Nanotechnology has not only provided us the possibility of developing quantum machines but also noncanonical power sources able to drive them. Here we focus on studying the performance of quantum machines driven by arbitrary combinations of equilibrium reservoirs and a form of engineered reservoirs consisting of noninteracting particles but whose distribution functions are nonthermal. We provide the expressions for calculating the maximum efficiency of those machines without needing any knowledge of how the nonequilibrium reservoirs were actually made. The formulas require the calculation of a quantity that we term entropy current, which we also derive. We illustrate our methodology through a solvable toy model where heat "spontaneously" flows against the temperature gradient.
We show that a current-carrying coherent electron conductor can be treated as effective bosonic energy reservoir involving different types of electron-hole pair excitation. For weak electron-boson coupling, hybrid energy transport between nonequilibrium electrons and bosons can be described by a Landauer-like formula. This allows for unified account of a variety of heat transport problems in hybrid electron-boson systems. As applications, we study the non-reciprocal heat transport between electrons and bosons, thermoelectric current from a cold-spot and electronic cooling of the bosons. Our un…
The interaction between coherent polaritons and incoherent excitons plays an important role in polariton physics. Using resonant pump-probe spectroscopy with selective excitation of single polariton branches, we investigate the different dephasing mechanisms responsible for generating a long-lived exciton reservoir. As expected, pumping the upper polariton results in a strong dephasing process that leads to the generation of a long lived reservoir. Unexpectedly, we observe an efficient reservoir creation while exciting only the lower polariton branch when the detuning is increased towards posi…
A solid state electronic nanodevice is an intrinsically open quantum system, exchanging both energy with the host material and carriers with connected reservoirs. Its out-of-equilibrium behavior is determined by a non-trivial interplay between electronic dissipation and decoherence induced by inelastic processes within the device, and the coupling of the latter to metallic electrodes. We propose a unified description, based on the density matrix formalism, that accounts for both these aspects, enabling to predict various steady-state as well as ultrafast nonequilibrium phenomena, nowadays expe…
We present a novel hierarchical quantum master equation (HQME) approach which provides a numerically exact description of nonequilibrium charge transport in nanosystems with electronic-vibrational coupling. In contrast to previous work [Phys. Rev. B $\bf{94}$, 201407 (2016)], the active vibrational degrees of freedom are treated in the reservoir subspace and are integrated out. This facilitates applications to systems with very high excitation levels, for example due to current-induced heating, while properties of the vibrational degrees of freedom, such as the excitation level and other momen…
With this work we investigate the stationary nonequilibrium density matrix of current carrying nonequilibrium steady states of in-between quantum systems that are connected to reservoirs. We describe the analytical procedure to obtain the explicit result for the reduced density matrix of quantum transport when the system, the connecting reservoirs and, as well, the system-reservoir interactions are described by quadratic Hamiltonians. Our procedure is detailed for both, electronic transport described by the tight-binding Hamiltonian and for phonon transport described by harmonic Hamiltonians. …
We study particle current and occupation distribution in a recently proposed model for coherent quantum transport. In this model a system connected to mesoscopic Fermi reservoirs (mesoreservoir) is driven out of equilibrium by the action of superreservoirs with prescribed temperatures and chemical potentials described by a simple dissipative mechanism with the Lindblad equation. We compare exact (numerical) results for the non-equilibrium steady state particle current with theoretical expectations based on the Landauer formula and show that the model reproduce the behavior of coherent quantum …
We study a pseudo-spin-1/2 quantum dot in the cotunneling regime close to the particle-hole symmetric point. For a generic tunneling matrix we find a generic fixed point with interesting nonequilibrium properties, characterized by effective reservoirs with compensating spin orientation vectors weighted by the polarizations and the tunneling rates. At large bias voltage we study the magnetic field dependence of the dot magnetization and the current. The fixed point can be clearly identified by analyzing the magnetization of the dot. We characterize in detail the universal properties for the cas…
A fundamental question in quantum transport is how quantum coherence influences charge transfer through nanostructures. We address this issue for linear triple quantum dots by comparison of a Lindblad density matrix description with a Pauli rate equation approach and analyze the corresponding zero-frequency counting statistics for coherent and sequential charge tunneling, respectively. The impact of decaying coherences of the density matrix due to dephasing is also studied. Our findings reveal that the sensitivity to coherence shown by shot noise and skewness, in particular in the limit of lar…
We suggest a generalisation of the expression of the nonequilibrium density matrix obtained by Hershfield's method for the cases where both heat and charge steady state currents are present in a quantum open system. The finite-size quantum system, connected to two temperature and particle reservoirs, is driven out of equilibrium by the presence of both a temperature gradient and a chemical potential gradient between the two reservoirs. We show that the NE density matrix is given by a generalised Gibbs-like ensemble, and is in full agreement with the general results of the McLennan-Zubarev none…
