A quantum dissipation theory is formulated in terms of hierarchically coupled equations of motion for an arbitrary electronic system coupled with grand canonical Fermion bath ensembles. The theoretical construction starts with the second--quantization influence functional in path integral formalism, in which the Fermion creation and annihilation operators are represented by Grassmann variables. Time--derivatives on influence functionals are then performed in a hierarchical manner, on the basis of calculus--on--path--integral algorithm. Both the multiple--frequency--dispersion and the non-Markovian reservoir parametrization schemes are considered for the desired hierarchy construction. The resulting formalism is in principle exact, applicable to interacting systems, with arbitrary time-dependent external fields. It renders an exact tool to evaluate various transient and stationary quantum transport properties of many-electron systems. At the second--tier truncation level the present theory recovers the real--time diagrammatic formalism developed by Schön and coworkers. For a single-particle system, the hierarchical formalism terminates at the second tier exactly, and the Landuer--Büttiker's transport current expression is readily recovered.
We propose a scheme for deterministic generation and long-term stabilization of entanglement between two electronic spin qubits confined in spatially separated quantum dots. Our approach relies on an electronic quantum bus, consisting either of quantum Hall edge channels or surface acoustic waves, that can mediate long-range coupling between localized spins over distances of tens of micrometers. Since the entanglement is actively stabilized by dissipative dynamics, our scheme is inherently robust against noise and imperfections.
We report an observation of charge conservation breaking in a model study of electronic current noise of transport through a dissipative double quantum dot within generalized master equation formalism. We study the current noise through a double quantum dot coupled to two electronic leads in the high bias limit and a dissipative heat bath in the weak coupling limit. Our calculations are based on the solution of a Markovian generalized master equation. Zero-frequency component of the current noise calculated within the system, i.e., between the two dots, via the quantum regression theorem exhib…
We theoretically investigate the evolution of the peak height of an energy resolved electronic wave-packets ballistically propagating along integer quantum Hall edge channels at filling factor $ν=2$. This is ultimately related to the elastic scattering amplitude for the fermionic excitations evaluated at different injection energy. We investigate this quantity assuming a short range capacitive coupling between the edges. Moreover, we also take into account phenomenologically the possibility of energy dissipation towards additional degrees of freedom both linear and quadratic in the injection e…
We present a theory for the dissipation of electronic spins trapped in quantum dots due to their coupling to the host lattice acoustic phonon modes. Based on the theory of dissipative two level systems for the spin dynamics, we derive a relation between the spin dissipative bath, the electron confinement, and the electron-phonon interaction. We find that there is an energy scale, typically smaller than the electronic lateral confinement energy, which sets the boundary between different dissipative regimes .
We have studied the dissipative dynamics of a driven electronic spin trapped in a quantum dot. We consider the dissipative mechanism as due to the indirect coupling of the electronic spin to acoustic phonons via the spin-orbit/electron-phonon couplings. Using an effective spectral function of the dissipative phonon bath, we evaluated the expectation values of the spin components through the Bloch-Redfield theory. We show that due to a sharp bath resonance present in the effective spectral function, with typical energy much smaller than the electronic confinement energy, the dissipative spin ha…
