To study the full counting statistics of quantum heat transfer in a driven nonequilibrium spin-boson model, we develop a generalized nonequilibrium polaron-transformed Redfield equation with an auxiliary counting field. This enables us to study the impact of qubit-bath coupling ranging from weak to strong regimes. Without external modulations, we observe maximal values of both steady state heat flux and noise power at moderate coupling regimes, below which we find those two transport quantities are enhanced by the finite qubit energy bias. With external modulations, the geometric-phase-induced heat flux shows monotonic decrease as increasing the qubit-bath coupling at zero qubit energy bias (without bias). While under finite qubit energy bias (with bias), the geometric-phase-induced heat flux exhibits an interesting reversal behavior in strong coupling regime. Our results unify the seemingly contradictory results in weak and strong qubit-bath coupling regimes, and provide detailed dissections for the quantum fluctuation of nonequilibrium heat transfer.
The time dependent full counting statistics of charge transport through an interacting quantum junction is evaluated from its generating function, controllably computed with the inchworm Monte Carlo method. Exact noninteracting results are reproduced; then, we continue to explore the effect of electron--electron interactions on the time-dependent charge cumulants, first-passage time distributions and $n$-electron transfer distributions. We observe a crossover in the noise from Coulomb blockade- to Kondo-dominated physics as the temperature is decreased. In addition, we uncover long-tailed spin…
We investigate nonequilibrium energy transfer in a single-site Bose-Hubbard model coupled to two thermal baths. By including a quantum kinetic equation combined with full counting statistics, we investigate the steady state energy flux and noise power. The influence of the nonlinear Bose-Hubbard interaction on the transfer behaviors is analyzed, and the nonmonotonic features are clearly exhibited. Particularly, in the strong on-site repulsion limit, the results become identical with the nonequilibrium spin-boson model. We also extend the quantum kinetic equation to study the geometric-phase-in…
We investigate the rectification and negative differential effects of full-counting statistics of conjugate thermal spin transport in a spin Seebeck engine. The engine is made by an electron/magnon interface diode driven by a temperature bias, of which the scaled cumulant generating function is formulated in the framework of nonequilibrium Green's function. The strongly fluctuating interfacial electron density of states induced by quantum dot is responsible for these intriguing properties. This work is relevant for designing efficient spin caloritronic engine and can broaden our view in nonequ…
We investigate the nonequilibrium quantum heat transfer in a triangle-coupled spin-boson system within a three-terminal setup. By including the nonequilibrium noninteracting blip approximation approach combined with the full counting statistics, we analytically obtain the steady state populations and heat currents. The negative differential thermal conductance and giant heat amplification factor are clearly observed at strong qubit-bath coupling. %and the heat amplification is dramatically suppressed in the moderate coupling regime. Moreover, the strong interaction between the gating qubit and…
We investigate the quantum thermal transistor effect in nonequilibrium three-level systems by applying the polaron transformed Redfield equation combined with full counting statistics. The steady state heat currents are obtained via this unified approach over a wide region of system-bath coupling, and can be analytically reduced to the Redfield and nonequilibrium noninteracting blip approximation results in the weak and strong coupling limits, respectively. A giant heat amplification phenomenon emerges in the strong system-bath coupling limit, where transitions mediated by the middle thermal b…
We expand the standard thermodynamic framework of a system coupled to a thermal reservoir by considering a stream of independently prepared units repeatedly put into contact with the system. These units can be in any nonequilibrium state and interact with the system with an arbitrary strength and duration. We show that this stream constitutes an effective resource of nonequilibrium free energy and identify the conditions under which it behaves as a heat, work or information reservoir. We also show that this setup provides a natural framework to analyze information erasure ("Landauer's principl…
The coupling of the charge carriers passing through a molecule bridging two bulky conductors with local vibrational modes of the molecule, gives rise to distinct features in the electronic transport properties on one hand, and to nonequilibrium features in the vibrations' properties, e.g., their population, on the other. Here we explore theoretically a generic model for a molecular junction biased by an arbitrary dc voltage in the weak-coupling regime. We analyze the signature of the electron-vibration interaction on the full-counting statistics of the current fluctuations (i.e., the cumulant …
Time-dependent driving influences the quantum and thermodynamic fluctuations of a system, changing the familiar physical picture of electronic noise which is an important source of information the about microscopic mechanism of quantum transport. Giving access to all cumulants of the current, the full counting statistics (FCS) is the powerful theoretical method to study fluctuations in nonequilibrium quantum systems. In this paper, we propose the application of FCS to consider periodic driven junctions. The combination of Floquet theory for time dynamics and nonequilibrium counting-field Green…
