Quantum vacuum fluctuations in presence of dissipative bodies: Dynamical approach for nonequilibrium and squeezed states

Abstract

The present work contributes to the study of nonequilibrium aspects of the Casimir forces with the introduction of squeezed states in the calculations. Throughout this article two main results can be found, being both strongly correlated. Primarily, the more formal result involves the development of a first-principles canonical quantization formalism to study the quantum vacuum in the presence of different dissipative material bodies in completely general scenarios. For this purpose, we consider a one-dimensional quantum scalar field interacting with the volume elements' degrees of freedom of the material bodies, which are modeled as a set of composite systems consisting of quantum harmonic oscillators interacting with an environment (provided as an infinite set of quantum harmonic oscillators acting as a thermal bath). Solving the full dynamics of the composite system through its Heisenberg equations, we study each contribution to the field operator by employing general properties of the Green function. We deduce the long-time limit of the contributions to the field operator. In agreement with previous works, we show that the expectation values of the components of the energy-momentum tensor present two contributions, one associated to the thermal baths and the other one associated to the field's initial conditions. This allows the direct study of steady situations involving different initial states for the field (keeping arbitrary thermal states for the baths). This leads to the other main result, consisting of computing the Casimir force when the field is initially in thermal or continuum-single-mode squeezed states (the latter being characterized by a given bandwidth and frequency). Time averaging is required for the squeezed case, showing that both results can be given in a unified way, while for the thermal state, all the well-known equilibrium results can be successfully reproduced. Finally, we compared the initial conditions' contribution and the total force for each case, showing that the latter can be tuned in a wide range of values through varying the size of the bandwidth.