Salvatore Butera

Phys. Rev. D 114, 079901 (2026)

We present a perturbative closed-time-path (in-in) formulation of an optomechanical system in which a quantum field interacts with a moving mirror via radiation-pressure. We derive the effective action governing the dynamics of the moving mirror, incorporating the full backreaction of the field. These effects are encoded in fluctuation and dissipation kernels, that we show satisfy fluctuation-dissipation relations, and whose spectral structure reveals a direct connection with the underlying physical mechanism responsible for the backreaction, that is particle creation by the dynamical Casimir effect. By deriving the semiclassical equations of motion for the moving mirror, and computing the energy radiated into the field using the in-out formalism of quantum field theory, we verify the energy balance between the mechanical energy dissipated by the optical backreaction forces acting on the mirror and the energy carried by the particles created in the field.

We extend the theory of the radiation pressure to include quadratic fluctuations in the position of a moving mirror. This enables the introduction of a generalized radiation pressure operator that captures higher-order effects in the mirror-field coupling. For mechanical resonators with frequencies comparable to the fundamental cavity frequency, the resulting corrections to the optomechanical Hamiltonian are quadratic in the standard radiation pressure coupling. These corrections are expected to play a significant role in the strong-coupling regime of optomechanics, electromechanics, and superconducting circuit analogs.

We theoretically study stimulated and spontaneous Hawking emission from an analog horizon for spin modes in a two-component Bose–Einstein condensate, both with and without a coherent coupling between the two components. We highlight the conceptual and practical advantages that these systems offer to the experimental observation of the phenomenon, namely the possibility of working with massive elementary excitations and the experimental accessibility of the different quadratures of the spin excitations. In particular, we go beyond the relativistic regimes previously addressed in the literature, and identify various observables that show a signature of the Hawking process, as well as additional features associated with the massive nature of the modes, such as undulations . Semi-analytical calculations of the scattering properties of the horizon and of two-point correlation functions of the emitted radiation in an ideal stationary setup are supported by time-dependent numerical simulations based on Gross–Pitaevskii and Bogoliubov theory.

We adopt an open quantum system approach to study the effects of the back-reaction from a quantum field onto the dynamics of a moving mirror. We describe the coupling between the mirror and the field by using a microscopic model from which the dielectric response of the mirror is obtained from first principles. Using second-order perturbation theory, we derive the master equation governing the mechanical motion of the mirror. Our analysis reveals that the mirror experiences coloured noise and non-local dissipation, which originate from the emission of particle pairs via the dynamical Casimir effect. We show that the noise and dissipation kernels, that enter in the definition of the time-dependent coefficients of the master equation, are related by standard fluctuation-dissipation relations.

We theoretically propose an atomic Bose-Einstein condensate as an analog model of backreaction effects during the preheating stage of the early Universe. In particular, we address the out-of-equilibrium dynamics where the initially excited inflaton field decays by parametrically exciting the matter fields. We consider a two-dimensional, ring-shaped BEC under a tight transverse confinement whose transverse breathing mode and the Goldstone and dipole excitation branches simulate the inflaton and quantum matter fields, respectively. A strong excitation of the breathing mode leads to an exponentially growing emission of dipole and Goldstone excitations via parametric pair creation: Our numerical simulations of the BEC dynamics show how the associated backreaction effect results not only in an effective friction of the breathing mode, but also in a quick loss of longitudinal spatial coherence of the initially in-phase excitations. Implications of this result on the validity of the usual semiclassical description of backreaction are finally discussed.

We study the effective dynamics of two mirrors, forming an optical cavity, and interacting with the cavity field via radiation pressure. We pursue a perturbative influence functional approach to trace out the degrees of freedom of the field, and obtain the second-order effective action for the system composed by the mirrors. We find that the interaction between the mirrors is mediated by pairs of field modes, which combine in such a way to give rise to two different interaction channels. We find that the quantum and thermal fluctuations of the cavity field result in colored, Gaussian stochastic noises acting on the mirrors. To each of these noises is associated a dissipative effect, and the corresponding power spectra and susceptibilities are related via generalized fluctuation-dissipation relations. We finally demonstrate that the dynamics of the mirrors admits a stochastic interpretation, and give the relative quantum Langevin equations.

We investigate the parametric amplification of the zero-point fluctuations in the spin modes of a two-component Bose-Einstein condensate, triggered by the dynamical evolution of the condensate density. We first make use of a Thomas-Fermi approximation to develop a tractable theoretical model of the quantum dynamics of the Bogoliubov excitations in a harmonically trapped condensate with a time-dependent trapping frequency. The predictions of this model are then compared to an ab initio numerical study of the correlation functions of density and spin fluctuations for general spatially inhomogeneous configurations. Results are shown for the two cases of expanding and oscillating condensates: while the quantum excitation of spin modes remains weak and relatively featureless in the case of an expanding condensate, clear and experimentally promising signatures of particle creation are anticipated for the oscillating case under suitable resonance conditions between the density and the spin modes.

We investigate the position- and momentum-space two-body correlations in a weakly interacting, harmonically trapped atomic Bose-Einstein condensed gas at low temperatures. The two-body correlations are computed within the Bogoliubov approximation and the consequences of the finite system size are highlighted in contrast to the spatially homogeneous case. In the position space, we recover the antibunching induced by the repulsive interatomic interaction in the condensed fraction localized around the trap center and the bunching in the outer thermal cloud. In the momentum space, bunching signatures appear for either equal or opposite values of the momentum and display peculiar features as a function of the momentum and the temperature. In analogy to the optical Hanbury-Brown and Twiss effect, the amplitude of the bunching signal at closeby momenta is fixed by the chaotic nature of the matter field state and its linewidth is shown to be set by the (inverse of the) finite spatial size of the associated in-trap momentum components. In contrast, the linewidth of the bunching signal at opposite momenta is only determined by the condensate size.