Entanglement between field modes mediated by a fluctuating conducting wall in a two-cavity system

We consider a system of two cavities separated by a conducting wall free to move; two massless one-dimensional scalar fields are defined in each sub-cavity. The movable wall is bound to its equilibrium position by a harmonic potential and its mechanical degrees of freedom are described quantum mechanically. The presence of the movable wall, and its quantum position fluctuations, yields an effective interaction between the field modes in each sub-cavity and between the wall and the two scalar fields that is described by a simple generalization of the Law effective Hamiltonian. This Hamiltonian is linear in the wall operators and quadratic in the field operators of each sub-cavity.

We first evaluate, up to the second order in the interaction, the system interacting ground state and the reduced density operator for the field quantities in the two sub-cavities. In order to quantify the entanglement between field observables in the two sub-cavities, we then evaluate the negativity associated with two field modes, one in each sub-cavity, as well as the multimode negativity. We find that the motion-induced interaction generates entanglement between field degrees of freedom in the two sub-cavities, an effect that is absent when all the three walls are fixed in space. We also evaluate the magnitude of this entanglement for values of the system parameters (the mass and oscillation frequency of the central movable wall, and its distances from the two external fixed walls) that are accessible in present and foreseeable experimental implementations.

Finally, we address the problem of renormalization of the movable wall mass due to its interaction with the two scalar fields at both sides of it.