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Physical Review A

Evolution of wave fields and atom-field interactions in a cavity with one oscillating mirror

Maciej Janowicz

Published Jun 1, 1998• 38 citations
Publisher

Abstract

In this paper the dynamics of wave fields in a cavity with one sinusoidally moving mirror are investigated. The wave equation is solved approximately using the method of multiple time scales. Frequency shifts as well as amplitude and phase modulations of cavity modes are given. In all cases when it is possible, an approximate effective field Hamiltonian operator is derived. In the adiabatic case it is then used to analyze the interaction of radiation with a two-level atom passing through the cavity. Corrections to the Rabi oscillations due to the time-dependent frequency of the cavity photons are investigated. It is shown that adiabatic motion of a mirror can lead to suppression of the Rabi oscillations of atomic inversion.

DOI
10.1103/physreva.57.4784

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Physica Scripta•Feb 1, 2012•3 citations
In this paper the dynamics of wave fields in a cavity with one sinusoidally moving mirror are investigated. The wave equation is solved approximately using the method of multiple time scales. Frequency shifts as well as amplitude and phase modulations of cavity modes are given. In all cases when it is possible, an approximate effective field Hamiltonian operator is derived. In the adiabatic case it is then used to analyze the interaction of radiation with a two-level atom passing through the cavity. Corrections to the Rabi oscillations due to the time-dependent frequency of the cavity photons are investigated. It is shown that adiabatic motion of a mirror can lead to suppression of the Rabi oscillations of atomic inversion.
In this paper the dynamics of wave fields in a cavity, part of which is filled with a dielectric, are investigated. The wave equation is solved approximately using the method of multiple time scales. Phase modulations of the cavity modes in an adiabatic case are given up to the first order. A simple effective field Hamiltonian operator is derived and then used to analyze the interaction of radiation with a two-level atom passing through the cavity. Corrections to the Rabi oscillations due to the time-dependent frequency of the cavity photons are investigated. It is shown that adiabatic time dependence of the refractive index of the dielectric can lead to suppression of the Rabi oscillations of atomic inversion.
It has great meaning to study the effect of a moving mirror in a cavity on the dynamic behavior of a two-level atom injected in the cavity. In this paper, for a system composed of a two-level injected atom and a single-mode field and a moving mirror in the cavity (the moving mirror to be regarded as a quantum harmonic oscillator with frequency ωm), the time-evolution of its state is obtained by means of complete quantum theory in the interaction picture. The time-evolution of the atomic population is derived on the basis of former investigations. It is found that the atomic population oscillates near its initial value. The result shows that the periodic motion of the mirror has a periodic effect on the atomic population.
The interaction of a two-level atom uniformly moving along a classical trajectory with a high-Q cavity quantum mode is analyzed. The dressed-state method is used to derive a recurrence formula for the transition probability of the atom with photon emission; the temporal dynamics of this probability qualitatively depends on the Doppler shift of the atomic transition frequency, on the Rabi frequency of the atom-field system, and on the detuning of the atomic transition frequency from the field mode frequency. The emission dynamics of a moving atom is very sensitive to the detuning. Rabi-type oscillations with a frequency equal to the Doppler shift can arise under certain conditions. At resonance, the emission probability of a moving atom can considerably exceed the emission probability of an atom at rest. A plane-parallel-mirror cavity and a confocal spherical-mirror cavity are considered. It is shown that the peculiarities of Doppler-Rabi oscillations must be taken into account in micromaser theory.
The propagation of light in a one-dimensional cavity bounded by moving mirrors is studied in the context of the theory of gas lasers. A canonical quantization of the free field is carried out by utilizing the symplectic structure of the space of solutions of the wave equation. It is shown that no Hamiltonian and no Schrodinger picture exists and that the photon number operator is in general not conserved. Changes in the number operator are, however, ordinarily too small to be observed experimentally. Automorphic coordinate transformations are used to develop adiabatic expansions for the mode functions of cavities with one fixed and one moving mirror. The coupling of the field to two-level atoms is done both quantum-mechanically and semi-classically. For the interacting quantum field an interaction Hamiltonian does exist, even though there is no total Hamiltonian. The semi-classical equations treat the atomic density matrix as a distribution in phase space. They possess traveling wave solutions which are expected to be important in understanding the behavior of mode-locked lasers. (Author)
The dynamics of interaction of an electromagnetic field with a two-level atom uniformly moving in an open resonator is analysed. The probability of the radiative transition of an excited atom to a lower state is studied as a function of the slope of its trajectory relative to the resonator axis and of the detuning of the atomic transition frequency from the resonator mode frequency. The study was performed in the case of strong coupling by the method of dressed states. The complicated dependences of the transition probability on the detuning and the slope of the atomic trajectory are analysed for small angles (~1°) for typical experimental conditions. It is shown that under certain conditions, a field can be efficiently excited in the resonator by atoms whose transition frequency considerably differs from the field-mode frequency when the detuning is not close to the Doppler shift.
An exact analytical approach to study the time evolution of the interaction between a system of N two-level atoms with a single-mode cavity field is proposed. Supposing that at the initial moment the system of radiators is prepared in a superposition of states, the wave functions of the atom–field interaction for three and four atoms are presented exactly. In the case of an odd number of atoms in the cavity, the quantum Rabi frequencies have non-zero values; otherwise one zero value of the quantum Rabi frequency is characteristic of the even number of atoms. It was shown that with an increase of the odd number of atoms the non-zero quantum Rabi frequencies in the system increase too. It was established that a single atom has one quantum Rabi frequency, three atoms have two frequencies and five atoms have three. For the even number of atoms, a zero value of eigenstates of radiators in the interaction with a single cavity mode is observed. In this case the number of collective levels in the system is odd and the trapping states of atoms in the cavity are possible. From analytical solutions it follows that it is possible to realize the micro-maser regimes for three atoms choosing the flying time for which the radiators pass totally in the ground state. The dependence of the flying time on the number of atoms is established as well as the cavity state for which the atomic ensemble comes back to its initial state. The behavior of quantum fluctuations of photon numbers and atomic inversion during collective absorption and radiation is exactly analytically and numerically studied. The exact quantum solutions for these qubits, formed from two-level atoms, can be used in quantum processing of information encapsuled in the initial states of the atomic ensemble and the cavity field.