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 exhibits unphysical negative values. On the other hand, current noise calculated for currents between the dots and the leads by the counting variable approach shows no anomalies and seems physically plausible. We inquire into the origin of this discrepancy between two nominally equivalent approaches and show that it stems from the simultaneous presence of the two types of baths, i.e., the electronic leads and the dissipative bosonic bath. This finding raises interesting questions concerning conceptual foundations of the theory describing multiple-baths open quantum systems widely encountered in nanoscience.
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 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.
Recently, novel Coulomb drag mechanisms in capacitively coupled double quantum dots were uncovered by the T-matrix based master equation (TME). The TME is so far the primary approach to studying Coulomb drag in the weak-coupling regime; however, its accuracy and reliability remain unexplored. Here, we evaluate the performance of the TME for Coulomb drag via a comparison with numerically exact results obtained by the hierarchical equation-of-motion approach. We find that the TME can capture qualitative current evolutions versus dot levels, temperature, and effective coupling strengths, but only…
We have studied the dissipative dynamics of a solid-state qubit with an extra electron confined to either one of two coupled quantum dots. Previous theoretical work based on Bloch-type rate equations gave an unphysical uniform occupation probability of the electron in the quantum dots even for non-identical dots. We show that this is due to neglecting higher order interactions in the analysis. By including higher order terms, we obtain expected asymmetric occupation probabilities for non-identical dots. Our work demonstrates that the high order interaction terms can lead to important qualitati…
We have measured the electromagnetic response of micron-size isolated mesoscopic GaAs/GaAlAs square dots down to temperature T=16mK, by coupling them to an electromagnetic micro-resonator. Both dissipative and non dissipative responses exhibit a large magnetic field dependent quantum correction, with a characteristic flux scale which corresponds to a flux quantum in a dot. The real (dissipative) magnetoconductance changes sign as a function of frequency for low enough density of electrons. The signal observed at frequency below the mean level spacing corresponds to a negative magnetoconductanc…
We study quantum dissipative dynamics of entanglement in the spin-boson model, described by the generalized master equation. We consider the two opposite limits of pure-dephasing and relaxation models, measuring the degree of entanglement with the concurrence. When the Markovian approximation is employed, entanglement is shown to decay exponentially in both cases. On the other hand, non-Markovian contributions alter the analytic structure of the master equation, resulting in logarithmic decay in the pure dephasing model.
An important class of approaches to the description of electronic transport through molecules and quantum dots is based on the master equation. We discuss various formalisms for deriving a master equation and their interrelations. It is shown that the master equations derived by Wangsness, Bloch, and Redfield and by Koenig et al. are equivalent. The roles of the large-reservoir and Markov approximations are clarified. The Markov approximation is traced back to nonzero bias voltage and temperature, whereas interactions and the corresponding rapid relaxation in the leads are shown to be irreleva…
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 …
Coulomb coupled quantum dot arrays with staircase ground state configuration have been proposed in literature for enhancing heat-harvesting and refrigeration performance. However, due to their mutual Coulomb interaction, a performance analysis of such systems remains complicated and necessitates consideration of microscopic physics using density matrix formulation. However the path of device analysis starting from the system Hamiltonian to density matrix formulation is complicated and lacks the simplicity and intuitive aspect of sequential electron transport conveyed by the quantum master equa…
We consider adiabatic charge transport through an almost open quantum dot. We show that the charge transmitted in one cycle is quantized in the limit of vanishing temperature and one-electron mean level spacing in the dot. The explicit analytic expression for the pumped charge at finite temperature is obtained for spinless electrons. The pumped charge is produced by both non-dissipative and dissipative currents. The latter are responsible for the corrections to charge quantization which are expressed through the conductance of the system.
