We derive a non-Markovian theory for waiting time distributions of consecutive single electron transfer events. The presented microscopic Pauli rate equation formalism couples the open electrodes to the many-body system, allowing to take finite bias and temperature into consideration. Numerical results reveal transient oscillations of distinct system frequencies due to memory in the waiting time distributions. Memory effects can be approximated by an expansion in non-Markovian corrections. This method is employed to calculate memory landscapes displaying preservation of memory over multiple consecutive electron transfers.
We formulate a quantum theory of electron waiting time distributions for charge transport in nano-structures described by non-Markovian generalized master equations. We illustrate our method by calculating the waiting time distribution of electron transport through a dissipative double quantum dot, where memory effects are present due to a strongly coupled heat bath. We consider the influence of non-Markovian dephasing on the distribution of electron waiting times and discuss how spectral properties of the heat bath may be detected through measurements of the electron waiting time.
We propose a reaction-transport model for CTRW with non-linear reactions and non-exponential waiting time distributions. We derive non-linear evolution equation for mesoscopic density of particles. We apply this equation to the problem of fronts propagation into unstable state of reaction-transport systems with anomalous diffusion. We have found an explicit expression for the speed of propagating front in the case of subdiffusion transport.
We present a statistical readout method for quantum interferences based on time series analysis of consecutive single electron transfers through a double quantum dot Aharonov-Bohm interferometer. Waiting time distributions qualitatively indicate the presence of interferences and provide information on orbital-detuning and coherent interdot-electron transfer. Interdot transfer induced oscillations are Aharonov-Bohm phase sensitive, while those due to level detuning are phase-independent. The signature of the quantum interference in the waiting time distribution is more apparent for weakly coupl…
The distribution of waiting times between elementary tunneling events is of fundamental importance for understanding the stochastic charge transfer processes in nanoscale conductors. Here we investigate the waiting time distributions (WTDs) of periodically driven single-electron emitters and evaluate them for the specific example of a mesoscopic capacitor. We show that the WTDs provide a particularly informative characterization of periodically driven devices and we demonstrate how the WTDs allow us to reconstruct the full counting statistics (FCS) of charges that have been transferred after a…
In the resonant tunneling regime sequential processes dominate single electron transport through quantum dots or molecules that are weakly coupled to macroscopic electrodes. In the Coulomb blockade regime, however, cotunneling processes dominate. Cotunneling is an inherently quantum phenomenon and thus gives rise to interesting observations, such as an increase in the current shot noise. Since cotunneling processes are inherently fast compared to the sequential processes, it is of interest to examine the short time behaviour of systems where cotunneling plays a role, and whether these systems …
The non-Markovian effects in the spin dynamics in diluted magnetic semiconductors found in quantum kinetic calculations can be reproduced very well by a much simpler effective single electron theory, if a finite memory is accounted for. The resulting integro-differential equation can be solved by a differential transform method, yielding the Taylor series of the solution. From the comparison of both theories it can be concluded that the non-Markovian effects are due to the spectral proximity of the excited electrons to the band edge.