In this paper we study the near-field thermodynamics of a photon gas at equilibrium as well as out-of-equilibrium in the presence of dissipative effects. As a consequence of Heisenberg's uncertainty principle, we are able to eliminate the low-frequency modes in both cases, providing an analytical expression for the near-field entropy. In addition, we obtain the entropic-force contributions to the Casimir effect. At zero temperature the well-known $l^{-4}$ behavior of the pressure is obtained. In the nonequilibrium case, we compute the entropy production, showing that the excess of heat in each…
We consider the generic model of a finite-size quantum electron system connected to two (temperature and particle) reservoirs. The quantum open system is driven out of equilibrium by the presence of both a temperature and a chemical potential differences between the two reservoirs. The nonequilibrium (NE) thermodynamical properties of such a quantum open system are studied for the steady state regime. In such a regime, the corresponding NE density matrix is built on the so-called generalised Gibbs ensembles. From different expressions of the NE density matrix, we can identify the terms related…
We develop an iterative, numerically exact approach for the treatment of nonequilibrium quantum transport and dissipation problems that avoids the real-time sign problem associated with standard Monte Carlo techniques. The method requires a well-defined decorrelation time of the non-local influence functional for proper convergence to the exact limit. Since finite decorrelation times may arise either from temperature or from a voltage drop at zero temperature, the approach is well suited for the description of the real-time dynamics of single-molecule devices and quantum dots driven to a stead…
We study a $3$-level quantum dot in the singly occupied cotunneling regime coupled via a generic tunneling matrix to several multi-channel leads in equilibrium or nonequilibrium. We derive an effective model where also each reservoir has three channels labelled by the quark flavors $u$, $d$ and $s$ with an effective d.o.s. polarized w.r.t. an eight-dimensional $F$-spin corresponding to the eight generators of $SU(3)$. In equilibrium we perform a standard poor man scaling analysis and show that tunneling via virtual intermediate states induces flavor fluctuations on the dot which become $SU(3)$…
We propose a model of nonequilibrium quantum transport of particles and energy in a system connected to mesoscopic Fermi reservoirs (meso-reservoir). The meso-reservoirs are in turn thermalized to prescribed temperatures and chemical potentials by a simple dissipative mechanism described by the Lindblad equation. As an example, we study transport in monoatomic and diatomic chains of non-interacting spinless fermions. We show numerically the breakdown of the Onsager reciprocity relation due to the dissipative terms of the model.
We expand iterative numerically-exact influence functional path-integral tools and present a method capable of following the nonequilibrium time evolution of subsystems coupled to multiple bosonic and fermionic reservoirs simultaneously. Using this method, we study the real-time dynamics of charge transfer and vibrational mode excitation in an electron conducting molecular junction. We focus on nonequilibrium vibrational effects, particularly, the development of vibrational instability in a current-rectifying junction. Our simulations are performed by assuming large molecular vibrational anhar…
Whether a small quantum mechanical system is able to equilibrate with its environment once an external local perturbation drives it out of thermal equilibrium is a central question which cuts across many different fields of science. Here we consider such a problem for a correlated quantum impurity coupled to a fermionic reservoir and driven out of equilibrium by local quantum quenches such as those recently realized in optical absorption experiments on single quantum dots. We argue that equilibration in this problem is deeply connected to the occurrence of Kondo Effect at low energy and that a…
We study nonequilibrium quantum phase transitions in XY spin 1/2 chain using the $C^*$ algebra. We show that the well-known quantum phase transition at magnetic field $h = 1$ persists also in the nonequilibrium setting as long as one of the reservoirs is set to absolute zero temperature. In addition, we find nonequilibrium phase transitions associated to imaginary part of the correlation matrix for any two different temperatures of the reservoirs at $h = 1$ and $h = h_{\rm c} \equiv|1-γ^2|$, where $γ$ is the anisotropy and $h$ the magnetic field strength. In particular, two nonequilibrium quan…
We investigate the dynamics of the spaser-based nanolaser in the strong incoherent pumping regime in the quantum limit when the photon number is the order of unity. We consider the situation where the newly irradiated photon finds itself in the cloud of earlier irradiated photons that are not thermalized. As the result the entanglement of nanoparticle with quantum dot degrees of freedom in the nanolaser and the lasing intensity increases several times. In fact the nonthermal bath effectively makes the nanolaser "more quantum" and master equation for the nanolaser density matrix nonlinear and s…
The carrier generation in insulators subjected to strong electric fields is characterized by the Landau-Zener formula for the tunneling probability with a nonperturbative exponent. Despite its long history with diverse applications and extensions, study of nonequilibrium steady states and associated current response in the presence of the generated carriers has been mainly limited to numerical simulations so far. Here, we develop a framework to calculate the nonequilibrium Green's function of generic insulating systems under a DC electric field, in the presence of a fermionic reservoir. Using …