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…
The time-convolutionless quantum master equation is an exact description of the nonequilibrium dynamics of open quantum systems, with the advantage of being local in time. We derive a perturbative expansion to arbitrary order in the system-reservoir coupling for its generator, which contains significantly fewer terms than the ordered-cumulant expansion. We show that the derived expansion also admits a simple recursive formulation. The derived series is then used to describe the nonequilibrium dynamics of a quantum dot, including coherences. We find a relation between the generator and a genera…
The master equation describing the non-equilibrium dynamics of a quantum dot coupled to metallic leads is considered. Employing a superoperator approach, we derive an exact time-convolutionless master equation for the probabilities of dot states, i.e., a time-convolutionless Pauli master equation. The generator of this master equation is derived order by order in the hybridization between dot and leads. Although the generator turns out to be closely related to the T-matrix expressions for the transition rates, which are plagued by divergences, in the time-convolutionless generator all divergen…
We develop a versatile master equation approach to describe the non-equilibrium dynamics of a two-level system in contact with a bosonic environment, which allows for the exploration of a wide range of parameter regimes within a single formalism. As an experimentally relevant example, we apply this technique to the study of excitonic Rabi rotations in a driven quantum dot, and compare its predictions to the numerical Feynman integral approach. We find excellent agreement between the two methods across a generally difficult range of parameters. In particular, the variational master equation tec…
Based on our recently developed quantum transport theory in term of an exact master equation, the corresponding particle-number resolved ($n$-resolved) master equation and the related shot noise spectrum formalism covering the full frequency range are constructed. We demonstrate that the noise spectra of transport current through single quantum dot and double quantum dots show characteristic steps and/or peak-dips in different tunneling frequency regimes through tuning the applied bias voltage and/or gate voltage at low temperatures. The peak-dips crossing the tunneling resonant frequencies is…
A quantum master equation (QME) is derived for the many-body density matrix of an open current-carrying system weakly coupled to two metal leads. The dynamics and the steady-state properties of the system for arbitrary bias are studied using projection operator techniques, which keep track of number of electrons in the system. We show that coherences between system states with different number of electrons, n, (Fock space coherences) do not contribute to the transport to second order in system-lead coupling. However, coherences between states with the same n may effect transport properties whe…
Unitary transformations can allow one to study open quantum systems in situations for which standard, weak-coupling type approximations are not valid. We develop here an extension of the variational (polaron) transformation approach to open system dynamics, which applies to arbitrarily large exciton transport networks with local environments. After deriving a time-local master equation in the transformed frame, we go on to compare the population dynamics predicted using our technique with other established master equations. The variational frame dynamics are found to agree with both weak coupl…
The operation of a source of entangled electron spins, based on a superconductor and two quantum dots in parallel\cite{loss}, is described in detail with the help of quantum master equations. These are derived including the main parasitic processes in a fully consistent and non-perturbative way, starting from a microscopic Hamiltonian. The average current is calculated, including the contribution of entangled and non-entangled pairs. The constraints on the operation of the device are illustrated by a calculation of the various charge state probabilities.
Dephasing of one-particle states in closed quantum dots is analyzed within the framework of random matrix theory and Master equation. Combination of this analysis with recent experiments on the magnetoconductance allows for the first time to evaluate the dephasing times of closed quantum dots. These dephasing times turn out to depend on the mean level spacing and to be significantly enhanced as compared with the case of open dots. Moreover, the experimental data available are consistent with the prediction that the dephasing of one-particle states in finite closed systems disappears at low eno…
In this paper we introduce a simple phenomenological model of the conduction between a couple of serial or parallel quantum dots. This model is extended to arbitrary of number and to a square array of quantum dots. The local potential is computed taking into account the net charge at the quantum dot. Master equation are presented for total current and charge number N taking considering both the local potential and the local current. Interesting results are reported, namely the Negative Differential Resistance for serial quantum dots as well as resonant conductance. A paradoxical asymmetric cur…
We analytically investigate the non-equilibrium pumping for a double quantum dots system on the basis of the quantum master equation (QME), where the double quantum dots are connected to two external leads by the spin coupling. Each of leads has two tunable parameters, temperature and chemical potential. Using QME formalism, we obtain an analytical expression of the Berry-like phase for eigenstate of the QME in the parameter space. We show that the Berry-like curvature is non zero in the whole region in the parameter space. We also show that the Berry-like curvature vanishes in the case of sin…
One-way nonreciprocal interactions between two quantum systems are typically described by a cascaded quantum master equation, and rely on an effective breaking of time-reversal symmetry as well as the balancing of coherent and dissipative interactions. Here, we present a new approach for obtaining nonreciprocal quantum interactions that is completely distinct from cascaded quantum systems, and that does not in general require broken TRS. Our method relies on a local gauge symmetry present in any Markovian Lindblad master equation. This new kind of quantum nonreciprocity has many implications, …
We consider a two level system coupled to a thermal bath and we investigate the variation of energy transferred to the reservoir as a function of time. The physical quantity under investigation is the time-dependent quantum average power. We compare quantum master equation approaches with functional influence method. Differences and similarities between the methods are analyzed, showing deviations at low temperature between the functional integral approach and the predictions based on master equations.
