The optically induced polarization of localized electron spins in an ensemble of quantum dots (QDs) dephases due to the interaction with the surrounding nuclear spins. Despite this dephasing, the spins in the QDs can be controlled to respond coherently by applying periodic laser pulses, leading to a revival of the spin polarization before each pulse. This effect, known as spin mode locking, strongly depends on an emerging selection of certain polarizations of the nuclear spin bath which is driven to a steady state far from equilibrium. We investigate the influence of the nuclear composition in In$_x$Ga$_{1-x}$As QDs on this nonequilibrium behavior and demonstrate that nuclear magnetic resonances (NMR) appear as very sharp minima in the magnetic field dependence of the revival amplitude. This suggests a novel kind of NMR spectroscopy.
We present a theory of zero-bias anomalies and dephasing rates for a Coulomb-blockaded quantum dot, driven out of equilibrium by coupling to voltage biased source and drain leads. We interpret our results in terms of the statistics of voltage fluctuations in the system.
Resonant electron transport through a mesoscopic region (quantum dot or single molecule) with electron-phonon interaction is considered at finite voltage. In this case the standard Landauer-Büttiker approach cannot be applied. Using the nonequilibrium Green function method we show that due to a nonequilibrium distribution function of electrons in the mesoscopic region, the inelastic scattering rate and spectral function of the dot become functions of the voltage and have to be calculated self-consistently.
Spin entanglement between two spatially separated electrons can be generated in nonequilibrium interacting quantum dots, coherently coupled to a common lead. In this system entangled two-electron states develop which are Werner states with an imbalance between singlet and triplet probabilities. We propose a multi-terminal, multiply-connected setup for the generation and detection of this imbalance. In particular, we identify a regime in which the formation of spin entanglement leads to a cancellation of Aharonov-Bohm oscillations.
We study the spin dynamics in charged quantum dots in the situation where the resident electron is coupled to only about 200 nuclear spins and where the electron spin splitting induced by the Overhauser field does not exceed markedly the spectral broadening. The formation of a dynamical nuclear polarization as well as its subsequent decay by the dipole-dipole interaction is directly resolved in time. Because not limited by intrinsic nonlinearities, almost complete nuclear polarization is achieved, even at elevated temperatures. The data suggest a nonequilibrium mode of nuclear polarization, di…
By nonperturbatively solving the nonequilibrium Anderson two-impurity model with the hierarchical equations of motion approach, we report a robust ferromagnetic (FM) phase in series-coupled double quantum dots, which can suppress the antiferromagnetic (AFM) phase and dominate the phase diagram at finite bias and detuning energy in the strongly correlated limit. The FM exchange interaction origins from the passive parallel spin arrangement caused by the Pauli exclusion principle during the electrons transport. At very low temperature, the Kondo screening of the magnetic moment in the FM phase i…
We develop a theory for charge and spin current between two canted magnetic leads flowing through a quantum dot with an arbitrary local interaction. For a noncollinear magnetic configuration, we calculate equilibrium and nonequilibrium current biased by voltage or temperature difference or pumped by magnetic dynamics. We are able to explicitly separate the equilibrium and nonequilibrium contributions to the current, both of which can be written in terms of the full retarded Green's function on the dot. Taking the specific example of a single-level quantum dot with a large on-site Coulomb inter…
We investigate the transient nonequilibrium dynamics of a molecular junction biased by a finite voltage and strongly coupled to internal vibrational degrees of freedom. Using two different, numerical exact techniques, diagrammatic Monte Carlo and the multilayer multiconfiguration time-dependent Hartree method, we show that the steady state current through the junction may depend sensitively on the initial preparation of the system, thus revealing signatures of bistability. The influence of the bias voltage and the transient dynamics on the phenomenon of bistability is analyzed. Furthermore, a …
We theoretically investigate the full time evolution of a nonequilibrium double quantum dot structure from initial conditions corresponding to different product states (no entanglement between dot and lead) to a nonequilibrium steady state. The structure is described by a two-level spinless Anderson model where the levels are coupled to two leads held at different chemical potentials. The problem is solved by a numerically exact hierarchical master equation technique and the results are compared to approximate ones obtained from Born-Markov theory. The methods allow us to study the time evolut…
Large-scale simulations of the spin dynamics in quantum dots subjected to trains of periodic laser pulses enable us to describe and understand related experiments. By comparing the data for different models to experimental results, we gain an improved understanding of the relevant physical mechanisms. Using sophisticated numerical approaches and an efficient implementation combined with extrapolation arguments, nonequilibrium stationary states are reached for parameter ranges close to the ones in real experiments. With the help of high performance computing, we can tune the experimental parame…
We develop a mapping of quantum steady-state nonequilibrium to an effective equilibrium and solve the problem using a quantum simulation technique. A systematic implementation of the nonequilibrium boundary condition in steady-state is made in the electronic transport on quantum dot structures. This formulation of quantum manybody problem in nonequilibrium enables the use of existing numerical quantum manybody techniques. The algorithm coherently demonstrates various transport behaviors from phonon-dephasing to I-V staircase and phonon-assisted tunneling.
