubits, or to couple single atoms with the optical modes of the cavity field. We explore numerically the population transfer in an atom + cavity system by using the

π

-pulse and adiabatic passage methods. While the first method is very efficient transferring the atomic population for no radiative decay of the intermediate level, the second method shows very interesting nonadiabatic, resonance-like properties that can be used to achieve very large transfer efficiencies without needing very large Rabi frequencies or very long interaction times. We introduce a simple analytical model to explore the origin of these properties and describe "qualitatively" the power-law dependence of the failure probability on the product of the pulse amplitude and the interaction time. We also examine numerically the transfer of interatomic coherence in a two-atom + cavity system by using adiabatic methods. For some specific symmetry conditions, we show that the dynamics of the original system can be studied as the individual evolution of a symmetric and an antisymmetric system, interacting separately with the classical field and the cavity mode, but mutually exchanging the atomic coherence.