We investigate quantum photovoltaic effect in double quantum dots by applying nonequilibrium quantum master equation. The drastic suppression of the photovoltaic current is observed near the open circuit voltage, which leads to the large filling factor. We find that there always exists an optimal inter-dot tunneling that significantly enhances the photovoltaic current. The maximal output power will also be obtained around the optimal inter-dot tunneling. Moreover, the open circuit voltage approximately behaves as the product of the eigen-level gap and the Carnot efficiency. These results sugge…
In quasiballistic semiconductor nanostructures, carrier exchange between the active region and dissipative contacts is the mechanism that governs relaxation. In this paper, we present a theoretical treatment of transient quantum transport in quasiballistic semiconductor nanostructures, which is based on the open system theory and valid on timescales much longer than the characteristic relaxation time in the contacts. The approach relies on a model interaction between the current-limiting active region and the contacts, given in the scattering-state basis. We derive a non-Markovian master equat…
We calculate the stationary current through two double quantum dots which are interacting via a common phonon environment. Numerical and analytical solutions of a master equation in the stationary limit show that the current can be increased as well as decreased due to a dissipation mediated interaction. This effect is closely related to collective, spontaneous emission of phonons (Dicke super- and subradiance effect), and the generation of a `cross-coherence' with entanglement of charges in singlet or triplet states between the dots. Furthermore, we discuss an inelastic `current switch' mecha…
We study the dynamics and decoherence of a system of two strongly driven qubits in a dissipative cavity. The two qubits have no direct interaction and are individually off-resonantly coupled to a single mode of quantized radiation. We derive analytical solutions to the Lindblad-type master equation and study the evolution of the entanglement of this system. We show that with non-zero detuning between the quantum and classical fields, the initial decay of the entanglement is followed by its revival periodic in time. We show that different Bell states follow evolutions with different rates.
We theoretically consider charge transport through two quantum dots coupled in series. The corresponding full counting statistics for noninteracting electrons is investigated in the limits of sequential and coherent tunneling by means of a master equation approach and a density matrix formalism, respectively. We clearly demonstrate the effect of quantum coherence on the zero-frequency cumulants of the transport process, focusing on noise and skewness. Moreover, we establish the continuous transition from the coherent to the incoherent tunneling limit in all cumulants of the transport process a…
A quantum-mechanical calculation of conductance in an open quantum dot is performed in the Landauer-Büttiker formalism using a tight binding Hamiltonian with direct Coulomb interaction. The charge distribution in the dot is calculated self-consistently as function of a gate potential, for various dot-leads couplings. The interaction is active only inside the dot, but not in the leads, its strength being an input parameter. Our calculations are complementary to the master-equation approach, go beyond the "orthodox theory", and account for the size, tunneling, and interaction effects in quantum …
Charge-neutral excitons in semiconductor quantum dots have a small finite energy separation caused by the anisotropic exchange splitting. Coherent excitation of neutral excitons will generally excite both exciton components, unless the excitation is parallel to one of the dipole axes. We present a polaron master equation model to describe two-exciton pumping using a coherent continuous wave pump field in the presence of a realistic anisotropic exchange splitting. We predict a five-peak incoherent spectrum, thus generalizing the Mollow triplet to become a Mollow quintuplet. We experimentally co…
Due to the Fermi-Dirac statistics of electrons the temporal correlations of tunneling events in a double barrier setup are typically negative. Here, we investigate the shot noise behavior of a system of two capacitively coupled quantum dot states by means of a Master equation model. In an asymmetric setup positive correlations in the tunneling current can arise due to the bunching of tunneling events. The underlying mechanism will be discussed in detail in terms of the current-current correlation function and the frequency-dependent Fano factor.
We derive the effective cavity pumping and decay rates for the master equation of a quantum dot-microcavity system in presence of $N$ weakly coupled dots. We show that the in-flow of photons is not linked to the out-flow by thermal equilibrium relationships.