We study qubit-mediated energy transfer between two electron reservoirs by adopting a numerically-exact influence functional path-integral method. This non-perturbative technique allows us to study the system's dynamics beyond the weak coupling limit. Our simulations for the energy current indicate that perturbative-Markovian Master equation predictions significantly deviate from exact numerical results already at intermediate coupling, $πρα_{j,j'}\gtrsim 0.4$, where $ρ$ is the metal (Fermi sea) density of states, taken as a constant, and $α_{j,j'}$ is the scattering potential energy of electr…
We investigate theoretically the influence of an external magnetic field on the spin dynamics of excitons in diluted magnetic semiconductor quantum wells. To this end, we apply a quantum kinetic theory beyond the Markov approximation which reveals that non-Markovian effects can significantly influence the exciton spin dynamics. If the magnetic field is oriented parallel to the growth direction of the well, the Markovian spin-transfer rate decreases monotonically with increasing field as predicted by Fermi's golden rule. The quantum kinetic theory follows this result qualitatively but predicts …
The electron waiting time is the time that passes between two subsequent charge transfers in an electronic conductor. Recently, theories of electron waiting times have been devised for quantum transport in Coulomb-blockade structures and for mesoscopic conductors, however, so far a proper description of a detector has been missing. Here we develop a quantum theory of a waiting time clock capable of measuring the distribution of waiting times between electrons above the Fermi sea in a mesoscopic conductor. The detector consists of a mesoscopic capacitor coupled to a quantum two-level system who…
We evaluate the joint distributions of electron waiting times in coherent conductors described by scattering theory. Successive electron waiting times in a single-channel conductor are found to be correlated due to the fermionic statistics encoded in the many-body state. Our formalism allows us also to investigate the waiting times between charge transfer events in different outgoing channels. As an application we consider a quantum point contact in a chiral setup with one or both input channels biased by either a static or a time-dependent periodic voltage described by Floquet theory. The the…
A quantum kinetic theory of the spin transfer between carriers and Mn atoms in a Mn doped diluted magnetic semiconductor is presented. It turns out that the typical memory time associated with these processes is orders of magnitude shorter than the time scale of the spin transfer. Nevertheless, Markovian rate equations, which are obtained by neglecting the memory, work well only for bulk systems. For quantum wells and wires the quantum kinetic results qualitatively deviate from the Markovian limit under certain conditions. Instead of a monotonic decay of an initially prepared excess electron s…
We propose simple protocols for performing quantum noise spectroscopy based on the method of transfer tensor maps (TTM), [Phys. Rev. Lett. 112, 110401 (2014)]. The TTM approach is a systematic way to deduce the memory kernel of a time-nonlocal quantum master equation via quantum process tomography. With access to the memory kernel it is possible to (1) assess the non-Markovianity of a quantum process, (2) reconstruct the noise spectral density beyond pure dephasing models, and (3) investigate collective decoherence in multiqubit devices. We illustrate the usefulness of TTM spectroscopy on the …
When electric current flows through a molecular junction, the molecule constantly charges and discharges by tunnelling electrons. These charging and discharging events occur at specific but random times and separated by stochastic time intervals. These time intervals can be associated with dwelling time for a charge (electron or hole) to reside on the molecule. In this paper, the statistical properties of these time intervals are studied and general formula for their distribution is derived. The theory is based on the Markovian master equation which takes into account transitions between vibra…
On the elementary level, electronic current consists of individual electron tunnelling events that are separated by random time intervals. The waiting time distribution is a probability to observe the electron transfer in the detector electrode at time $t+τ$ given that an electron was detected in the same electrode at earlier time $t$. We study waiting time distribution for quantum transport in a vibrating molecular junction. By treating the electron-vibration interaction exactly and molecule-electrode coupling perturbatively, we obtain master equation and compute the distribution of waiting t…
Waiting time is an important transport quantity that is complementary to average current and its fluctuation. So far all the studies of waiting time distribution (WTD) are limited to steady state transport (either dc or ac). In this work, we present a theory to calculate WTD for coherent electronic systems in transient regime. We express the generating function of full counting statistics using Keldysh non-equilibrium Green's functions formalism. Our analysis goes beyond the wideband approximation and is suitable for first principles calculation on realistic systems. Analytic solution has been…
We develop a theoretical approach to study the transient dynamics and the time-dependent statistics for the Anderson-Holstein model in the regime of strong electron-phonon coupling. For this purpose we adapt a recently introduced diagrammatic approach to the time domain. The generating function for the time-dependent charge transfer probabilities is evaluated numerically by discretizing the Keldysh contour. The method allows us to analyze the system evolution to the steady state after a sudden connection of the dot to the leads, starting from different initial conditions. Simple analytical res…
