Time-dependent quantum transport: causal superfermions, exact fermion-parity protected decay mode, and Pauli exclusion principle for mixed quantum states

We extend the recently developed causal superfermion approach to the real-time transport theory to time-dependent decay problems.Its usefulness is illustrated for the Anderson model of a quantum dot with tunneling rates depending on spin due to the ferromagnetic electrodes and/or spin polarization of the tunnel junction. We set up a second quantization scheme for density operators in the Liouville-Fock space constructing causal field superoperators using the fundamental physical principles of causality/probability conservation and the fermion-parity superselection (univalence). The time-dependent perturbation series for the time-evolution is renormalized by explicitly performing the wide-band limit on the superoperator level. The short and long-time reservoir correlations are shown to be tightly linked to the occurrence of causal field destruction and creation superoperators, respectively. The effective theory takes as a reference a damped local system, providing an interesting starting point for numerical calculations of memory kernels in real-time. A remarkable feature of this approach is the natural appearance of a measurable fermion-parity protected decay mode. It already can be calculated exactly in the Markovian, infinite temperature limit by leading order perturbation theory, yet persists unaltered for the finite temperature, interaction and tunneling spin polarization. Furthermore, we show how a Liouville-space analog of the Pauli principle directly leads to the exact result in the noninteracting limit: surprisingly, it is obtained in finite (second) order renormalized perturbation theory, both for the self-energy as well as the time-evolution propagator. For this limit we calculate the time-evolution of the full density operator starting from an arbitrary initial state on the quantum dot, including spin and pairing coherences and two-particle correlations.Comment: This version contains the more extensive introduction and the conclusion, discussing an experimental relevance of the obtained exact result for the new decay mode. A lot of new references have been added. The more detailed comparison of the results obtained for the noninteracting case with the known results has been done. Small typos have been fixe

Density-operator evolution: Complete positivity and the Keldysh real-time expansion

We study the reduced time-evolution of open quantum systems by combining quantum-information and statistical field theory. Inspired by prior work [EPL 102, 60001 (2013) and Phys. Rev. Lett. 111, 050402 (2013)] we establish the explicit structure guaranteeing the complete positivity (CP) and trace-preservation (TP) of the real-time evolution expansion in terms of the microscopic system-environment coupling. This reveals a fundamental two-stage structure of the coupling expansion: Whereas the first stage defines the dissipative timescales of the system --before having integrated out the environment completely-- the second stage sums up elementary physical processes described by CP superoperators. This allows us to establish the nontrivial relation between the (Nakajima-Zwanzig) memory-kernel superoperator for the density operator and novel memory-kernel operators that generate the Kraus operators of an operator-sum. Importantly, this operational approach can be implemented in the existing Keldysh real-time technique and allows approximations for general time-nonlocal quantum master equations to be systematically compared and developed while keeping the CP and TP structure explicit. Our considerations build on the result that a Kraus operator for a physical measurement process on the environment can be obtained by 'cutting' a group of Keldysh real-time diagrams 'in half'. This naturally leads to Kraus operators lifted to the system plus environment which have a diagrammatic expansion in terms of time-nonlocal memory-kernel operators. These lifted Kraus operators obey coupled time-evolution equations which constitute an unraveling of the original Schr\"odinger equation for system plus environment. Whereas both equations lead to the same reduced dynamics, only the former explicitly encodes the operator-sum structure of the coupling expansion.Comment: Submission to SciPost Physics, 49 pages including 6 appendices, 13 figures. Significant improvement of introduction and conclusion, added discussions, fixed typos, no results change

Transport signature of pseudo-Jahn-Teller dynamics in a single-molecule transistor

We calculate the electronic transport through a molecular dimer, in which an excess electron is delocalized over equivalent monomers, which can be locally distorted. In this system the Born-Oppenheimer approximation breaks down resulting in quantum entanglement of the mechanical and electronic motion. We show that pseudo Jahn-Teller (pJT) dynamics of the molecule gives rise to conductance peaks that indicate this violation. Their magnitude, sign and position sharply depend on the electro-mechanical properties of the molecule, which can be varied in recently developed three-terminal junctions with mechanical control. The predicted effect depends crucially on the degree of intramolecular delocalization of the excess electron, a parameter which is also of fundamental importance in physical chemistry.Comment: 6 pages, 3 figure

Non-linear thermoelectrics of molecular junctions with vibrational coupling

We present a detailed study of the non-linear thermoelectric properties of a molecular junction, represented by a dissipative Anderson-Holstein model. A single orbital level with strong Coulomb interaction is coupled to a localized vibrational mode and we account for both electron and phonon exchange with both electrodes, investigating how these contribute to the heat and charge transport. We calculate the efficiency and power output of the device operated as a heat to electric power converter and identify the optimal operating conditions, which are found to be qualitatively changed by the presence of the vibrational mode. Based on this study of a generic model system, we discuss the desirable properties of molecular junctions for thermoelectric applications.Comment: 8 pages, 5 figure