The coherent time evolution of electrons in double quantum dots induced by fast bias-voltage switches is studied theoretically. As it was shown experimentally, such driven double quantum dots are potential devices for controlled manipulation of charge qubits. By numerically solving a quantum master equation we obtain the energy- and time-resolved electron transfer through the device which resembles the measured data. The observed oscillations are found to depend on the level offset of the two dots during the manipulation and, most surprisingly, also the on initialization stage. By means of an …
We study the current noise spectrum of qubits under transport conditions in a dissipative bosonic environment. We combine (non-)Markovian master equations with correlation functions in Laplace-space to derive a noise formula for both weak and strong coupling to the bath. The coherence-induced reduction of noise is diminished by weak dissipation and/or a large level separation (bias). For weak dissipation, we demonstrate that the dephasing and relaxation rates of the two-level system can be extracted from noise. In the strong dissipation regime, the localisation-delocalisation transition become…
We describe how complex fluctuations of the local environment of an optically active quantum dot can leave rich fingerprints in its emission spectrum. A new feature, termed "Fluctuation Induced Luminescence" (FIL), is observed to arise from extremely rare fluctuation events that have a dramatic impact on the response of the system-so called "black swan" events. A quantum dissipative master equation formalism is developed to describe this effect phenomenologically. Experiments performed on single quantum dots subject to electrical noise show excellent agreement with our theory, producing the ch…
A new generalised group-theoretical approach, based on master Maxwell-pseudospin equations, is proposed to explain recently observed enhanced circular dichroism in the excited state emission from p-doped quantum dot ensembles under resonant circularly polarised excitation into hot trion states, herein referred to as "spin-filtering effect". The theory agrees remarkably well with polarised time-resolved photoluminescence experiments, yielding largely unknown inter- and intra-shell spin relaxation time scales. This approach allows to predict optimum pulse parameters for control of spin dynamics,…
A recent experiment [E. A. Chekhovich et al., Phys. Rev. Lett. 104, 066804 (2010)] has demonstrated that high nuclear spin polarization can be achieved in self-assembled quantum dots by exploiting an optically forbidden transition between a heavy hole and a trion state. However, a fully polarized state is not achieved as expected from a classical rate equation. Here, we theoretically investigate this problem with the help of a quantum master equation and we demonstrate that a fully polarized state cannot be achieved due to formation of a nuclear dark state. Moreover, we show that the maximal d…
The low-frequency shot noise properties of two electrostatically coupled semiconductor quantum dot states which are connected to emitter/collector contacts are studied. A master equation approach is used to analyze the bias voltage dependence of the Fano factor as a measure of temporal correlations in tunneling current caused by Pauli's exclusion principle and the Coulomb interaction. In particular, the influence of the Coulomb interaction on the shot noise behavior is discussed in detail and predictions for future experiments will be given. Furthermore, we propose a mechanism for negative dif…
We present quantum transport measurements of interacting parallel quantum dots formed in the strands of a carbon nanotube rope. In this molecular quantum dot system, transport is dominated by one quantum dot, while additional resonances from parallel side dots appear, which exhibit a weak gate coupling. This differential gating effect provides a tunability of the quantum dot system with only one gate electrode and provides control over the carbon nanotube strand that carries the current. By tuning the system to different states we use quantum transport as a spectroscopic tool to investigate th…
Using time-resolved transconductance spectroscopy, we study the tunneling dynamics between a two-dimensional electron gas (2DEG) and self-assembled quantum dots (QDs), embedded in a field-effect transistor structure. We find that the tunneling of electrons from the 2DEG into the QDs is governed by a different time constant than the reverse process, i.e., tunneling from the QDs to the 2DEG. This asymmetry is a clear signature of Coulomb interaction and makes it possible to determine the degeneracy of the quantum dot orbitals even when the individual states cannot be resolved energetically becau…
For an open quantum system, we investigate the pumped current induced by a slow modulation of control parameters on the basis of the quantum master equation and full counting statistics. We find that the average and the cumulant generating function of the pumped quantity are characterized by the geometrical Berry-phase-like quantities in the parameter space, which is associated with the generator of the master equation. From our formulation, we can discuss the geometrical pumping under the control of the chemical potentials and temperatures of reservoirs. We demonstrate the formulation by spin…
We provide a self-contained review of master equation approaches to modelling phonon effects in optically driven self-assembled quantum dots. Coupling of the (quasi) two-level excitonic system to phonons leads to dissipation and dephasing, the rates of which depend on the excitation conditions, intrinsic properties of the QD sample, and its temperature. We describe several techniques, which include weak-coupling master equations that are perturbative in the exciton-phonon coupling, as well as those based on the polaron transformation that can remain valid for strong phonon interactions. We add…
The superconducting reservoir effect on the current carrying transport of a double quantum dot in Markovian regime is investigated. For this purpose, a quantum master equation (QME) at finite temperature is derived for the many-body density matrix of an open quantum system. The dynamics and the steady-state properties of the double quantum dot system for arbitrary bias are studied. We will show that how the populations and coherencies of the system states are affected by superconducting leads. The energy parameter of system contains essentially four contributions due to dots system-electrodes …
Photovoltaic effect of double quantum dots under nonuniform light field intensity has been studied theoretically. Comparing with the traditional p-n type photovoltaic effect, the inhomogeneous light field provides asymmetric potential creating polarization of electron number distribution in the neighboring quantum dots and furthermore gives rise to net current. Current density and efficiency of such kind solar cells are estimated to be comparable to the traditional p-n type material based solar cells. Motion of electron is described using quantum master equation around room temperature. The in…
We propose a new implementation of a universal set of one- and two-qubit gates for quantum computation using the spin states of coupled single-electron quantum dots. Desired operations are effected by the gating of the tunneling barrier between neighboring dots. Several measures of the gate quality are computed within a newly derived spin master equation incorporating decoherence caused by a prototypical magnetic environment. Dot-array experiments which would provide an initial demonstration of the desired non-equilibrium spin dynamics are proposed.