We develop and test a computational framework to study heat exchange in interacting, nonequilibrium open quantum systems. Our iterative full counting statistics path integral (iFCSPI) approach extends a previously well-established influence functional path integral method, by going beyond reduced system dynamics to provide the cumulant generating function of heat exchange. The method is straightforward; we implement it for the nonequilibrium spin boson model to calculate transient and long-time observables, focusing on the steady-state heat current flowing through the system under a temperatur…
Models of nonequilibrium quantum transport underpin all modern electronic devices, from the largest scales to the smallest. Past simplifications such as coarse graining and bulk self-averaging served well to understand electronic materials. Such particular notions become inapplicable at mesoscopic dimensions, edging towards the truly quantum regime. Nevertheless a unifying thread continues to run through transport physics, animating the design of small-scale electronic technology: microscopic conservation and nonequilibrium dissipation. These fundamentals are inherent in quantum transport and …
We report the investigation of full-counting statistics (FCS) of transferred charge and spin in the transient regime where the connection between central scattering region (quantum dot) and leads are turned on at $t=0$. A general theoretical formulation for the generating function (GF) is presented using a nonequilibrium Green's function approach for the quantum dot system. In particular, we give a detailed derivation on how to use the method of path integral together with nonequilibrium Green's function technique to obtain the GF of FCS in electron transport systems based on the two-time quan…
We study the full counting statistics (FCS) of electron tunneling through a multi-terminal quantum dot in the Kondo regime within the slave-boson mean field theory. By employing the A.O. Gogolin and A. Komnik's method of calculating the FCS generating function based on the nonequilibrium Green's function [Phys. Rev. B {\bf 73}, 195301 (2006)], we obtain the counting field $λ$-dependent self-consistent equations for the mean values of the slave-boson fields and the explicit expression for the derivative of the adiabatic potential of the system with respect to the counting fields. Performing per…
Phase transitions occur in a wide range of physical systems and are characterized by the abrupt change of a physical observable in response to the variation of an external control parameter. Phase transitions are not restricted to equilibrium situations but can also be found in nonequilibrium settings, both for classical and quantum mechanical systems. Here, we investigate a nonequilibrium phase transition in a single-electron micromaser consisting of a microwave cavity that is driven by the electron transport in a double quantum dot. For weak electron-photon couplings, only a tiny fraction of…
We develop a general approach to nonequilibrium nanostructures formed by one-dimensional channels coupled by tunnel junctions and/or by impurity scattering. The formalism is based on nonequilibrium version of functional bosonization. A central role in this approach is played by the Keldysh action that has a form reminiscent of the theory of full counting statistics. To proceed with evaluation of physical observables, we assume the weak-tunneling regime and develop a real-time instanton method. A detailed exposition of the formalism is supplemented by two important applications: (i) tunneling i…
We present a hierarchical quantum master equation (HQME) approach, which allows the numerically exact evaluation of higher-order current cumulants in the framework of full counting statistics for nonequilibrium charge transport in nanosystems. The novel methodology is exemplarily applied to a model of vibrationally coupled electron transport in a molecular nanojunction. We investigate the influence of cotunneling on avalanche-like transport, in particular in the nonresonant transport regime, where we find that inelastic cotunneling acts as trigger process for resonant avalanches. In this regim…
We review connections between the cumulant generating function of full counting statistics of particle number and the Rényi entanglement entropy. We calculate these quantities based on the fermionic and bosonic path-integral defined on multiple Keldysh contours. We relate the Rényi entropy with the information generating function, from which the probability distribution function of self-information is obtained in the nonequilibrium steady state. By exploiting the distribution, we analyze the information content carried by a single bosonic particle through a narrow-band quantum communication ch…
We present a theory of modified reduced dynamics in the presence of counting fields. Reduced dynamics techniques are useful for describing open quantum systems at long emergent timescales when the memory timescales are short. However, they can be difficult to formulate for observables spanning the system and its environment, such as those characterizing transport properties. A large variety of mixed system--environment observables, as well as their statistical properties, can be evaluated by considering counting fields. Given a numerical method able to simulate the field-modified dynamics over…
We investigate theoretically and experimentally the full counting statistics of bidirectional single-electron tunneling through a double quantum dot in a GaAs/GaAlAs heterostructure and compare with predictions of the fluctuation theorem (FT) for Markovian stochastic processes. We observe that the quantum point contact electrometer used to study the transport induces nonequilibrium shot noise and dot-level fluctuations and strongly modifies the tunneling statistics. As a result, the FT appears to be violated. We show that it is satisfied if the back-action of the electrometer is taken into acc…