We report on capacitance-voltage spectroscopy of self-assembled InAs quantum dots under constant illumination. Besides the electronic and excitonic charging peaks in the spectrum reported earlier, we find additional resonances associated with nonequilibrium state tunneling unseen in C(V) measurements before. We derive a master-equation based model to assign the corresponding quantum state tunneling to the observed peaks. C(V) spectroscopy in a magnetic field is used to verify the model-assigned nonequilibrium peaks. The model is able to quantitatively address various experimental findings in C…
We extend a perturbative, nonequilibrium renormalization group approach to multi-orbital systems and apply it for studying transport through two parallel quantum dots coupled electrostatically. In general, the conductance shows pronounced Kondoesque peaks at three voltages. One of these peaks disappears if, as in some experiments, one of the dots is decoupled from one of the two leads. For an asymmetric coupling to the leads, also negative differential conductances are possible. This is a genuine nonequilibrium effect, accompanying the Kondoesque peaks. Moreover, a criterion to distinguish spi…
Double quantum dots are one of the promising two-state quantum systems for realizing qubits. In the quest of successfully manipulating and reading information in qubit systems, it is of prime interest to control the charge response of the system to a gate voltage, as filled in by the dynamical charge susceptibility. We theoretically study this quantity for a nonequilibrium double quantum dot by using the functional integral approach and derive its general analytical expression. One highlights the existence of two lines of maxima as a function of the dot level energies, each of them being split…
We develop a non-equilibrium theory to describe weak Coulomb blockade effects in open quantum dots. Working within the bosonized description of electrons in the point contacts, we expose deficiencies in earlier applications of this method, and address them using a 1/N expansion in the inverse number of channels. At leading order this yields the self-consistent potential for the charging interaction. Coulomb blockade effects arise as quantum corrections to transport at the next order. Our approach unifies the phase functional and bosonization approaches to the problem, as well as providing a si…
We present a microscopic theory for both equilibrium and nonequilibrium transport properties of coupled double quantum dots (DQD). A general formula for current tunneling through the DQD is derived by the nonequilibrium Green's function method. Using a Hartree-Fock approach, effects of multi-level coupling and nonequilibrium electron distributions in resonant tunneling are considered. We find that the peak in the resonant tunneling current through two symmetric dots will split only when the inter-dot coupling is stronger than dot-lead coupling. We predict that population inversion can be achie…
We develop a perturbative renormalization-group method in real time to describe nonequilibrium properties of discrete quantum systems coupled linearly to an environment. We include energy broadening and dissipation and develop a cutoff-independent formalism. We present quantitatively reliable results for the nonlinear conductance in the mixed-valence and empty-orbital regime of the nonequilibrium Anderson impurity model with finite on-site Coulomb repulsion.
We analyze the decoherence of charge states in double quantum dots due to cotunneling. The system is treated using the Bloch-Redfield generalized master equation for the Schrieffer-Wolff transformed Hamiltonian. We show that the decoherence, characterized through a relaxation $τ_{r}$ and a dephasing time $τ_ϕ$, can be controlled through the external voltage and that the optimum point, where these times are maximum, is not necessarily in equilibrium. We outline the mechanism of this nonequilibrium-induced enhancement of lifetime and coherence. We discuss the relevance of our results for recent …
We propose schemes for generating spatially-separated spin entanglement in systems of two quantum dots with onsite Coulomb repulsion weakly coupled to a joint electron reservoir. An enhanced probability for the formation of spin entanglement is found in nonequilibrium situations with one extra electron on each dot, either in the transient state after rapid changes of the gate voltage, or in the steady state with applied bias voltage. In both cases so-called Werner states with spin singlet fidelity exceeding 1/2 are generated, which indicates entanglement.
