Environment-induced uncertainties on moving mirrors in quantum critical theories via holography

Environment effects on a $n$-dimensional mirror from the strongly coupled d-dimensional quantum critical fields with a dynamic exponent $z$ in weakly squeezed states are studied by the holographic approach. The dual description is a $n+1$-dimensional probe brane moving in the $d+1$-dimensional asymptotic Lifshitz geometry with gravitational wave perturbations. Using the holographic influence functional method, we find that the large coupling constant of the fields reduces the position uncertainty of the mirror, but enhances the momentum uncertainty. As such, the product of the position and momentum uncertainties is independent of the coupling constant. The proper choices of the phase of the squeezing parameter might reduce the uncertainties, nevertheless large values of its amplitude always lead to the larger uncertainties due to the fact that more quanta are excited as compared with the corresponding normal vacuum and thermal states. In the squeezed vacuum state, the position and momentum of the mirror gain maximum uncertainties from the field at the dynamic exponent $z=n+2$ when the same squeezed mode is considered. As for the squeezed thermal state, the contributions of thermal fluctuations to the uncertainties decrease as the temperature increases in the case $1 n+2$ the contributions increase as the temperature increases. These results are in sharp contrast with those in the environments of the relativistic free field. Some possible observable effects are discussed.