Nonequilibrium steady states of ideal bosonic and fermionic quantum gases

Minimal quantum heat pump based on high-frequency driving and non-Markovianity

We propose a minimal setup for a quantum heat pump consisting of two tunnel-coupled quantum dots, each hosting a single level and each being coupled to a different fermionic reservoir. The working principle relies on both non-Markovian system-bath coupling and driving-induced resonant coupling. We describe the system using a reaction-coordinate mapping in combination with Floquet-Born-Markov theory and characterize its performance.

Lindbladian approximation beyond ultraweak coupling

Away from equilibrium, the properties of open quantum systems depend on the details of their environment. A microscopic derivation of a master equation (ME) is therefore crucial. Of particular interest are Lindblad-type equations, not only because they provide the most general class of Markovian MEs, but also since they are the starting point for efficient quantum trajectory simulations. Lindblad-type MEs are commonly derived from the Born-Markov-Redfield equation via a rotating-wave approximation (RWA). However the RWA is valid only for ultraweak system-bath coupling and often fails to accurately describe nonequilibrium processes. Here we derive an alternative Lindbladian approximation to the Redfield equation, which does not rely on ultraweak system-bath coupling. Applying it to an extended Hubbard model coupled to Ohmic baths, we show that, especially away from equilibrium, it provides a good approximation in large parameter regimes where the RWA fails.

The Rabi problem with elliptical polarization

We consider the solution of the equation of motion of a classical/quantum spin subject to a monochromatical, elliptically polarized external field. The classical Rabi problem can be reduced to third-order differential equations with polynomial coefficients and hence solved in terms of power series in close analogy to the confluent Heun equation occurring for linear polarization. Application of Floquet theory yields physically interesting quantities like the quasienergy as a function of the problem’s parameters and expressions for the Bloch–Siegert shift of resonance frequencies. Various limit cases are thoroughly investigated.

Design and characterization of a quantum heat pump in a driven quantum gas

We propose the implementation of a quantum heat pump with ultracold atoms. It is based on two periodically driven coherently coupled quantum dots using ultracold atoms. Each dot possesses two relevant quantum states and is coupled to a fermionic reservoir. The working principle is based on energy-selective driving-induced resonant tunneling processes, where a particle that tunnels from one dot to the other either absorbs or emits the energy quantum ℏω associated with the driving frequency, depending on its energy. We characterize the device using Floquet theory and compare simple analytical estimates to numerical simulations based on the Floquet-Born-Markov formalism. In particular, we show that driving-induced heating is directly linked to the micromotion of the Floquet states of the system.

Periodic thermodynamics of the Rabi model with circular polarization for arbitrary spin quantum numbers

We consider a spin s subjected to both a static and an orthogonally applied oscillating, circularly polarized magnetic field while being coupled to a heat bath and analytically determine the quasistationary distribution of its Floquet-state occupation probabilities for arbitrarily strong driving. This distribution is shown to be Boltzmannian with a quasitemperature which is different from the temperature of the bath and independent of the spin quantum number. We discover a remarkable formal analogy between the quasithermal magnetism of the nonequilibrium steady state of a driven ideal paramagnetic material and the usual thermal paramagnetism. Nonetheless, the response of such a material to the combined fields is predicted to show several unexpected features, even allowing one to turn a paramagnet into a diamagnet under strong driving. Thus, we argue that experimental measurements of this response may provide key paradigms for the emerging field of periodic thermodynamics.

Bath-Induced Decay of Stark Many-Body Localization

We investigate the relaxation dynamics of an interacting Stark-localized system coupled to a dephasing bath, and compare its behavior to the conventional disorder-induced many body localized system. Specifically, we study the dynamics of population imbalance between even and odd sites, and the growth of the von Neumann entropy. For a large potential gradient, the imbalance is found to decay on a timescale τ that grows quadratically with the Wannier-Stark tilt. For the noninteracting system, it shows an exponential decay, which becomes a stretched exponential decay in the presence of finite interactions. This is different from a system with disorder-induced localization, where the imbalance exhibits a stretched exponential decay also for vanishing interactions. As another clear qualitative difference, we do not find a logarithmically slow growth of the von Neumann entropy as it is found for the disordered system. Our findings can immediately be tested experimentally with ultracold atoms in optical lattices.

Absence of Criticality in the Phase Transitions of Open Floquet Systems

We address the nature of phase transitions in periodically driven systems coupled to a bath. The latter enables a synchronized nonequilibrium Floquet steady state at finite entropy, which we analyze for rapid drives within a nonequilibrium renormalization group (RG) approach. While the infinitely rapidly driven limit exhibits a second-order phase transition, here we reveal that fluctuations turn the transition first order when the driving frequency is finite. This can be traced back to a universal mechanism, which crucially hinges on the competition of degenerate, near critical modes associated with higher Floquet Brillouin zones. The critical exponents of the infinitely rapidly driven system-including a new, independent one-can yet be probed experimentally upon smoothly tuning towards that limit.