We study the electronic waiting time distributions (WTDs) in a non-interacting quantum dot spin valve by varying spin polarization and the noncollinear angle between the magnetizations of the leads using scattering matrix approach. Since the quantum dot spin valve involves two channels (spin up and down) in both the incoming and outgoing channels, we study three different kinds of WTDs, which are two-channel WTD, spin-resolved single-channel WTD and cross-channel WTD. We analyze the behaviors of WTDs in short times, correlated with the current behaviors for different spin polarizations and non…
We have studied the Waiting Time Distributions (WTDs) for sub-gap transport through a single-level quantum dot tunnel coupled to one normal and one superconducting lead. The WTDs reveal the internal dynamics of the system in particular the coherent transfer of Cooper pairs between the dot and the superconductor. The WTDs exhibit oscillations that can be directly associated to the coherent oscillation between the empty and doubly occupied dot. The oscillation frequency is equal to the energy splitting between the Andreev bound states. These effects are more pronounced when the empty state and d…
New features of molecular wires can be observed when they are irradiated by laser fields. These effects can be achieved by periodically oscillating fields but also by short laser pulses. The theoretical foundation used for these investigations is a density matrix formalism where the full system is partitioned into a relevant part and a thermal fermionic bath. The derivation of a quantum master equation, either based on a time-convolutionless or time-convolution projection-operator approach, incorporates the interaction with time-dependent laser fields non-perturbatively and is valid at low tem…
The waiting time distribution has, in recent years, proven to be a useful statistical tool for characterising transport in nanoscale quantum transport. In particular, as opposed to moments of the distribution of transferred charge, which have historically been calculated in the long-time limit, waiting times are able to detect non-renewal behaviour in mesoscopic systems. They have failed, however, to correctly incorporate backtunneling events. Recently, a method has been developed that can describe unidirectional and bidirectional transport on an equal footing: the distribution of first-passag…
We study transitions of a particle between two wells, separated by a reservoir, under the condition that the particle is not detected in the reservoir. Conventional quantum trajectory theory predicts that such no-result continuous measurement would not affect these transitions. We demonstrate that it holds only for Markovian reservoirs (infinite bandwidth $Λ$). In the case of finite $Λ$, the probability of the particle's interwell transition is a function of the ratio $Λ/ν$, where $ν$ is the frequency of measurements. This scaling tells us that in the limit $ν\to\infty$, the measurement freeze…
The charge transfer from an adatom to a semiconductor substrate of one-dimensional quantum dot array is evaluated theoretically. Due to the Van Hove singularity in the density of electron states at the band edges, the charge transfer decay rate is enhanced nonanalytically in terms of the coupling constant $g$ as $g^{4/3}$. The optical absorption spectrum for the ionization of a core level electron of the adatom to the conduction band is also calculated. The reversible non-Markovian process and irreversible Markovian process in the time evolution of the adatom localized state manifest themselve…
Quantum transport of electrons through a molecule is a series of individual electron tunnelling events separated by stochastic waiting time intervals. We study the emergence of temporal correlations between successive waiting times for the electron transport in a vibrating molecular junction. Using master equation approach, we compute joint probability distribution for waiting times of two successive tunnelling events. We show that the probability distribution is completely reset after each tunnelling event if molecular vibrations are thermally equilibrated. If we treat vibrational dynamics ex…
We formalize the derivation of a generalized coarse-graining $n$-resolved master equation by introducing a virtual detector counting the number of transferred charges in single-electron transport. Our approach enables the convenient inclusion of coherences and Lamb shift in counting statistics. As a Markovian example with Lindblad-type density matrices, we consider the Born-Markov-Secular (BMS) approximation which is a special case of the non-Markovian dynamical coarse graining (DCG) approach. For illustration we consider transport through two interacting levels that are either serially or par…
In quantum communication and distributed quantum computing, one-dimensional waveguides provide directional transfer of quantum information. A single-mode waveguide has a density-of-states singularity at the lower cut-off frequency, which resembles sharp resonances of a cavity but with non-Markovian dynamics. Thus we put forward schemes of coupling atomic transitions and a waveguide continuum edge. We first present a scheme of spin-photon quantum interface operating in the non-Markovian regime for a $Λ$-type three-level system coupled to a waveguide. Then we show that strong coupling between at…
Efficient simulations of the dynamics of open systems is of wide importance for quantum science and tech-nology. Here, we introduce a generalization of the transfer-tensor, or discrete-time memory kernel, formalism to multi-time measurement scenarios. The transfer-tensor method sets out to compute the state of an open few-body quantum system at long times, given that only short-time system trajectories are available. Here, we showthat the transfer-tensor method can be extended to processes which include multiple interrogations (e.g. measurements) of the open system dynamics as it evolves, allo…
In organic photovoltaic systems, a photogenerated molecular exciton in the donor domain dissociates into a hole and an electron at the donor/acceptor heterojunction, and subsequently separate into free charge carriers that can be extracted as photocurrents. The recombination of the once-separated electron and hole is a major loss mechanism in photovoltaic systems, which controls their performance. Hence, efficient photovoltaic systems need built-in ratchet mechanisms, namely, ultrafast charge separation and retarded charge recombination. In order to obtain insight into the internal working of …