We extend the time-dependent Gutzwiller variational approach, recently introduced by Schirò and Fabrizio, Phys. Rev. Lett. 105 076401 (2010), to impurity problems. Furthermore, we derive a consistent theory for the steady state, and show its equivalence with the previously introduced nonequilibrium steady-state extension of the Gutzwiller approach. The method is shown to be able to capture dissipation in the leads, so that a steady state is reached after a sufficiently long relaxation time. The time-dependent method is applied to the single orbital Anderson impurity model at half-filling, mode…
Quantum tunneling dominates coherent transport at low temperatures in many systems of great interest. In this work we report a many--body tunneling (MBT), by nonperturbatively solving the Anderson multi-impurity model, and identify it a fundamental tunneling process on top of the well--acknowledged sequential tunneling and cotunneling. We show that the MBT involves the dynamics of doublons in strongly correlated systems. Proportional to the numbers of dynamical doublons, the MBT can dominate the off--resonant transport in the strongly correlated regime. A $T^{3/2}$--dependence of the MBT curre…
Correlations in fluids in nonequilibrium steady states are long ranged. Hence, finite-size effects have important consequences in the nonequilibrium thermodynamics of fluids. One consequence is that nonequilibrium temperature fluctuations induce nonequilibrium Casimir-like pressures proportional to the square of the temperature gradient. Hence, fluctuations cause a breakdown of the concept of local thermal equilibrium. Furthermore, transport coefficients become dependent on boundary conditions and on gravity. Thus nonequilibrium fluctuations affect some traditional concepts in nonequilibrium t…
Electron transport through a strongly correlated quantum dot (QD) embedded in an Aharonov-Bohm (AB) ring is investigated with the aid of the finite-U slave-boson mean-field (SBMF) approach extended to nonequilibrium regime. A nonequilibrium steady state (NESS) of the mean-field Hamiltonian is constructed with the aid of the C*-algebraic approach for studying infinitely extended systems. In the linear response regime, the Fano-Kondo resonances and AB oscillations of the conductance obtained from the SBMF approach are in good agreement with those from the numerical renormalization group techniqu…
Double quantum dots can provide an experimental realization of the 2 impurity Kondo model which exhibits a non-Fermi liquid quantum critical point (QCP) at a special value of its parameters. We generalize our recent study of double quantum dots in series \cite{Sela08} to a parallel configuration with an Aharonov-Bohm flux. We present an exact universal result for the finite temperature and finite voltage conductance $G[V,T]$ along the crossover from the QCP to the low energy Fermi liquid phase. Compared to the series configuration, here generically $G[V,T] \ne G[-V,T]$, leading to current rect…
The interplay between interference effects and electron-electron interactions in electron transport through an interacting double quantum dot system is investigated using a hierarchical quantum master equation approach which becomes exact if carried to infinite order and converges well if the temperature is not too low. Decoherence due to electron-electron interactions is found to give rise to pronounced negative differential resistance, enhanced broadening of structures in current-voltage characteristics and an inversion of the electronic population. Dependence on gate voltage is shown to be …
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…
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 a double quantum dot in the regime where each dot carries a spin-1/2. This system is described by the 2-impurity Kondo model, having a non-Fermi liquid fixed point for a critical value of the inter-impurity coupling. The Hamiltonian describing the vicinity of the critical point, including the relevant potential scattering perturbations, can be cast in quadratic form. This allows us to predict a universal scaling function for the finite temperature nonlinear conductance along the crossover from the critical point to the surrounding stable fixed points.
We extend the imaginary-time formulation of the equilibrium quantum many-body theory to steady-state nonequilibrium with an application to strongly correlated transport. By introducing Matsubara voltage, we keep the finite chemical potential shifts in the Fermi-Dirac function, in agreement with the Keldysh formulation. The formulation is applied to strongly correlated transport in the Kondo regime using the quantum Monte Carlo method.