We extend a standard stochastic theory to study open quantum systems coupled to generic quantum environments including the three fundamental classes of noninteracting particles: bosons, fermions and spins. In this unified stochastic approach, the generalized stochastic Liouville equation (SLE) formally captures the exact quantum dissipations when noise variables with appropriate statistics for different bath models are applied. Anharmonic effects of a non-Gaussian bath are precisely encoded in the bath multi-time correlation functions that noise variables have to satisfy. Staring from the SLE,…
We investigate the influence of a dissipative environment which effectively comprises the effects of counterions and hydration shells, on the transport properties of short \DNA wires. Their electronic structure is captured by a tight-binding model which is embedded in a bath consisting of a collection of harmonic oscillators. Without coupling to the bath a temperature independent gap opens in the electronic spectrum. Upon allowing for electron-bath interaction the gap becomes temperature dependent. It increases with temperature in the weak-coupling limit to the bath degrees of freedom. In the …
Utilizing the non-coherent quantum transport formalism, we investigate thermoelectric performance across dissipative superlattice configurations in the linear regime of operation. Using the {\it{dissipative}} non-equilibrium Green's function formalism coupled self-consistently with the Poisson's equation, we report an enhanced figure of merit $zT$ in the multi-barrier device designs. The proposed enhancement, we show, is a result of a drastic reduction in the electronic thermal conductance triggered via non-coherent transport. We show that a maximum $zT$ value of 18 can be achieved via the inc…
The anomalous behavior of electron induced phonon transport is investigated using an Anderson-Holstein based dissipative quantum dot setup under two relevant bias situations: (a) a voltage bias in the absence of an electronic temperature gradient and (b) an electronic temperature gradient at zero voltage. It is shown that the direction of phonon transport in the non-linear regime is different in the two cases since the first case facilitates the accumulation of phonons in the dot and the second case leads to the absorption of phonons in the dot. In the linear regime, both the phonon and electr…
A new approach to calculating current-induced forces in charge transport through nanosystems is introduced. Starting from the fully quantum mechanical hierarchical equations of motion formalism, a timescale separation between electronic and vibrational degrees of freedom is used to derive a classical Langevin equation of motion for the vibrational dynamics as influenced by current-induced forces, such as the electronic friction. The resulting form of the friction is shown to be equivalent to previously derived expressions. The numerical exactness of the hierarchical equations of motion approac…
Ultrafast Dissipative Localization of Electronic Energy in AuPt Superlattices
Universität Potsdam（波茨坦大学）；Max Born Institute for Nonlinear Optics and Short Pulse Spectroscopy（马克斯·玻恩非线性光学和短脉冲光谱研究所）；European X-ray Free-Electron Laser Facility（欧洲X射线自由电子激光设施）；Helmholtz-Zentrum Berlin（赫尔姆霍兹柏林中心）；MAX IV Laboratory, Lund University（隆德大学MAX IV实验室）；University of Regensburg（雷根斯堡大学）
Within the hierarchical quantum master equation (HQME) framework, an approach is presented, which allows a numerically exact description of nonequilibrium charge transport in nanosystems with strong electronic-vibrational coupling. The method is applied to a generic model of vibrationally coupled transport considering a broad spectrum of parameters ranging from the nonadiabatic to the adiabatic regime and including both resonant and off-resonant transport. We show that nonequilibrium effects are important in all these regimes. In particular in the off-resonant transport regime, the inelastic c…
We study the non-equilibrium transport properties of a one-dimensional array of dissipative quantum dots. Using the Keldysh formalism, we show that the dots' dissipative nature leads to a spatial variation of the chemical potential, which in disordered arrays, breaks the invariance of the current, I, under bias reversal. Moreover, the array's nanoscopic size results in an algebraic low-temperature dependence of I. Finally, we show that a local Coulomb interaction splits the dots' electronic levels, resulting in a Coulomb blockade, which is softened with increasing dissipation and array size.