Pair-tunneling resonance in the single-electron transport regime

We predict a new electron pair-tunneling (PT) resonance in non-linear transport through quantum dots with positive charging energies exceeding the broadening due to thermal and quantum fluctuations. The PT resonance shows up in the single-electron transport (SET) regime as a peak in the derivative of the non-linear conductance when the electrochemical potential of one electrode matches the average of two subsequent charge addition energies. For a single level quantum dot (Anderson model) we find the analytic peak shape and the dependence on temperature, magnetic field and junction asymmetry and compare with the inelastic cotunneling peak which is of the same order of magnitude. In experimental transport data the PT resonance may be mistaken for a weak SET resonance judging only by the voltage dependence of its position. Our results provide essential clues to avoid such erroneous interpretation of transport spectroscopy data.Comment: 5 pages, 2 figures, published versio

Duality for open fermion systems: energy-dependent weak coupling and quantum master equations

Open fermion systems with energy-independent bilinear coupling to a fermionic environment have been shown to obey a general duality relation [Phys. Rev. B 93, 81411 (2016)] which allows for a drastic simplification of time-evolution calculations. In the weak-coupling limit, such a system can be associated with a unique dual physical system in which all energies are inverted, in particular the internal interaction. This paper generalizes this fermionic duality in two ways: we allow for weak coupling with arbitrary energy dependence and describe both occupations and coherences coupled by a quantum master equation for the density operator. We also show that whenever generalized detailed balance holds (Kolmogorov criterion), the stationary probabilities for the dual system can be expressed explicitly in terms of the stationary recurrence times of the original system, even at large bias. We illustrate the generalized duality by a detailed analysis of the rate equation for a quantum dot with strong onsite Coulomb repulsion, going beyond the commonly assumed wideband limit. We present predictions for (i) the decay rates for transient charge and heat currents after a gate-voltage quench and (ii) the thermoelectric linear response coefficients in the stationary limit. We show that even for pronouncedly energy-dependent coupling, all nontrivial parameter dependence in these problems is entirely captured by just two well-understood stationary variables, the average charge of the system and of the dual system. Remarkably, it is the latter that often dictates the most striking features of the measurable quantities (e.g., positions of resonances), underscoring the importance of the dual system for understanding the actual one.Comment: 25 pages + 2 pages appendix + 2 pages references, 7 figures. To be submitted to Phys. Rev.

Spin quantum tunneling in single molecular magnets: fingerprints in transport spectroscopy of current and noise

We demonstrate that transport spectroscopy of single molecular magnets shows signatures of quantum tunneling at low temperatures. We find current and noise oscillations as function of bias voltage due to a weak violation of spin selection rules by quantum tunneling processes. The interplay with Boltzmann suppression factors leads to fake resonances with temperature-dependent position which do not correspond to any charge excitation energy. Furthermore, we find that quantum tunneling can completely suppress transport if the easy-plane anisotropy has a high symmetry.Comment: 4 pages, 3 figure

Qubit quantum-dot sensors: noise cancellation by coherent backaction, initial slips, and elliptical precession

We theoretically investigate the backaction of a sensor quantum dot with strong local Coulomb repulsion on the transient dynamics of a qubit that is probed capacitively. We show that the measurement backaction induced by the noise of electron cotunneling through the sensor is surprisingly mitigated by the recently identified coherent backaction [PRB 89, 195405] arising from quantum fluctuations. This renormalization effect is missing in semiclassical stochastic fluctuator models and typically also in Born-Markov approaches, which try to avoid the calculation of the nonstationary, nonequilibrium state of the qubit plus sensor. Technically, we integrate out the current-carrying electrodes to obtain kinetic equations for the joint, nonequilibrium detector-qubit dynamics. We show that the sensor-current response, level renormalization, cotunneling, and leading non-Markovian corrections always appear together and cannot be turned off individually in an experiment or ignored theoretically. We analyze the backaction on the reduced qubit state - capturing the full non-Markovian effects imposed by the sensor quantum dot on the qubit - by applying a Liouville-space decomposition into quasistationary and rapidly decaying modes. Importantly, the sensor cannot be eliminated completely even in the simplest high-temperature, weak-measurement limit: The qubit state experiences an initial slip that persists over many qubit cycles and depends on the initial preparation of qubit plus sensor quantum dot. A quantum-dot sensor can thus not be modeled as a 'black box' without accounting for its dynamical variables. We furthermore find that the Bloch vector relaxes (T1) along an axis that is not orthogonal to the plane in which the Bloch vector dephases (T2), blurring the notions of T1 and T2 times. Finally, the precessional motion of the Bloch vector is distorted into an ellipse in the tilted dephasing plane.Comment: This is the version published in Phys. Rev.