Generalized input-output method to quantum transport junctions. II. Applications

Abstract

The interaction of electrons with atomic motion critically influences charge transport properties in molecular conducting junctions and quantum dot systems, and it is responsible for a plethora of transport phenomena. Nevertheless, theoretical tools are still limited to treat simple model junctions in specific parameter regimes. In this work, we put forward a generalized input-output method (GIOM) for studying charge transport in molecular junctions accounting for strong electron-vibration interactions and including electronic and phononic environments. The method radically expands the scope of the input-output theory, which was originally put forward to treat quantum optic problems. Based on the GIOM we derive a Langevin-type equation of motion for molecular operators, which posses a great generality and accuracy, and permits the derivation of a stationary charge current expression involving only two types of transfer rates. Furthermore, we devise the so-called "Polaron Transport in Electronic Resonance" (PoTER) approximation, which allows to feasibly simulate electron dynamics in generic tight-binding models with strong electron-vibration interactions. To illustrate the breadth of applications of the GIOM-PoTER technique, we analyze prototype molecular junction models with primary and secondary vibrational modes. For short chains, the charge current reduces to known limits and reasonably agrees with exact numerical simulations (when available). For extended junctions the current displays a turnover from phonon-assisted to phonon-suppressed transport. Nevertheless, the onset of ohmic behavior requires extensions beyond the PoTER approximation. As an additional application, we consider a cavity-coupled molecule junction. Here we identify a cavity-induced suppression of charge current in the single-site case, and observe signatures of polariton formation in the current-voltage characteristics in the strong light-matter coupling regime. A critical understanding gained from the GIOM-PoTER scheme is that the single-site vibrationally-coupled model is deceptively simpler, and amenable to approximations than multi-site models. Therefore, benchmarking of methods should not be concluded with the single-site case. The work manifests that the input-output framework, which is normally employed in quantum optics, can serve as a powerful and feasible tool in the realm of electron transport junctions.

Temporal switching to extend the bandwidth of thin absorbers

“…To establish a thorough analysis of temporal switching in open systems, input-output techniques appear to be an ideal tool, since they can treat the field redistribution in a scatterer in time domain after the abrupt change of its properties as initial conditions to study the field evolution and associated scattering processes. This approach, initially established in quantum optics [24]- [25], has been applied to quantum networks [26]- [28], photon and charge transport [29]- [32] and quantum scattering [33]. As a variant for classical wave physics, coupled-mode theory (CMT) has been extensively used to model coupled resonator systems, well suited in regimes near resonance [34]- [36].…”

Quantum Nondemolition Photon Counting With a Hybrid Electromechanical Probe

“…In this supplementary material we present the derivation of the steady state charge current expression used in the main text by resorting to a generalized input-output method [61,62].…”

“…Adopting a recently developed generalized input-output method for electronic systems [61,62], we treat the hybrid quantum system within a unified input-output picture. As the system H0 contains both fermionic and bosonic operators, we should treat them separately.…”

“…Current-voltage characteristics of the SET.-The steady state charge current of the SET serves to probe the photon number. Based on a generalized input-output method [60][61][62], we arrive at the current expression out of the source…”

Fully differentiable optimization protocols for non-equilibrium steady states

“…In open quantum systems (OQSs), the time-evolution of a subsystem interacting with either a single or multiple environments, is modeled by a quantum master equation (QME) where ρ is the reduced density matrix, and F is the Liouvillian [1]. The simulation of open quantum many-body systems has lead to the development of various algorithms, e.g., renormalization group [2][3][4], meanfield methods [5][6][7], tensor networks [8][9][10][11][12], hierarchical equations of motion [13][14][15], Heisenberg equation of motion approaches [16,17], secular and non-secular Redfield theory [18,19], tensor transfer methods [20][21][22], and mixed quantum-classical methods [23][24][25].…”