We study the driven-dissipative dynamics of photons interacting with an array of micromechanical membranes in an optical cavity. Periodic membrane driving and phonon creation result in an effective photon-number conserving non-unitary dynamics, which features a steady state with long-range photonic coherence. If the leakage of photons out of the cavity is counteracted by incoherent driving of the photonic modes, we show that the system undergoes a dynamical phase transition to the state with long-range coherence. A minimal system, composed of two micromechanical membranes in a cavity, is studi…
We present a new approach to treat correlations in nonequilibrium quantum many-particle system. The method is based on ideas of configuration interaction theory of exact nonperturbative ground state electronic structure calculations. We use superoperator techniques in Liouville-Fock space and represent the nonequilibrium density matrix as a linear combination of all possible nonequilibrium quasiparticle excitations built on the appropriate reference state. As an example we consider the electron transport through the system with electron-phonon interaction. The concept of embedding (buffer zone…
We explore the effects of quantum mechanical squeezing on the nonequilibrium thermodynamics of a coherent heat engine with squeezed reservoirs coupled to a squeezed cavity. We observe that the standard known phenomenon of flux-optimization beyond the classical limit with respect to quantum coherence is destroyed in presence of squeezing. Under extreme nonequilibrium conditions, the flux is rendered independent of squeezing. The efficiency at maximum power (EMP) obtained by optimizing the cavity's squeezing parameter is greater than what was predicted by Curzon and Ahlborn even in the absence o…
An overview is given of recent advances in the nonequilibrium statistical mechanics of quantum systems and, especially, of time-reversal symmetry relations that have been discovered in this context. The systems considered are driven out of equilibrium by time-dependent forces or by coupling to large reservoirs of particles and energy. The symmetry relations are established for the exchange of energy and particles between the subsystem and its environment. These results have important consequences. In particular, generalizations of the Kubo formula and the Casimir-Onsager reciprocity relations …
We derive an efficiency bound for continuous quantum heat engines absorbing heat from squeezed thermal reservoirs. Our approach relies on a full-counting statistics description of nonequilibrium transport and it is not limited to the framework of irreversible thermodynamics. Our result, a generalized Carnot efficiency bound, is valid beyond the small squeezing and high temperature limit. Our findings are embodied in a prototype three-terminal quantum photoelectric engine where a qubit converts heat absorbed from a squeezed thermal reservoir into electrical power. We demonstrate that in the qua…
We investigate both analytically and numerically violations of a Leggett-Garg inequality (LGI) for a composite quantum system in contact with two separate reservoirs at different temperatures. Remarkably we find that LGI violations can be enhanced when a heat current is established at low temperatures in a steady-state regime. Based on a Kraus operator decomposition of the non-unitary evolution for a system formed by two interacting spins or quantum bits, we provide analytical support for power law relations between dissipation strength and mean temperature in the borderlines separating parame…
The generation of photocurrents due to coupling of electrons to both classical and quantized electromagnetic fields in thin semiconductor films is described within the framework of the nonequilibrium Green's function formalism. For the coherent coupling to classical fields corresponding to single field operator averages, an effective two-time intraband self-energy is derived from a band decoupling procedure. The evaluation of coherent photogeneration is performed self-consistently with the propagation of the fields by using for the latter a transfer matrix formalism with an extinction coeffici…
We study the time-dependent properties of double quantum dots coupled to two reservoirs using the nonequilibrium Green function method. For an arbitrary time-dependent bias, we derive an expression for the time-dependent electron density of a dot and several currents, including the current between the dots in the wide-band-limit approximation. For the special case of a constant bias, we calculate the electron density and the currents numerically. As a result, we find that these quantities oscillate and that the number of crests in a single period of the current from a dot changes with the bias…
Exciton-polaritons in an optical microcavity can form a macroscopically coherent state despite being an inherently driven-dissipative system. In comparison with equilibrium bosonic fluids, polaritonic condensates possess multiple peculiarities that make them behave differently from well-known textbook examples. One such peculiarity is the presence of dark excitons which are created by the pump together with optically-active particles. They can considerably affect the spectrum of elementary excitations of the condensate and hence change its superfluid properties. Here, we theoretically analyze …
Redfield theory provides a closed kinetic description of a quantum system in weak contact with a very dense reservoir. Landau-Zener theory does the same for a time-dependent driven system in contact with a sparse reservoir. Using a simple model, we analyze the validity of these two theories by comparing their predictions with exact numerical results. We show that despite their a priori different range of validity, these two descriptions can give rise to an identical quantum master equation. Both theories can be used for a nonequilibrium thermodynamic description which we show is consistent wit…
