Detecting gravitational waves via coherence degradation induced by the Unruh effect

Abstract

We investigate the effects of a gravitational wave background on the coherence degradation induced by the Unruh effect of a uniformly accelerated single-qubit and quantum interferometric circuit. In both systems, we use the formalism of the evolution of the density matrix of the detector-field system, where after the interaction the field degrees of freedom are traced out to obtain the reduced density matrix of the detector. In this background, we calculate the quantum coherence and interferometric visibility in the long-wavelength regime and large interaction time. Our results indicate that the gravitational wave transfers energy to the internal states of the detector, causing, together with the Unruh effect, changes in them, amplifying the coherence degradation of the system. This amplification occurs when the polarization modes of the gravitational wave are in resonance and have modulated amplitudes. For the case of a short-wavelength, the detector does not respond to the gravitational wave because its oscillation is so fast that the detector does not have time to respond within the system timescale. Therefore, it is possible to detect the signature of gravitational waves in the coherence degradation induced by the Unruh effect within the regimes studied here.