The Moore-Read Pfaffian $ν=5/2$ quantum Hall state is a p-wave super-conductor of composite fermions. Small deviations from $ν=5/2$ result in the formation of an array of vortices within this super-conductor, each supporting a Majorana zero mode near its core. Here we consider how tunneling between these cores is reflected in the electronic response to an electric field of non-zero wave vector $\bf q$ and frequency $ω$. We find a mechanism for dissipative transport at frequencies below the $ν=5/2$ gap, and calculate the ${\bf q},ω$ dependence of the dissipative conductivity. The contributions …
Hydrodynamic and viscous effects in electronic liquids are at the focus of much current research. Most intriguing is perhaps the non-dissipative Hall viscosity, which, due to its symmetry-protected topological nature, can help identify complex topological orders. In this work we study the effects of viscosity in general, and Hall viscosity in particular, on the dispersion relation of edge magnetoplasmons in 2D electronic systems. Using an extension of the standard Wiener-Hopf technique we derive a general solution to the problem, accounting for the long-range Coulomb potential. Among other fea…
Valley is a useful degree of freedom for non-dissipative electronics since valley current that can flow even in an insulating material does not accompany electronic current. We use dual-gated bilayer graphene in the Hall bar geometry to electrically control broken inversion symmetry or Berry curvature as well as the carrier density to generate and detect the pure valley current. We find a large nonlocal resistance and a cubic scaling between the nonlocal resistance and the local resistivity in the insulating regime at zero-magnetic field and 70 K as evidence of the pure valley current. The ele…
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…
We employ the Wigner function formalism to simulate partially coherent, dissipative electron transport in biased semiconductor superlattices. We introduce a model collision integral with terms that describe energy dissipation, momentum relaxation, and the decay of spatial coherences (localization). Based on a particle-based solution to the Wigner transport equation with the model collision integral, we simulate quantum electronic transport at 10 K in a GaAs/AlGaAs superlattice and accurately reproduce its current density vs field characteristics obtained in experiment.
Electronic transport through DNA wires in the presence of a strong dissipative environment is investigated. We show that new bath-induced electronic states are formed within the bandgap. These states show up in the linear conductance spectrum as a temperature dependent background and lead to a crossover from tunneling to thermal activated behavior with increasing temperature. Depending on the strength of the electron-bath coupling, the conductance at the Fermi level can show a weak exponential or even an algebraic length dependence. Our results suggest a new environmental-induced transport mec…
We examine the influence of the edge electronic density profile and of dissipation on edge magnetoplasmons in the quantum Hall regime, in a semiclassical calculation. The equilibrium electron density on the edge, obtained using a Thomas-Fermi approach, has incompressible stripes produced by energy gaps responsible for the quantum Hall effect. We find that these stripes have an unobservably small effect on the edge magnetoplasmons. But dissipation, included phenomenologically in the local conductivity, proves to produce significant oscillations in the strength and speed of edge magnetoplasmons …
We study the nonequilibrium dynamics of a mesoscopic metallic ring threaded by a time-dependent magnetic field and coupled to an electronic reservoir. We analyze the relation between the (non-stationary) real-time Keldysh and retarded Green functions and we find that, in the linear response regime with weak heat transfer to the environment, an effective temperature accounts for the modification of the equilibrium fluctuation-dissipation relation. We discuss possible extensions of this analysis.
Time-dependent currents in molecular junctions can be caused by structural fluctuations or interaction with external fields. In this publication, we demonstrate how the hierarchical quantum master equation approach can be used to study time-dependent transport in a molecular junction. This reduced density matrix methodology provides a numerically exact solution to the transport problem including time-dependent energy levels, molecule-lead coupling strengths and transitions between electronic states of the molecular bridge. Based on a representative model, the influence of a time-dependent mole…
Nonadiabatic Dynamics of Molecules Interacting with Metal Surfaces: Extending the Hierarchical Equations of Motion and Langevin Dynamics Approach to Position-Dependent Metal-Molecule Couplings
The dynamics of chaotic systems are, by definition, exponentially sensitive to initial conditions and may appear rather random. In this work, we explore relations between the chaotic dynamics of an observable and the dynamics of information (entropy) contained in this observable, focussing on a disordered metal coupled to a dissipative, e.g. phononic, bath. The chaotic dynamics is characterised by Lyapunov exponents $λ$, the rates of growth of out-of-time order correlators (OTOCs), quantities of the form $\langle[\hat A(t),\hat B(0)]^{2}\rangle\propto\exp(2λt)$, where $\hat A$ and $\hat B$ are…
