Mirror-field entanglement in a microscopic model for quantum optomechanics

Abstract

We use a microscopic model, the Mirror-Oscillator-Field (MOF) model proposed in [1], to describe the quantum entanglement between a mirror's center of mass (CoM) motion and a field. In contrast with the conventional approach where the mirror-field entanglement is understood as arising from the radiation pressure of an optical field inducing the motion of the mirror's CoM, the MOF model incorporates the dynamics of the internal degrees of freedom of the mirror that couple to the optical field directly. The major advantage in this approach is that it provides a self-consistent treatment of the three pertinent subsystems (the mirror's CoM motion, its internal degrees of freedom and the field) including their back-actions on each other, thereby giving a more accurate account of the quantum correlations between the individual subsystems. The optical and the mechanical properties of a mirror arising from its dynamical interaction with a quantum field are obtained without imposing any boundary conditions on the field additionally, as is done in the conventional way. As one of the new physical features that arise from this self-consistent treatment of the coupled optics and mechanics behavior we observe a coherent transfer of quantum correlations from the field to the mirror via its internal degrees of freedom. We find the quantum entanglement between the optical field and the mirror's center of mass motion upon coarse-graining over the internal degree of freedom. Further, we show that in certain parameter regimes the mirror-field entanglement is enhanced when the field interacts resonantly with the mirror's internal degree of freedom, a new result which highlights the importance of including the internal structure of the mirror in quantum optomechanical considerations.

Equivalence principle for quantum systems: dephasing and phase shift of free-falling particles

“…While this phase shift is a purely quantum effect, for some initial states it has a natural classical interpretation in terms of gravitational red-shift and special relativistic time-dilation. Similar effects of entanglement between translational and internal degrees of freedom (dof) show up in the motional decoherence of an atom [19] and in moving mirrors with internal dof [20,21]. The difference is that the phase shift derived here is universal, like the dephasing, i.e., it applies to all particles and it is independent of the particle's mass.…”

Mechanical backreaction effect of the dynamical Casimir emission

“…In the case of Hawking radiation, one instead expects from purely thermodynamic considerations that the horizon of a black-hole must shrink as a consequence of the emitted particles [25][26][27][28][29]. In the DCE case, the particles created out of the vacuum provide a friction force on the moving mirror [30][31][32][33][34]. Despite the efforts devoted to this topic, most works so far assume that the background interacts with expectation values of quantum field observables such as the stress-energy tensor.…”

Fluctuation-dissipation and correlation-propagation relations from the nonequilibrium dynamics of detector-quantum field systems

“…The internal degree of freedom of the detector Q will undergo nonequilibrium evolution but its dynamics will not affect the external motion z of the detector. In a model like what is used in [31,32] where z is dynamical there will be interplay between the idf and the mdf through the field.…”

“…Similar detector-field systems are also used in the newly emergent field of relativistic quantum information [25] to examine theoretical issues like environmental influences on quantum coherence [26] and entanglement [28][29][30] which are essential for projected applications in quantum communications and teleportation [27]. They can represent not only atoms distributed in space, but also mirrors with some internal degrees of freedom describing their optical properties such as reflectivity (e.g., [31][32][33]), or even those degrees of freedom entering as basic constituents in a dielectric (e.g., [34]). In this capacity the investigation of detector-field interactions in this paper carries as much importance in terms of experimental capabilities for relativistic quantum information as atom-field interactions have provided for the bounty achievements in atomic and optical physics.…”