Non-Markovian transmission through two quantum dots connected by a continuum

Abstract

We consider a transport setup containing a double-dot connected by a continuum. Via an exact solution of the time-dependent Schrödinger equation, we demonstrate a highly non-Markovian quantum-coherence-mediated transport through this dot-continuum-dot (DCD) system, which is in contrast with the common premise since in typical case a quantum particle does not reenter the system of interest once it irreversibly decayed into a continuum (such as the spontaneous emission of a photon). We also find that this DCD system supports an unusual steady state with unequal source and drain currents, owing to electrons irreversibly entering the continuum and floating there.PACS numbers: 03.65. Yz, Coupling of a finite-size system to a reservoir with continuum energy spectrum is relevant to many fundamental issues of physics, e.g., the emergence of classicality from a quantum world [1], and the origin of irreversibility in statistical physics. Simple example of such type of coupling can be a small system, with discrete states, coupled to a continuum in terms of quantum tunneling.In most cases, coupling with a continuum would result in an irreversible decay of the discrete state, with the particle never coming back, such as the spontaneous emission of photon from an atom. However, in a recent study [2], where a double-dot connected by a continuum was considered, it was found that the second dot can affect the decay from the first dot via quantum interference, and finally lead to a formation of stationary bound state embedded in the continuum. In subsequent related studies [3,4], also concerning this dot-continuum-dot (DCD) system, it was demonstrated that the electron's motion through the continuum is very unusual, say, revealing an undetectable feature in the transfer process, and the information lost into the continuum can be retrieved without generating more disturbance.In the present work we consider inserting the DCD system into a transport configuration, as schematically shown by Fig. 1, which allows for an investigation for the behavior of continuous current through the DCD setup. Moreover, beyond the above DCD studies [2][3][4], where a wideband-limit (WBL) model was assumed for the central continuum, we will generalize our study to a finite-bandwidth Lorentzian spectrum (FBLS) for both the leads and the continuum. As a consequence, the transient transport process is highly non-Markovian, much stronger than in the WBL [5]. Particularly, associated with the peculiar DCD setup, we will discuss and uncover other features in relation with the coherence-mediated transfer and electron accumulation (floating) in the continuum, basing both on an exact treatment for the non-Markovian transport. The issue of non-Markovian transport through quantum dots has received considerable attention in the past years [6-13], * Electronic address: lixinqi@bnu.edu.cn where the non-Markovian transient dynamics are usually manifested in the current noise spectrum or in terms of full counting statistics. Moreover, exploiting the nature of non-Mark...

Transport probe of nonadiabatic transition caused by Majorana moving

“…where the edge states |e In this work, we would like to employ the singleelectron wavefunction (SEWF) approach [38][39][40][41][42] for the highly time-dependent transport problem under study, which is actually a time-dependent generalization of the stationary S matrix scattering theory. The basic idea of the SEWF approach is keeping track of the quantum evolution of a single electron initially in the lead, and computing the time-dependent transport coefficients.…”

“…We are thus required to apply a time dependent transport theory. In this work, we will apply the single-electron wavefunction (SEWF) approach [38][39][40][41], which is a timedependent generalization of the stationary S matrix scattering theory. In particular, this approach was recently extended to the context of superconductor-induced Andreev reflections [42].…”

Revisit the non-locality of Majorana zero modes and teleportation: Bogoliubov-de Gennes equation based treatment

“…For mesoscopic quantum transports, there exist well known approaches such as the nonequilibrium Green's function (nGF) method [44,45] and the S-matrix quantum scattering theory [45,46] which are particularly suitable, in the absence of many-body interactions, to study transport through a large system modeled by the tightbinding lattice model and with superconductors involved (either as the leads or a central device). Another lessdeveloped method, say, the single particle wavefunction (SPWF) approach [47][48][49][50], is an alternative but attractive choice. This method, directly based on the timedependent Schrödinger equation, was developed in the context of transport through small systems such as quantum dots and has been applied skillfully to study some interesting problems [50].…”