We apply a recently developed 1/(N-1) expansion to the full counting statistics for the N-fold degenerate Anderson impurity model in the Kondo regime. This approach is based on the perturbation theory in the Coulomb interaction U and is different from the conventional large N theories, such as the usual 1/N expansion and non-crossing approximation. We have confirmed that the calculations carried out up to order 1/(N-1)^2 agree closely with those of the numerical renormalization group at N=4, where the degeneracy is still not so large. This ensures the applicability of our approach for N>4. We …
We investigate the full counting statistics of a single quantum dot strongly coupled to a local phonon and weakly tunnel-connected to two metallic electrodes. By employing the generalized nonequilibrium Green function method and the Lang-Firsov transformation, we derive an explicit analytical formula for the cumulant generating function, which makes one to be able to identify distinctly the elastic and inelastic contributions to the current and zero-frequency shot noise. We find that at zero temperature, the inelastic effect causes upward steps in the current and downward jumps in the noise at…
We analyze the effects of a distortion of the nuclear potential of a molecular quantum dot (QD), as well as a shift of its equilibrium position, on nonequilibrium-vibration-assisted tunneling through the QD with a single level ($ε_d$) coupled to the vibrational mode. For this purpose, we derive an explicit analytical expression for the Franck-Condon (FC) factor for a displaced-distorted oscillator surface of the molecule and establish rate equations in the joint electron-phonon representation to examine the current-voltage characteristics and zero-frequency shot noise, and skewness as well. Ou…
Full counting statistics of electron transport is a powerful diagnostic tool for probing the nature of quantum transport beyond what is obtainable from the average current or conductance measurement alone. In particular, the non-Markovian dynamics of quantum dot molecule plays an important role in the nonequilibrium electron tunneling processes. It is thus necessary to understand the non-Markovian full counting statistics in a quantum dot molecule. Here we study the non-Markovian full counting statistics in two typical quantum dot molecules, namely, serially coupled and side-coupled double qua…
Progress in experimental techniques at nanoscale made measurements of noise in molecular junctions possible. These data are important source of information not accessible through average flux measurements. Emergence of optoelectronics, recently shown possibility of strong light-matter couplings, and developments in the field of quantum thermodynamics are making counting statistics measurements of even higher importance. Theoretical methods for noise evaluation in first principles simulations can be roughly divided into approaches applicable in the case of weak intra-system interactions, and th…
This review deals with the nonequilibrium Green's function (NEGF) method applied to the problems of energy transport due to atomic vibrations (phonons), primarily for small junction systems. We present a pedagogical introduction to the subject, deriving some of the well-known results such as the Laudauer-like formula for heat current in ballistic systems. The main aim of the review is to build the machinery of the method so that it can be applied to other situations, which are not directly treated here. In addition to the above, we consider a number of applications of NEGF, not in routine mode…
We study the full-counting statistics of charges transmitted through a single-level quantum dot weakly coupled to a local Einstein phonon which causes fluctuations in the dot energy. An analytic expression for the cumulant generating function, accurate up to second order in the electron-phonon coupling and valid for finite voltages and temperatures, is obtained in the extended wide-band limit. The result accounts for nonequilibrium phonon distributions induced by the source-drain bias voltage, and concomitantly satisfies the fluctuation theorem. Extending the counting field to the complex plan…
We present a method, based on characterizing efficiency fluctuations, to asses the performance of nanoscale thermoelectric junctions. This method accounts for effects typically arising in small junctions, namely, stochasticity in the junction's performance, quantum effects, and nonequilibrium features preventing a linear response analysis. It is based on a nonequilibrium Green's function (NEGF) approach, which we use to derive the full counting statistics (FCS) for heat and work, and which in turn allows us to calculate the statistical properties of efficiency fluctuations. We simulate the lat…
We propose to investigate the full counting statistics of nonequilibrium spin transport with an ultracold atomic quantum gas. The setup makes use of the spin control available in atomic systems to generate spin transport induced by an impurity atom immersed in a spin-imbalanced two-component Fermi gas. In contrast to solid-state realizations, in ultracold atoms spin relaxation and the decoherence from external sources is largely suppressed. As a consequence, once the spin current is turned off by manipulating the internal spin degrees of freedom of the Fermi system, the nonequilibrium spin pop…
We analyze the nonequilibrium transport properties of a parallel double quantum dot in terms of its full counting statistics (FCS). The parameters of the setup are assumed to be such that both subsystems are driven into the Kondo regime. After a series of transformations the Hamiltonian is then mapped onto a Majorana resonant level model, which effectively describes the Toulouse point of the respective double impurity two-terminal Kondo model. Its FCS is then obtained at arbitrary constellation of voltage, temperature, and local magnetic fields. We identify two different transport processes co…
