The circumstances under which a system reaches thermal equilibrium, and how to derive this from basic dynamical laws, has been a major question from the very beginning of thermodynamics and statistical mechanics. Despite considerable progress, it remains an open problem. Motivated by this issue, we address the more general question of equilibration. We prove, with virtually full generality, that reaching equilibrium is a universal property of quantum systems: Almost any subsystem in interaction with a large enough bath will reach an equilibrium state and remain close to it for almost all times. We also prove several general results about other aspects of thermalisation besides equilibration, for example, that the equilibrium state does not depend on the detailed micro-state of the bath.
Fluctuation theorems are fundamental extensions of the second law of thermodynamics for small nonequilibrium systems. While work and heat are equally important forms of energy exchange, fluctuation relations have not been experimentally assessed for the generic situation of simultaneous mechanical and thermal changes. Thermal driving is indeed generally slow and more difficult to realize than mechanical driving. Here, we use feedback cooling techniques to implement fast and controlled temperature variations of an underdamped levitated microparticle that are one order of magnitude faster than t…
A framework for the investigation of disordered quantum systems in thermal equilibrium is proposed. The approach is based on a dynamical model--which consists of a combination of a double-bracket gradient flow and a uniform Brownian fluctuation--that `equilibrates' the Hamiltonian into a canonical distribution. The resulting equilibrium state is used to calculate quenched and annealed averages of quantum observables.
The question of whether sunlight induces coherent dynamics in biological systems is under debate. Here we show, on the basis of an exact fully quantum mechanical treatment, that thermal light induces excited-state coherences in matter similar to those induced by a coherent state. We demonstrate the phenomenon on a V-type model system and a two-state Born-Oppenheimer molecular system. Remarkably, wavepacket-like dynamics is induced in the excited molecular potential-energy surface.
We report the experimental observation of two-mode squeezing in the oscillation quadratures of a thermal micro-oscillator. This effect is obtained by parametric modulation of the optical spring in a cavity opto-mechanical system. In addition to stationary variance measurements, we describe the dynamic behavior in the regime of pulsed parametric excitation, showing enhanced squeezing effect surpassing the stationary 3dB limit. While the present experiment is in the classical regime, our technique can be exploited to produce entangled, macroscopic quantum opto-mechanical modes.
A quantum mechanical path integral derivation is given of a thermal propagator in non-static Gui spacetime. The thermal nature of the propagator is understood in terms of homotopically non-trivial paths in the configuration space appropriate to tortoise coordinates. The connection to thermal emission from collapsing black holes is discussed.
Recent experiments aim at cooling nanomechanical resonators to the ground state by coupling them to non-equilibrium environments in order to observe quantum effects such as entanglement. This raises the general question of how such environments affect entanglement. Here we show that there is an optimal dissipation strength for which the entanglement between two coupled oscillators is maximized. Our results are established with the help of a general framework of exact quantum Langevin equations valid for arbitrary bath spectra, in and out of equilibrium. We point out why the commonly employed L…
Based on the view that thermal equilibrium should be characterized through macroscopic observations, we develop a general theory about typicality of thermal equilibrium and the approach to thermal equilibrium in macroscopic quantum systems. We first formulate the notion that a pure state in an isolated quantum system represents thermal equilibrium. Then by assuming, or proving in certain classes of nontrivial models (including that of two bodies in thermal contact), large-deviation type bounds (which we call thermodynamic bounds) for the microcanonical ensemble, we prove that to represent ther…
We revisist the issue of entanglement of thermal equilibrium states in composite quantum systems. The possible scenarios are exemplified in bipartite qubit/qubit and qubit/qutrit systems.
We critically discuss the common belief that the thermal Casimir-Polder force can always be represented as a Matsubara sum, as it is true for the Casimir force. On the contrary, an exact treatment of the atom-field coupling reveals that for a ground-state atom, terms associated with virtual-photon absorption contribute to the force which are identified as a signature of non-equilibrium dynamics. Even the equilibrium force on a thermalized atom or molecule may be overestimated when using the ground-state polarizability instead of its thermal counterpart.
Adding or subtracting a single quantum of excitation to a thermal state of a bosonic system has the counter-intuitive effect of approximately doubling its mean occupation. We perform the first experimental demonstration of this effect outside optics by implementing single-phonon addition and subtraction to a thermal state of a mechanical oscillator via Brillouin optomechanics in an optical whispering-gallery microresonator. Using a detection scheme that combines single-photon counting and optical heterodyne detection, we observe this doubling of the mechanical thermal fluctuations to a high pr…
It is shown, that Bose-Einstein condensation can occur not only in spatially extended equilibrium systems, but also in the systems far from thermal equilibrium, which show order-disorder phase transition. The investigation is performed by solving the Complex Ginzburg-Landau equation, a universal model for nonequilibrium order-disorder phase transitions.