In this work, dissipative effects from a phonon bath on the resonance fluorescence of a solid state two level system embedded in a high quality semiconductor microcavity and driven by an intense laser, are investigated. Within the density operator formalism, we derive a variational master equation valid for broader ranges of temperatures, pumping rates, and radiation-matter couplings, than previous studies. From the obtained master equation, fluorescence spectra for various thermal and exciting conditions are numerically calculated, and compared to those computed from weak coupling and polaron…
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 consider a laser-driven and dissipative system of two coupled cavities with Jaynes-Cummings nonlinearity. In particular, we investigate both incoherent and coherent laser driving, corresponding to different experimental situations. We employ Arnoldi time evolution as a numerical tool to solve exactly the many-body master equation describing the non-equilibrium quantum system. We evaluate the fluorescence spectrum and the spectrum of the second-order correlation function of the emitted light field. Finally, we relate the measured spectra of the dissipative quantum system to excitations of th…
We present rigorous and intuitive master equation models to study on-demand single photon sources from pulse-excited quantum dots coupled to cavities. We consider three methods of source excitation: resonant pi-pulse, off-resonant phonon-assisted inversion, and two-photon excitation of a biexciton-exciton cascade, and investigate the effect of the pulse excitation process on the quantum indistinguishability, efficiency, and purity of emitted photons. By explicitly modelling the time-dependent pulsed excitation process in a manner which captures non-Markovian effects associated with coupling to…
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 investigate the influence of dissipation on one- and two-qubit rotations in coupled semiconductor quantum dots, using a (pseudo) spin-boson model with adiabatically varying parameters. For weak dissipation, we solve a master equation, compare with direct perturbation theory, and derive an expression for the `fidelity loss' during a simple operation that adiabatically moves an electron between two coupled dots. We discuss the possibility of visualizing coherent quantum oscillations in electron `pump' currents, combining quantum adiabaticity and Coulomb blockade. In two-qubit spin-swap operat…
We investigate transient dynamic response of an Anderson impurity quantum dot to a family of ramp-up driving voltage applied to the single coupling lead. Transient current is calculated based on a hierarchical equations of motion formalism for open dissipative systems [J. Chem. Phys. 128, 234703 (2008)]. In the nonlinear response and nonadiabatic charging regime, characteristic resonance features of transient response current reveal distinctly and faithfully the energetic configuration of the quantum dot. We also discuss and comment on both the physical and numerical aspects of the theoretical…
We obtain the finite-temperature unconditional master equation of the density matrix for two coupled quantum dots (CQD) when one dot is subjected to a measurement of its electron occupation number using a point contact (PC). To determine how the CQD system state depends on the actual current through the PC device, we use the so-called quantum trajectory method to derive the zero-temperature conditional master equation. We first treat the electron tunneling through the PC barrier as a classical stochastic point process (a quantum-jump model). Then we show explicitly that our results can be exte…
We deduce a class of non-Markovian completely positive master equations which describe a system in a composite bipartite environment, consisting of a Markovian reservoir and additional stationary unobserved degrees of freedom that modulate the dissipative coupling. The entanglement-induced memory effects can persist for arbitrary long times and affect the relaxation to equilibrium, as well as induce corrections to the quantum-regression theorem. By considering the extra degrees of freedom as a discrete manifold of energy levels, strong non-exponential behavior can arise, as for example power l…
