Numerical simulations of time-resolved quantum electronics

Benoit Gaury (1) , Joseph Weston (1, 2) , Matthieu Santin (1) , Manuel Houzet (1, 2) , Christoph Groth (1, 2) , Xavier Waintal (1, 2)

1 SPSMS - UMR 9001 - Service de Physique Statistique, Magnétisme et Supraconductivité
2 GT - Laboratory of Quantum Theory

Numerical simulation has become a major tool in quantum electronics both for fundamental and applied purposes. While for a long time those simulations focused on stationary properties (e.g. DC currents), the recent experimental trend toward GHz frequencies and beyond has triggered a new interest for handling time-dependent perturbations. As the experimental frequencies get higher, it becomes possible to conceive experiments which are both time-resolved and fast enough to probe the internal quantum dynamics of the system. This paper discusses the technical aspects-mathematical and numerical-associated with the numerical simulations of such a setup in the time domain (i.e. beyond the single-frequency AC limit). After a short review of the state of the art, we develop a theoretical framework for the calculation of time-resolved observables in a general multiterminal system subject to an arbitrary time-dependent perturbation (oscillating electrostatic gates, voltage pulses, time-varying magnetic fields, etc.) The approach is mathematically equivalent to (i) the time-dependent scattering formalism, (ii) the time-resolved non-equilibrium Green's function (NEGF) formalism and (iii) the partition-free approach. The central object of our theory is a wave function that obeys a simple Schrödinger equation with an additional source term that accounts for the electrons injected from the electrodes. The time-resolved observables (current, density, etc.) and the (inelastic) scattering matrix are simply expressed in term of this wave function. We use our approach to develop a numerical technique for simulating time-resolved quantum transport. We find that the use of this wave function is advantageous for numerical simulations resulting in a speed up of many orders of magnitude with respect to the direct integration of NEGF equations. Our technique allows one to simulate realistic situations beyond simple models, a subject that was until now beyond the simulation capabilities of available approaches.

Domaines: Physique [physics]

Benoit Gaury, Joseph Weston, Matthieu Santin, Manuel Houzet, Christoph Groth, et al.. Numerical simulations of time-resolved quantum electronics. Physics Reports, 2014, 534 (1), pp.1-37. ⟨10.1016/j.physrep.2013.09.001⟩. ⟨hal-02007850⟩