Intrinsic Hall conductivity, emerging when chiral symmetry is broken, is at the heart of future low energy consumption devices because it can generate non-dissipative charge neutral current. A symmetry breaking state is also induced by electronic correlation even for the centro-symmetric crystalline materials. However, generation of non-dissipative charge neutral current by intrinsic Hall conductivity induced by such spontaneous symmetry breaking is experimentally elusive. Here we report intrinsic Hall conductivity and generation of a non-dissipative charge neutral current in a spontaneous ant…
We develop the hydrodynamical theory of collinear spin currents coupled to magnetization dynamics in metallic ferromagnets. The collective spin density couples to the spin current through a U(1) Berry-phase gauge field determined by the local texture and dynamics of the magnetization. We determine phenomenologically the dissipative corrections to the equation of motion for the electronic current, which consist of a dissipative spin-motive force generated by magnetization dynamics and a magnetic texture-dependent resistivity tensor. The reciprocal dissipative, adiabatic spin torque on the magne…
We investigate the electron (hole) transport through short double-stranded DNA wires in which the electrons are strongly coupled to the specific vibrational modes (vibrons) of the DNA. We analyze the problem starting from a tight-binding model of DNA, with parameters derived from ab-initio calculations, and describe the dissipative transport by equation-of-motion techniques. For homogeneous DNA sequences like Poly- (Guanine-Cytosine) we find the transport to be quasi-ballistic with an effective density of states which is modified by the electron-vibron coupling. At low temperatures the linear …
We study the non-Gaussian dynamics of a quasiclassical electronic circuit inductively coupled to a mesoscopic conductor. Non-Gaussian noise accompanying the nonequilibrium transport through the conductor significantly modifies the steady-state probability density function (PDF) of the flux in the dissipative circuit. We evaluate the quantum correction of the steady-state PDF by incorporating the quantum fluctuation of the circuit. The inverse formula to infer the statistical properties of the non-Gaussian noise from the steady-state PDF is extended to the classical-quantum crossover regime.
The interaction between electronic and vibrational degrees of freedom is an important mechanism in nonequilibrium charge transport through molecular nanojunctions. While adiabatic polaron-type coupling has been studied in great detail, new transport phenomena arise for nonadiabatic coupling scenarios corresponding to a breakdown of the Born-Oppenheimer approximation. Employing the numerically exact hierarchical equations of motion approach, we analyze the effect of nonadiabatic electronic-vibrational coupling on electron transport in molecular junctions considering a series of models with incr…
Many-Body Non-Hermitian Skin Effect with Exact Steady States in the Dissipative Quantum Link Model
Institute for Advanced Study, Tsinghua University（清华大学高等研究院）；Max Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）；Department of Physics, Princeton University（普林斯顿大学物理系）
Nonadiabatic Dynamics of Molecules Interacting with Metal Surfaces: A Quantum-Classical Approach Based on Langevin Dynamics and the Hierarchical Equations of Motion
Topological phase transitions can occur in the dissipative dynamics of a quantum system when the ratio of matrix elements for competing transport channels is varied. Here we establish a relation between such behavior in a class of non-Hermitian quantum walk problems [M. S. Rudner and L. S. Levitov, Phys. Rev. Lett. 102, 065703 (2009)] and nuclear spin pumping in double quantum dots, which is mediated by the decay of a spin-blockaded electron triplet state in the presence of spin-orbit and hyperfine interactions. The transition occurs when the strength of spin-orbit coupling exceeds the strengt…
A novel quantum dynamical method to simulate vibronic reaction dynamics in molecules at metal surfaces is proposed. The method is based on the hierarchical quantum master equation approach and uses a discrete variable representation of the nuclear degrees of freedom in combination with complex absorbing potentials and an auxiliary source term. It provides numerically exact results for a range of models. By taking the coupling to the continuum of electronic states of the surface properly into account, nonadiabatic processes can be described and the effect of electronic friction is included in a…
On the way to solid-state quantum computing, overcoming decoherence is the central issue. In this contribution, we discuss the modeling of decoherence of a superonducting flux qubit coupled to dissipative electronic circuitry. We discuss its impact on single qubit decoherence rates and on the performance of two-qubit gates. These results can be used for designing decoherence-optimal setups.