We present a theoretical investigation for the full counting statistics of the Andreev tunneling through a quantum dot (QD) embedded between superconducting (SC) and normal leads in the presence of a strong on-site electron-phonon interaction using nonequilibrium Green function method. For this purpose, we generalize the dressed tunneling approximation (DTA) recently developed in dealing with inelastic tunneling in a normal QD system to the Andreev transport issue, which takes account of vibrational effect in evaluation of electronic tunneling self energy in comparison with other simple approa…
We investigate the full-counting statistics (FCS) of energy transport carried by electrons in molecular junctions for the Anderson-Holstein model in the polaronic regime. Using two-time quantum measurement scheme, generating function (GF) for the energy transport is derived and expressed as a Fredholm determinant in terms of Keldysh nonequilibrium Green's function in the time domain. Dressed tunneling approximation is used in decoupling the phonon cloud operator in the polaronic regime. This formalism enables us to analyze the time evolution of energy transport dynamics after a sudden switch-o…
For open systems described by the quantum master equation (QME), we investigate the excess entropy production under quasistatic operations between nonequilibrium steady states. The average entropy production is composed of the time integral of the instantaneous steady entropy production rate and the excess entropy production. We propose to define average entropy production rate using the average energy and particle currents, which are calculated by using the full counting statistics with QME. The excess entropy production is given by a line integral in the control parameter space and its integ…
Entanglement plays a prominent role in the study of condensed matter many-body systems: Entanglement measures not only quantify the possible use of these systems in quantum information protocols, but also shed light on their physics. However, exact analytical results remain scarce, especially for systems out of equilibrium. In this work we examine a paradigmatic one-dimensional fermionic system that consists of a uniform tight-binding chain with an arbitrary scattering region near its center, which is subject to a DC bias voltage at zero temperature. The system is thus held in a current-carryi…
We analyze the nonequilibrium transport properties of a quantum dot with a harmonic degree of freedom (Holstein phonon) coupled to metallic leads, and derive its full counting statistics (FCS). Using the Lang-Firsov (polaron) transformation, we construct a diagrammatic scheme to calculate the cumulant generating function. The electron-phonon interaction is taken into account exactly, and the employed approximation represents a summation of a diagram subset with respect to the tunneling amplitude. By comparison to Monte Carlo data the formalism is shown to capture the basic properties of the st…
We present a method for calculating the full counting statistics of a nonequilibrium quantum system based on the propagator noncrossing approximation (NCA). This numerically inexpensive method can provide higher order cumulants for extended parameter regimes, rendering it attractive for a wide variety of purposes. We compare NCA results to Born-Markov quantum master equations (QME) results to show that they can access different physics, and to numerically exact inchworm quantum Monte-Carlo data to assess their validity. As a demonstration of its power, the NCA method is employed to study the i…
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…
A full quantum theory beyond the mean-field regime is developed for an exciton polariton condensate, to gain a complete understanding of quantum fluctuations. We find analytical solution for the polariton density matrix, showing the polariton nonlinearity causing fast relaxation correlated with the pump so as to yield the condensation at threshold. Increasing the pump intensity, a nonequilibrium phase transition towards the condensation of lower polaritons emerges, with a statistics transiting from a thermal, through a super-Poissonian and to a nonclassical distribution beyond the understandin…
We provide a thermodynamically consistent description of energy, charge and spin transfers in a thermoelectric quantum-dot spin valve in the collinear configuration based on nonequilibrium Green's function and full counting statistics. We use the fluctuation theorem symmetry and the concept of entropy production to characterize the efficiency with which thermal gradients can transduce charges or spins against their chemical potentials, arbitrary far from equilibrium. Close to equilibrium, we recover the Onsager reciprocal relations and the connection to linear response notions of performance s…
We investigate the full counting statistics of extreme-near-field radiative heat transfer using nonequilibrium Green's function formalism. In the extreme near field, the electron-electron interactions between two metallic bodies dominate the heat transfer process. We start from a general tight-binding electron Hamiltonian and obtain a Levitov-Lesovik like scaled cumulant generating function (SCGF) using random phase approximation to deal with electron-electron interaction. The expressions of heat current and its fluctuation (second cumulant) are obtained from the SCGF. The fluctuation symmetry…
We present a {\it nonequilibrium nonperturbative} field theory for the Kondo effect in strongly interacting quantum dots at finite temperatures. Unifying the slave-boson representation with the Keldysh field integral an effective Keldysh action is derived and explored in the vicinity of the zero slave-bosonic field configuration. The theory properly reflects the essential features of the Kondo physics and at the same time significantly simplifies a field-theoretic treatment of the phenomenon, avoiding complicated saddle point analysis or 1/N expansions, used so far. Importantly, our theory adm…
