Physics
Scientific paper
Aug 1992
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1992phrvd..46.1239g&link_type=abstract
Physical Review D (Particles, Fields, Gravitation, and Cosmology), Volume 46, Issue 4, 15 August 1992, pp.1239-1262
Physics
10
Scientific paper
What is the rate of information transfer from a gravitational wave (GW) transmitter to a receiver\? To this end we consider how electromagnetic modes in a cylindrical cavity respond to circularly polarized gravitational radiation. It is found that a GW changes the refractive index inside the cavity. In fact, the cavity interior becomes birefringent for electromagnetic modes circulating in opposite directions. A linearly polarized cavity mode is thus subjected to Faraday rotation by the GW. In addition, for a cavity mode circulating in the same sense as the GW, the refractive index becomes complex: the cavity interior exhibits antidamping, but only over a finite interval of the applied GW frequency. Inside this interval the cavity mode becomes unstable and its frequency locks onto one-half the GW frequency (``parametric excitation''). Outside this interval the cavity mode breaks the lock-in synchronization with the GW. Instead, the mode evolves in a stable fashion and, like a counterrotating mode, only suffers a frequency pulling away from its unperturbed value. The quantum-mechanical response of the cavity oscillator is expressed as a spinning top precessing around a fictitious magnetic field in a fictitious three-dimensional Lorentz space. In the absence of any impinging GW this magnetic field is timelike and straight up. In the presence of a GW this magnetic field gets changed. The vectorial change is directly related to the frequency and the maximum amplitude of the GW. The resultant magnetic field is tilted and timelike for stable evolution, but spacelike for unstable evolution. The set of observables of a simple harmonic oscillator (SHO) is decomposed into mutually exclusive and jointly exhaustive sets of spin-j objects. They make up the finite representations of the symmetry group of the three-dimensional Lorentz space arena for the cavity oscillator influenced by a GW. Squeezed quantum states of a SHO are shown to be due to pseudorotations, i.e., elements of the symmetry group SU(1,1) which is the covering group of SO(2,1).
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