We investigate experimentally an exotic state of electronic matter obtained by fine-tuning to a quantum critical point (QCP), realized in a spin-polarized resonant level coupled to strongly dissipative electrodes. Several transport scaling laws near and far from equilibrium are measured, and then accounted for theoretically. Our analysis reveals a splitting of the resonant level into two quasi-independent Majorana modes, one strongly hybridized to the leads, and the other tightly bound to the quantum dot. Residual interactions involving these Majorana fermions result in the observation of a st…
The investigation of novel electronic phases in low-dimensional quantum materials demands for the concurrent development of new measurement techniques that combine surface sensitivity with high spatial resolution and high measurement accuracy. We propose a new quantum sensing imaging modality based on superconducting charge qubits to study dissipative charge carrier dynamics with nanometer spatial and high temporal resolution. Using analytical and numerical calculations we show that superconducting charge qubit microscopy (SCQM) has the potential to resolve temperature and resistivity changes …
In the microscopic modeling of new-generation electronic quantum nanodevices a variety of simulation strategies have been proposed and employed. Aim of this Letter is to point out virtues versus intrinsic limitations of non-Markovian density-matrix approaches; we shall show that the usual mean-field treatment may lead to highly unphysical results, like negative distribution probabilities and non-dissipative behaviours, which are particularly severe in zero-dimensional electronic systems coupled to dispersionless phonon modes. This is in striking contrast with Markovian treatments, where a prop…
Well--defined criteria are proposed for assessing the accuracy of quantum master equations whose memory functions are approximated by Padé resummation of the first two moments in the electronic coupling. These criteria partition the parameter space into distinct levels of expected accuracy, ranging from quantitatively accurate regimes to regions of parameter space where the approach is not expected to be applicable. Extensive comparison of Padé--resummed master equations with numerically exact results in the context of the spin--boson model demonstrate that the proposed criteria correctly dema…
Half a century after its discovery, the Josephson junction has become the most important nonlinear quantum electronic component at our disposal. It has helped reshape the SI system around quantum effects and is used in scores of quantum devices. By itself, the use of Josephson junctions in the volt metrology seems to imply an exquisite understanding of the component in every aspect. Yet, surprisingly, there have been long-standing subtle issues regarding the modeling of the interaction of a junction with its electromagnetic environment. Here, we find that a Josephson junction connected to a re…
In this work, we have investigated conduction through an artificial molecule comprising two coupled quantum dots. The question addressed is the role of inter-dot coupling on electronic transport. We find that the current through the molecule exhibits step-like features as a function of the voltage between the leads, where the step size increases as the inter-dot coupling is increased. These step-like features disappear with increasing tunneling rate from the leads, but we find that in the presence of coupling, this smooth behavior is not observed rather two kinks are seen in the current voltag…
Numerical renormalization group (NRG) calculations of quantum impurity models, based on a logarithmic discretization in energy of electronic or bosonic Hamiltonians, provide a powerful tool to describe physics involving widely separated energy scales, as typically encountered in nanostructures and strongly correlated materials. This main advantage of the NRG was however considered a drawback for resolving sharp spectral features at finite energy, such as dissipative atomic peaks. Surprisingly, we find a bunching of many-body levels in NRG spectra near dissipative resonances, and exploit this b…
We consider theoretically the transport properties of a spinless resonant electronic level coupled to strongly dissipative leads, in the regime of circuit impedance near the resistance quantum. Using the Luttinger liquid analogy, one obtains an effective Hamiltonian expressed in terms of interacting Majorana fermions, in which all environmental degrees of freedom (leads and electromagnetic modes) are encapsulated in a single fermionic bath. General transport equations for this system are then derived in terms of the Majorana T-matrix. Perturbative treatment of the Majorana interaction term yie…