Quantum optical measurement techniques offer a rich avenue for quantum control of mechanical oscillators via cavity optomechanics. In particular, a powerful yet little explored combination utilizes optical measurements to perform heralded non-Gaussian mechanical state preparation followed by tomography to determine the mechanical phase-space distribution. Here, we experimentally perform heralded single- and multi-phonon subtraction via photon counting to a laser-cooled mechanical thermal state with a Brillouin optomechanical system at room temperature, and use optical heterodyne detection to m…
Quantum nonclassicality is the basic building stone for the vast majority of quantum information applications and methods of its generation are at the forefront of research. One of the obstacles any method needs to clear is the looming presence of decohorence and noise which act against the nonclassicality and often erase it completely. In this paper we show that nonclassical states of a quantum harmonic oscillators initially in thermal equilibrium states can be deterministically created by coupling it to a single two level system. This can be achieved even in the absorption regime in which th…
We provide an explicit analytical calculation that shows the asymptotic approach of the one dimensional Caldeira-Leggett model to thermal equilibrium in the high temperature and weak coupling limit. We investigate a free particle and a harmonic oscillator system, using both the Lindblad and the non-Lindblad type master equations for each case, and show that thermal equilibrium is reached exactly for the free particle and aproximately for the harmonic oscillator, irrespective of the initial preparation of the system. We also generalize our calculation to higher dimensions.
The surface-atom Casimir-Polder-Lifshitz force out of thermal equilibrium is investigated in the framework of macroscopic electrodynamics. Particular attention is devoted to its large distance limit that shows a new, stronger behaviour with respect to the equilibrium case. The frequency shift produced by the surface-atom force on the the center-of-mass oscillations of a harmonically trapped Bose-Einstein condensate and on the Bloch oscillations of an ultra-cold fermionic gas in an optical lattice are discussed for configurations out of thermal equilibrium.
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 …
To understand under which conditions thermodynamics emerges from the microscopic dynamics is the ultimate goal of statistical mechanics. Despite the fact that the theory is more than 100 years old, we are still discussing its foundations and its regime of applicability. A point of crucial importance is the definition of the notion of thermal equilibrium, which is given as the state that maximises the von Neumann entropy. Here we argue that it is necessary to propose a new way of describing thermal equilibrium, focused on observables rather than on the full state of the quantum system. We chara…
We study two two-level atomic quantum systems (qubits) placed close to a body held at a temperature different from that of the surrounding walls. While at thermal equilibrium the two-qubit dynamics is characterized by not entangled steady thermal states, we show that absence of thermal equilibrium may bring to the generation of entangled steady states. Remarkably, this entanglement emerges from the two-qubit dissipative dynamic itself, without any further external action on the two qubits, suggesting a new protocol to produce and protect entanglement which is intrinsically robust to environmen…
We report the confinement of an optomechanical micro-oscillator in a squeezed thermal state, obtained by parametric modulation of the optical spring. We propose and implement an experimental scheme based on parametric feedback control of the oscillator, which stabilizes the amplified quadrature while leaving the orthogonal one unaffected. This technique allows us to surpass the -3dB limit in the noise reduction, associated to parametric resonance, with a best experimental result of -7.4dB. In a moderately cooled system, our technique can be efficiently exploited to produce strong squeezing of …
The thermal Casimir-Lifshitz force among two bodies held at different temperatures displays striking features that are absent in systems in thermal equilibrium. The manifestation of this force has been observed so far only in Bose-Einstein condensates close to a heated substrate, but never between two macroscopic bodies. Observation of the thermal Casimir-Lifhitz force out of thermal equilibrium with conventional Casimir setups is very difficult, because for experimentally accessible separations the thermal force is small compared to the zero-temperature quantum Casimir force, unless prohibiti…
Thermalization is the dynamical process by which a many-body system evolves toward a thermal equilibrium state that maximizes its entropy. In certain cases, however, the establishment of thermal equilibrium is significantly slowed down and a phenomenon of pre-thermalization can emerge. It describes the initial relaxation toward a quasi-steady state after a perturbation. While having similar properties to their thermal counterparts, pre-thermal states exhibit a partial memory of initial conditions. Here, we observe the dynamical formation of a pre-thermal state in a non-equilibrium, two-dimensi…
The propagator of a spinless particle is calculated from the quantum mechanical path integral formalism in static curved spacetimes endowed with event-horizons. A toy model, the Gui spacetime, and the 2D and 4D Schwarzschild black holes are considered. The role of the topology of the coordinates configuration space is emphasised in this framework. To cover entirely the above spacetimes with a single set of coordinates, tortoise coordinates are extended to complex values. It is shown that the homotopic properties of the complex tortoise configuration space imply the thermal behaviour of the pro…
We develop an exact method for computing Casimir forces and the power of radiative heat transfer between two arbitrary nanostructured surfaces out of thermal equilibrium. The method is based on a generalization of the scattering approach recently used in investigations on the Casimir effect. Analogously to the equilibrium case, we find that also out of thermal equilibrium the shape and composition of the surfaces enter only through their scattering matrices. The expressions derived provide exact results in terms of the scattering matrices of the intervening surfaces.
We study the thermalization of an elementary quantum system modeled by a two-level atom interacting with stationary electromagnetic fields out of thermal equilibrium near a dielectric slab. The slab is held at a temperature different from that of the region where the atom is located. We find that when the slab is a nonabsorbing and nondispersive dielectric of a finite thickness $ d$, no out of thermal equilibrium effects appear as far as the thermalization of the atom is concerned, and a finite thick dielectric slab with a tiny imaginary part in the relative permittivity $\operatorname{Im} ε$ …
We consider the thermal equilibrium distribution at inverse temperature $β$, or canonical ensemble, of the wave function $Ψ$ of a quantum system. Since $L^2$ spaces contain more nondifferentiable than differentiable functions, and since the thermal equilibrium distribution is very spread-out, one might expect that $Ψ$ has probability zero to be differentiable. However, we show that for relevant Hamiltonians the contrary is the case: with probability one, $Ψ$ is infinitely often differentiable and even analytic. We also show that with probability one, $Ψ$ lies in the domain of the Hamiltonian.