On the number of Bose-selected modes in driven-dissipative ideal Bose gases

In an ideal Bose gas that is driven into a steady state far from thermal equilibrium, a generalized form of Bose condensation can occur. Namely, the single-particle states unambiguously separate into two groups: the group of Bose-selected states, whose occupations increase linearly with the total particle number, and the group of all other states whose occupations saturate [Phys. Rev. Lett. 111, 240405 (2013)PRLTAO0031-900710.1103/PhysRevLett.111.240405]. However, so far very little is known about how the number of Bose-selected states depends on the properties of the system and its coupling to the environment. The answer to this question is crucial since systems hosting a single, a few, or an extensive number of Bose-selected states will show rather different behavior. While in the former two scenarios each selected mode acquires a macroscopic occupation, corresponding to (fragmented) Bose condensation, the latter case rather bears resemblance to a high-temperature state of matter. In this paper, we systematically investigate the number of Bose-selected states, considering different classes of the rate matrices that characterize the driven-dissipative ideal Bose gases in the limit of weak system-bath coupling. These include rate matrices with continuum limit, rate matrices of chaotic driven systems, random rate matrices, and rate matrices resulting from thermal baths that couple to a few observables only.

High-Temperature Nonequilibrium Bose Condensation Induced by a Hot Needle

We investigate theoretically a one-dimensional ideal Bose gas that is driven into a steady state far from equilibrium via the coupling to two heat baths: a global bath of temperature T and a "hot needle," a bath of temperature T_{h}≫T with localized coupling to the system. Remarkably, this system features a crossover to finite-size Bose condensation at temperatures T that are orders of magnitude larger than the equilibrium condensation temperature. This counterintuitive effect is explained by a suppression of long-wavelength excitations resulting from the competition between both baths. Moreover, for sufficiently large needle temperatures ground-state condensation is superseded by condensation into an excited state, which is favored by its weaker coupling to the hot needle. Our results suggest a general strategy for the preparation of quantum degenerate nonequilibrium steady states with unconventional properties and at large temperatures.

Master equations and the theory of stochastic path integrals

This review provides a pedagogic and self-contained introduction to master equations and to their representation by path integrals. Since the 1930s, master equations have served as a fundamental tool to understand the role of fluctuations in complex biological, chemical, and physical systems. Despite their simple appearance, analyses of master equations most often rely on low-noise approximations such as the Kramers-Moyal or the system size expansion, or require ad-hoc closure schemes for the derivation of low-order moment equations. We focus on numerical and analytical methods going beyond the low-noise limit and provide a unified framework for the study of master equations. After deriving the forward and backward master equations from the Chapman-Kolmogorov equation, we show how the two master equations can be cast into either of four linear partial differential equations (PDEs). Three of these PDEs are discussed in detail. The first PDE governs the time evolution of a generalized probability generating function whose basis depends on the stochastic process under consideration. Spectral methods, WKB approximations, and a variational approach have been proposed for the analysis of the PDE. The second PDE is novel and is obeyed by a distribution that is marginalized over an initial state. It proves useful for the computation of mean extinction times. The third PDE describes the time evolution of a 'generating functional', which generalizes the so-called Poisson representation. Subsequently, the solutions of the PDEs are expressed in terms of two path integrals: a 'forward' and a 'backward' path integral. Combined with inverse transformations, one obtains two distinct path integral representations of the conditional probability distribution solving the master equations. We exemplify both path integrals in analysing elementary chemical reactions. Moreover, we show how a well-known path integral representation of averaged observables can be recovered from them. Upon expanding the forward and the backward path integrals around stationary paths, we then discuss and extend a recent method for the computation of rare event probabilities. Besides, we also derive path integral representations for processes with continuous state spaces whose forward and backward master equations admit Kramers-Moyal expansions. A truncation of the backward expansion at the level of a diffusion approximation recovers a classic path integral representation of the (backward) Fokker-Planck equation. One can rewrite this path integral in terms of an Onsager-Machlup function and, for purely diffusive Brownian motion, it simplifies to the path integral of Wiener. To make this review accessible to a broad community, we have used the language of probability theory rather than quantum (field) theory and do not assume any knowledge of the latter. The probabilistic structures underpinning various technical concepts, such as coherent states, the Doi-shift, and normal-ordered observables, are thereby made explicit.

Microscopic theory of a nonequilibrium open bosonic chain

Quantum master equations form an important tool in the description of transport problems in open quantum systems. However, they suffer from the difficulty that the shape of the Lindblad dissipator depends sensibly on the system Hamiltonian. Consequently, most of the work done in this field has focused on phenomenological dissipators which act locally on different parts of the system. In this paper we show how to construct Lindblad dissipators to model a one-dimensional bosonic tight-binding chain connected to two baths at the first and last site, kept at different temperatures and chemical potentials. We show that even though the bath coupling is local, the effective Lindblad dissipator stemming from this interaction is inherently nonlocal, affecting all normal modes of the system. We then use this formalism to study the current of particles and energy through the system and find that they have the structure of Landauer's formula, with the bath spectral density playing the role of the transfer integral. Finally, we consider infinitesimal temperature and chemical potential gradients and show that the currents satisfy Onsager's reciprocal relations, which is a consequence of the fact that the microscopic quantum dynamics obeys detailed balance.

Nonequilibrium quantum chains under multisite Lindblad baths

We study a quantum XX chain coupled to two heat reservoirs that act on multiple sites and are kept at different temperatures and chemical potentials. The baths are described by Lindblad dissipators, which are constructed by direct coupling to the fermionic normal modes of the chain. Using a perturbative method, we are able to find analytical formulas for all steady-state properties of the system. We compute both the particle or magnetization current and the energy current, both of which are found to have the structure of Landauer's formula. We also obtain exact formulas for the Onsager coefficients. All properties are found to differ substantially from those of a single-site bath. In particular, we find a strong dependence on the intensity of the bath couplings. In the weak-coupling regime, we show that the Onsager reciprocal relations are satisfied.