We analyze the real-time dynamics of a quantum two-state system in the presence of nonequilibrium quantum fluctuations. The latter are generated by a coupling of the two-state system to a single electronic level of a quantum dot which carries a nonequilibrium tunneling current. We restrict to the sequential tunneling regime and calculate the dynamics of the two-state system, of the dot population, and of the nonequilibrium charge current on the basis of a diagrammatic perturbative method valid for a weak tunneling coupling. We find a nontrivial dependence of the relaxation and dephasing rates …
We study the interplay between charge transport and light-matter interactions in a confined geometry, by considering an open, mesoscopic chain of two-orbital systems resonantly coupled to a single bosonic mode close to its vacuum state. We introduce and benchmark different methods based on self-consistent solutions of non-equilibrium Green's functions and numerical simulations of the quantum master equation, and derive both analytical and numerical results. It is shown that in the dissipative regime where the cavity photon decay rate is the largest parameter, the light-matter coupling is respo…
We study a generic spin-fermion model, where a two-level system (spin) is coupled to two metallic leads with different chemical potentials, in the presence of monochromatic driving fields. The real-time dynamics of the system is simulated beyond the Markovian limit by an iterative numerically exact influence functional path integral method. Our results show that although both system-bath coupling and chemical potential difference contribute to dissipation, their effects are distinct. In particular, under certain drivings the asymptotic Floquet states of the system exhibit robustness against a …
Using the Calogero model as an example, we show that the transport in interacting non-dissipative electronic systems is essentially non-linear. Non-linear effects are due to the curvature of the electronic spectrum near the Fermi energy. As is typical for non-linear systems, propagating wave packets are unstable. At finite time shock wave singularities develop, the wave packet collapses, and oscillatory features arise. They evolve into regularly structured localized pulses carrying a fractionally quantized charge - {\it soliton trains}. We briefly discuss perspectives of observation of Quantum…
We present a comprehensive theoretical investigation on the dynamic electronic response of a noninteracting quantum dot system to various forms of time-dependent voltage applied to the single contact lead. Numerical simulations are carried out by implementing a recently developed hierarchical equations of motion formalism [J. Chem. Phys. 128, 234703 (2008)], which is formally exact for a fermionic system interacting with grand canonical fermionic reservoirs, in the presence of arbitrary time-dependent applied chemical potentials. The dynamical characteristics of the transient transport current…
The interplay of synchronization and topological band structures with symmetry protected midgap states under the influence of driving and dissipation is largely unexplored. Here we consider a trimer chain of electron shuttles, each consisting of a harmonic oscillator coupled to a quantum dot positioned between two electronic leads. Each shuttle is subject to thermal dissipation and undergoes a bifurcation towards self-oscillation with a stable limit cycle if driven by a bias voltage between the leads. By mechanically coupling the oscillators together, we observe synchronized motion at the ends…
We use the "generalized hierarchical equation of motion" proposed in Paper I to study decoherence in a system coupled to a spin bath. The present methodology allows a systematic incorporation of higher order anharmonic effects of the bath in dynamical calculations. We investigate the leading order corrections to the linear response approximations for spin bath models. Two types of spin-based environments are considered: (1) a bath of spins discretized from a continuous spectral density and (2) a bath of physical spins such as nuclear or electron spins. The main difference resides with how the …
We introduce a theoretical approach to study the quantum-dissipative dynamics of electronic excitations in macromolecules, which enables to perform calculations in large systems and cover long time intervals. All the parameters of the underlying microscopic Hamiltonian are obtained from \emph{ab-initio} electronic structure calculations, ensuring chemical detail. In the short-time regime, the theory is solvable using a diagrammatic perturbation theory, enabling analytic insight. To compute the time evolution of the density matrix at intermediate times, typically $\lesssim$~ps, we develop a Mon…
