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Physical Review A

Dynamics of the quantized radiation field in a cavity vibrating at the fundamental frequency

Ying Wu, M.-C. Chu, P. T. Leung

Published Apr 1, 1999• 41 citations
Publisher

Abstract

We present a method to solve exactly a one-dimensional model of quantized radiations in a cavity oscillating in the fundamental resonance, using the effective Hamiltonian derived by C. K. Law [Phys. Rev. A 49, 433 (1994)]. With this method, we derived explicit analytical expressions for the diagonalized Hamiltonian, the time-varying annihilation, creation, and photon number operators for the radiation field, which completely specify the dynamics of the system.

DOI
10.1103/physreva.59.3032

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We present a method to solve exactly a one-dimensional model of quantized radiations in a cavity oscillating in the fundamental resonance, using the effective Hamiltonian derived by C. K. Law [Phys. Rev. A 49, 433 (1994)]. With this method, we derived explicit analytical expressions for the diagonalized Hamiltonian, the time-varying annihilation, creation, and photon number operators for the radiation field, which completely specify the dynamics of the system.
We investigate the dynamics of the quantized radiation field in an oscillating cavity described by the effective resonance Hamiltonians + where characterizes the oscillating amplitude of the moving boundary of the cavity, the boundary oscillates with the j th unperturbed eigenfrequency ( j = 1,2,3, ... ) and the parametric oscillator part H ( p ) contains only a few terms to be specified in the main text. We present the exact diagonalization forms of the effective Hamiltonians for j = 1,2,3, ... in the absence of the parametric oscillator part H ( p ) . A systematic procedure is then developed to obtain the analytical solutions of the Hamiltonians in the presence of the part H ( p ) accurate up to order k for an arbitrary positive integer k . In this way, we can investigate the dynamics of the corresponding quantized radiative field by explicitly presenting the analytical expressions of the diagonalized Hamiltonians, the time-varying annihilation and creation operators as well as photon number operators for the radiative field, accurate up to any desired order of the dimensionless oscillating amplitude. The analytical expressions of these quantities up to order 4 are also explicitly presented.
We study the quantized field in a one-dimensional electromagnetic resonant cavity. The cavity contains a linear and lossless dielectric medium with frequency-independent polarizability. The dielectric permittivity is an externally prescribed function of both the space and the time. We also allow one of the cavity's mirrors to move in a given trajectory. Unlike other previous studies on the same system, we formulate an effective Hamiltonian so that the dynamics of the cavity field can be described in the Schr\"odinger picture. The effective Hamiltonian is quadratic in structure, therefore two-photon generation from the vacuum state can occur. We also discuss the case of resonant behavior of the system.
We describe the dynamics of an exactly solvable Raman coupled model interacting with two modes of a quantized cavity electromagnetic field. The model consists of a three-level atom in the \ensuremath{\Lambda} configuration whose excited state is considered to be far off resonance and is adiabatically eliminated. The effective Hamiltonian for this system contains products of the transition operators between the two ground-state levels and a field annihilation operator from one mode and a creation operator from the other. This Hamiltonian provides an example of a zero-photon process. We study the atomic inversion and investigate the production of nonclassical effects such as antibunched light, violations of the Cauchy-Schwartz inequality, and squeezing.
The quantum theory of a one-dimensional optical cavity is developed with emphasis on the presence of output coupling. First the resonant mode is defined and calculated classically. Then the field is decomposed into a sequence of modes by introducing an imaginary boundary at a large distance. The mode functions are proved to be orthogonal with respect to an integration with the dielectric constant as a weighting factor. The Hamiltonian of the field is shown to be equivalent to that of a collection of independent harmonic oscillators, the mass of which is a function of the frequency of oscillation. This equivalent of mass appears on normalizing the mode functions and proves to carry information on the structure of the cavity. Quantization of the field is carried out, and the commutation relation for the electric fields inside and outside the cavity is derived. The commutator is composed of an infinite set of derivatives of $\ensuremath{\delta}$ functions, which discloses the effect of the presence of output coupling and that of the small size of the cavity on the radiation field. Also, the commutator is shown to have some properties common with the classical resonant mode, i.e., the property of exponential decay and its rate.
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.