Thermal equilibrium in Gaussian dynamical semigroups

We characterize all Gaussian dynamical semigroups in continuous variables quantum systems of n-bosonic modes which have a thermal Gibbs state as a stationary solution. This is performed through an explicit relation between the diffusion and dissipation matrices, which characterize the semigroup dynamic, and the covariance matrix of the thermal equilibrium state. We also show that Alicki's quantum detailed-balance condition, based on a Gelfand-Naimark-Segal inner product, allows the determination of the temperature dependence of the diffusion and dissipation matrices, and the identification of different Gaussian dynamical semigroups which shares the same thermal equilibrium state.Comment: 14 pages; submmited to Phys. Rev.

Determining stationary-state quantum properties directly from system-environment interactions

Considering stationary states of continuous-variable systems undergoing an open dynamics, we unveil the connection between properties and symmetries of the latter and the dynamical parameters. In particular, we explore the relation between the Lyapunov equation for dynamical systems and the steady-state solutions of a time-independent Lindblad master equation for bosonic modes. Exploiting bona-fide relations that characterize some genuine quantum properties (entanglement, classicality, and steerability), we obtain conditions on the dynamical parameters for which the system is driven to a steady-state possessing such properties. We also develop a method to capture the symmetries of a steady state based on symmetries of the Lyapunov equation. All the results and examples can be useful for steady-state engineering process.Comment: 12 pages, 2 figure

Capacitive Coupling of Two Transmission Line Resonators Mediated by the Phonon Number of a Nanoelectromechanical Oscillator

Detection of quantum features in mechanical systems at the nanoscale constitutes a challenging task, given the weak interaction with other elements and the available technics. Here we describe how the interaction between two monomodal transmission-line resonators (TLRs) mediated by vibrations of a nano-electromechanical oscillator can be described. This scheme is then employed for quantum non-demolition detection of the number of phonons in the nano-electromechanical oscillator through a direct current measurement in the output of one of the TLRs. For that to be possible an undepleted field inside one of the TLR works as a amplifier for the interaction between the mechanical resonator and the remaining TLR. We also show how how the non-classical nature of this system can be used for generation of tripartite entanglement and conditioned mechanical coherent superposition states, which may be further explored for detection processes.Comment: 6 pages, 5 figure

Thermal transport in out of equilibrium quantum harmonic chains

We address the problem of heat transport in a chain of coupled quantum harmonic oscillators, exposed to the influences of local environments of various nature, stressing the effects that the specific nature of the environment has on the phenomenology of the transport process. We study in detail the behavior of thermodynamically relevant quantities such as heat currents and mean energies of the oscillators, establishing rigorous analytical conditions for the existence of a steady state, whose features we analyse carefully. In particular we assess the conditions that should be faced to recover trends reminiscent of the classical Fourier law of heat conduction and highlight how such a possibility depends on the environment linked to our system.Comment: 11 pages, 15 figure