Theory of quantum radiation observed as sonoluminescence

Abstract

Sonoluminescence is explained in terms of quantum radiation by moving interfaces between media of different polarizability. In a stationary dielectric the zero-point fluctuations of the electromagnetic field excite virtual two-photon states, which become real under perturbation due to motion of the dielectric. The sonoluminescent bubble is modeled as an optically empty cavity in a homogeneous dielectric. The problem of the photon emission by a cavity of time-dependent radius is handled in a Hamiltonian formalism, which is dealt with perturbatively up to first order in the velocity of the bubble surface over the speed of light. A parameter dependence of the zeroth-order Hamiltonian in addition to the first-order perturbation calls for a novel perturbative method combining standard perturbation theory with an adiabatic approximation. In this way the transition amplitude from the vacuum into a two-photon state is obtained, and expressions for the single-photon spectrum and the total energy radiated during one flash are given both in full and in the short-wavelength approximation when the bubble is larger than the wavelengths of the emitted light. A model profile is assumed for the time dependence of the bubble during the collapse, and in this model the radiated energy and the spectrum are calculated numerically and in the short-wavelength limit also analytically. It is shown analytically that the spectral density has the same frequency dependence as blackbody radiation; this is purely an effect of correlated quantum fluctuations at zero temperature. The present theory clarifies a number of hitherto unsolved problems and suggests explanations for several more. Possible experiments that discriminate this from other theories of sonoluminescence are proposed. © 1996 The American Physical Society.