Accelerated Detector Response Function in Squeezed Vacuum

Abstract

Casimir/squeezed vacuum breaks Lorentz symmetry, by allowing light to propagate faster than c. We looked at the possible transformation symmetry group such vacuum could obey. By solving the semi-classical Einstein field equation in squeezed vacuum, we have found that the background geometry describes an Anti-deSitter (AdS) geometry. Therefore, the proper transformation symmetry group is the (A)dS group. One can describe quantum field theory in a finite volume as a quantum field theory (QFT) on AdS background, or vice versa. In particular, one might think of QFT vacuum on AdS as a QFT that posses a squeezed vacuum with boundary conditions proportional to R 2 AdS . Applying this correspondence to an accelerating detector-scalar field system, we notice at low acceleration the system is at equilibrium at ground state, however if the detector's acceleration (a) is greater than a critical acceleration, the system experience a phase transition similar to Hawking-Page Phase transition at the detector gets excited, with equivalent temperature Θ = a 2 −R 2 AdS 2π.