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Evolvement of the Atomic Translational Motion Wave Functions and Internal State Population in High Q-cavity

Tang Jing

Published Jan 1, 2004• 0 citations
OpenAlex

Abstract

On the basis of resonance interaction between the atcm and the cavity field and with aid of the atomic - field dressed state,the influence between the atomic internal state population and cuantized translational motion in a quantized standing - wave cavity was discussed.Specially,when the atom was at the superpositions of two internal state equal weight same phase, the translational motion wave function presented the very stable characteristics.

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On the basis of resonance interaction between the atcm and the cavity field and with aid of the atomic - field dressed state,the influence between the atomic internal state population and cuantized translational motion in a quantized standing - wave cavity was discussed.Specially,when the atom was at the superpositions of two internal state equal weight same phase, the translational motion wave function presented the very stable characteristics.
The influence of the atomic internal state population on its translational motion in a quantized standing-wave cavity field with spatial periodic structure is investigated for the intensity-dependent coupling case.On the basis of resonance interaction between the atom and the cavity field and with the aid of the atomic-field dressed state,the Schrodinger equations satisfied by the atomic translational motion for the two different atomic dressed internal states are built and their general relation for a spatial periodic cavity field is obtained.And under an appropriate approximation,the state vector of the whole system is derived and allows us to study the interaction between the atomic internal state and its translational dynamics.It is found that the scalar product of the translational motion wave functions in Hilbert space determines the atomic internal state population,as well as,the distortion of the atomic translational motion wave-packet is sensitivity to its initial internal state population for a quantized standing-wave cavity field at coherent state.
We present an in-depth study on the behavior of an atomic wave packet which is placed in a standing wave cavity prepared in various states of light. We extract a simple classical oscillator model out of the dynamics of the quantum system. We quantitatively resolve the states of the spatially reorganized wave packet by the dressed state spatial probability distribution functions we developed. We also report a novel type of the “quantum collapse and revival” behavior of the Rabi nutation which is originated from the effect of the quantized atomic center-of-mass motion on the atomic internal motion.
We analyze some aspects of the internal and translational dynamics of a two-level atom interacting with a resonant standing wave of an ideal cavity. We show that the cavity vacuum field can split the incoming wave packet of the excited two-level atom into two parts, whose scalar product in the Hilbert space determines the behavior of the Rabi oscillations. The state of the whole system is derived and allows us to study the correlations between the internal and the translational atomic dynamics. We find that these correlations become negligible when the two parts are sufficiently away from each other in the space.
We use a basis of Bloch wave functions to solve the problem of spontaneous emission from an atom inside a standing-wave cavity. In this way we incorporate the effects of the atom’s quantized center-mass-motion in the periodic light-force potential of the one-quantum dressed states during the spontaneous emission process. We calculate emission spectra and the momentum distribution of the atom. Under strong-coupling conditions, “vacuum” Rabi spectra become asymmetric, with an increased relative weight given to the red side of the spectrum because of the transfer of energy to the center-of-mass motion of the atom. Because of the nonperturbative interaction between the atom and the cavity mode, many momentum quanta are transferred to the atom from the cavity mirrors during the irreversible emission of just one photon. Thus, the atom is diffracted by its own radiation reaction field. We analyze these effects using the Bloch-state basis. Use of the secular approximation provides a simple rate equation description of transitions from the Bloch states excited in the initial state to the atom-cavity ground state. We compare this approach with other ways of doing the calculations and discuss the accuracy of the secular approximation. We consider the extension of these calculations to treat the effects of photon statistics on the momentum distribution of atoms traversing a standing-wave cavity.