By mapping steady-state nonequilibrium to an effective equilibrium, we formulate nonequilibrium problems within an equilibrium picture where we can apply existing equilibrium many-body techniques to steady-state electron transport problems. We study the analytic properties of many-body scattering states, reduce the boundary condition operator in a simple form and prove that this mapping is equivalent to the correct linear-response theory. In an example of infinite-U Anderson impurity model, we approximately solve for the scattering state creation operators, based on which we derive the bias op…
The concept of temperature in nonequilibrium thermodynamics is an outstanding theoretical issue. We propose an energy repartition principle that leads to a spectral (mode-dependent) temperature in steady-state nonequilibrium systems. The general concepts are illustrated by analytic solutions of the classical Heisenberg spin chain connected to Langevin heat reservoirs with arbitrary temperature profiles. Gradients of external magnetic fields are shown to localize spin waves in a Wannier-Zeemann fashion, while magnon interactions renormalize the spectral temperature. Our generic results are appl…
The effect of electron-electron scattering on the equilibrium properties of few-electron quantum dots is investigated by means of nonequilibrium Green's functions theory. The ground and equilibrium state is self-consistently computed from the Matsubara (imaginary time) Green's function for the spatially inhomogeneous quantum dot system whose constituent charge carriers are treated as spin-polarized. To include correlations, the Dyson equation is solved, starting from a Hartree-Fock reference state, within a conserving (second order) self-energy approximation where direct and exchange contribut…
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…
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 develop a low-energy nonequilibrium field theory for weakly interacting quantum dots. The theory is based on the Keldysh field integral in the spin channel of the quantum dot described by the single impurity Anderson Hamiltonian. The effective Keldysh action is a functional of the Hubbard-Stratonovich magnetization field decoupling the quantum dot spin channel. We expand this action up to the second order with respect to the magnetization field, which allows to describe nonequilibrium interacting quantum dots at low temperatures and weak electron-electron interactions,up to the contacts-dot…
We develop an exact non-perturbative framework to compute steady-state properties of quantum-impurities subject to a finite bias. We show that the steady-state physics of these systems is captured by nonequilibrium scattering eigenstates which satisfy an appropriate Lippman-Schwinger equation. Introducing a generalization of the equilibrium Bethe-Ansatz - the Nonequilibrium Bethe-Ansatz (NEBA), we explicitly construct the scattering eigenstates for the Interacting Resonance Level model and derive exact, nonperturbative results for the steady-state properties of the system.
We examine the recently proposed imaginary-time formulation for strongly correlated steady-state nonequilibrium for its range of validity and discuss significant improvements in the analytic continuation of the Matsubara voltage as well as the fermionic Matsubara frequency. The discretization error in the conventional Hirsch-Fye algorithm has been compensated in the Fourier transformation with reliable small frequency behavior of self-energy. Here we give detailed discussions for generalized spectral representation ansatz by including high order vertex corrections and its numerical analytic co…
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…
Nonperturbative dynamic theory has a particular advantage in studying the transport in a quantum impurity system in a steady state. Here, we develop a new approach for obtaining the retarded Green's function expressed in resolvent form. We use the Heisenberg picture to facilitate dynamic theory and propose a new systematic method of collecting the basis vectors spanning the Liouville space, which is the most crucial step in obtaining the resolvent Green's function. We obtain all the linearly independent basis vectors for studying the single-impurity Anderson models with one and two reservoirs.…
We investigate the nonequilibrium response of quasiperiodic systems to boundary driving. In particular we focus on the Aubry-André-Harper model at its metal-insulator transition and the diagonal Fibonacci model. We find that opening the system at the boundaries provides a transparent and experimentally viable technique to probe its underlying fractality, which is reflected in the fractal spatial dependence of simple observables (such as magnetization) in the nonequilibrium steady state. We also find that the dynamics in the nonequilibrium steady state depends on the length of the chain chosen:…
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 study how translationally invariant couplings of many-particle systems and nonequilibrium baths can be used to rectify particle currents, for which we consider minimal setups to realize bath-induced currents in nonequilibrium steady states of one-dimensional open fermionic systems. We first analyze dissipative dynamics associated with a nonreciprocal Lindblad operator and identify a class of Lindblad operators that are sufficient to acquire a unidirectional current. We show that unidirectional particle transport can in general occur when a Lindblad operator is reciprocal provided that the i…
Quantum dots play a promising role in the development of novel optical and biosensing devices. In this study, we investigated steady-state and time-dependent luminescence properties of InGaP/ZnS core/shell colloidal quantum dots in a solution phase at room temperature. The steady state experiments exhibited an emission maximum at 650 nm with full width at half maximum of ~ 85 nm, and strong first-excitonic absorption peak at 600 nm. The time-resolved luminescence measurements depicted a bi-exponential decay profile with lifetimes of τ1\sim 47 ns and τ 2\sim 142 ns at the emission maximum. Addi…
