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Physical Review A

Moving mirrors and time-varying dielectrics

Harry Johnston, Sarben Sarkar

Published May 1, 1995• 37 citations
Publisher

Abstract

The spectral distribution of light generated by a finite cavity with one moving mirror is compared with that produced by a fixed cavity containing a time-varying dielectric. In both cases a motion over a finite time interval is considered. Although the moving mirror is usually considered to be an idealization for the time-varying dielectric, there are qualitative differences in the spectra produced. The spectral distribution for the moving mirror case behaves as 1/${\mathit{n}}^{3}$, while that for the time-varying dielectric behaves on average as 1/${\mathit{n}}^{4}$ but is rapidly oscillating.

DOI
10.1103/physreva.51.4109

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The spectral distribution of light generated by a finite cavity with one moving mirror is compared with that produced by a fixed cavity containing a time-varying dielectric. In both cases a motion over a finite time interval is considered. Although the moving mirror is usually considered to be an idealization for the time-varying dielectric, there are qualitative differences in the spectra produced. The spectral distribution for the moving mirror case behaves as 1/n3{\mathit{n}}^{3}n3, while that for the time-varying dielectric behaves on average as 1/n4{\mathit{n}}^{4}n4 but is rapidly oscillating.
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.
An accelerated mirror generates photons from vacuum. This process is known as Unruh radiation.1 A uniform distribution of dielectric sheets spaced much less than a wavelength apart produces a net change in the effective index. When the sheets are displaced in a spatially periodic manner, a grating is formed. Motion of the sheets results in a time dependent (parametrically varying) grating that can produce squeezing. In this configuration, the squeezing is ascribed to Unruh radiation. A field analysis of moving dielectric sheets in the background of the zero-point fluctuation field is presented in this paper and shown to correspond to the Unruh formula. Recently, Yablonovitch proposed to use laser-generated exploding plasmas to simulate an accelerating mirror surface.2 We propose another simulation of accelerating mirrors with laser light that could lead to a laboratory experiment. If a grating is produced in a nonlinear fiber ring resonator, with one port of the 50/50 beam splitter fed by the pump, the other used as the signal port, the Unruh radiation emerges from the signal port and the pump is separated out automatically.