We investigate the dynamics of a single phonon (oscillator) mode linearly coupled to an electronic few-level system in contact with external particle reservoirs (leads). A stationary electronic current through the system generates non-trivial dynamical behaviour of the oscillator. Using FeynmanVernon influence functional theory, we derive a Langevin equation for the oscillator trajectory that is non-perturbative in the system-leads coupling and from which we extract effective oscillator potentials and friction coefficients. For the two simplest cases of a single and two coupled electronic levels, we discuss various regimes of the oscillator dynamics.

We consider the sub-gap physics of a hybrid double-quantum dot Cooper-pair splitter with large single-level spacings, in the presence of tunnelling between the dots and finite Coulomb intra-and inter-dot Coulomb repulsion. In the limit of a large superconducting gap, we treat the coupling of the dots to the superconductor exactly. We employ a generalized master-equation method which easily yields currents, noise and cross-correlators. In particular, for finite inter-and intra-dot Coulomb interaction, we investigate how the transport properties are determined by the interplay between local and nonlocal tunneling processes between the superconductor and the dots. We examine the effect of inter-dot tunneling on the particle-hole symmetry of the currents with and without spinorbit interaction. We show that spin-orbit interaction in combination with finite Coulomb energy opens the possibility to control the nonlocal entanglement and its symmetry (singlet/triplet). We demonstrate that the generation of nonlocal entanglement can be achieved even without any direct nonlocal coupling to the superconducting lead.

We investigate the nonlocal thermoelectric transport in a Cooper-pair splitter based on a doublequantum-dot-superconductor three-terminal hybrid structure. We find that the nonlocal coupling between the superconductor and the quantum dots gives rise to nonlocal thermoelectric effects which originate from the nonlocal particle-hole breaking of the system. We show that Cooper-pair splitting induces the generation of a thermo-current in the superconducting lead without any transfer of charge between the two normal metal leads. Conversely, we show that a nonlocal heat exchange between the normal leads is mediated by non-local Andreev reflection. We discuss the influence of finite Coulomb interaction and study under which conditions nonlocal power generation becomes possible, and when the Cooper-pair splitter can be employed as a cooling device.

We investigate to which extent a many-body Bloch-Redfield master-equation description of quantum transport is consistent with the exact generalized equilibrium conditions known as exchange fluctuation theorems. Thereby, we identify a class of master equations for which this is the case. Beyond this class, we find deviations which exhibit characteristic scaling laws as functions of the dot-lead tunneling, the interdot tunneling, and the temperature. These deviations are accompanied by an increase of lead energy fluctuations inherent in the Bloch-Redfield equation beyond a rotating-wave approximation. We illustrate our results with numerical data for a double quantum dot attached to four leads.

The control of nonlocal entanglement in solid state systems is a crucial ingredient of quantum technologies. We investigate a Cooper-pair splitter based on a double quantum dot realised in a semiconducting nanowire. In the presence of interdot tunnelling the system provides a simple mechanism to develop spatial entanglement even in absence of nonlocal coupling with the superconducting lead. We discuss the possibility to control the symmetry (singlet or triplet) of spatially separated, entangled electron pairs taking advantage of the spin-orbit coupling of the nanowire. We also demonstrate that the spin-orbit coupling does not impact over the entanglement purity of the nonlocal state generated in the double quantum dot system.Comment: 7 pages, 3 figure