Excitation of collective modes in a quantum flute

TL;DR

This paper models non-equilibrium electron transport in a quantum wire with time-dependent contacts, revealing standing wave patterns and current behaviors akin to a musical flute, influenced by pulse shape and contact position.

Contribution

It introduces a generalized master equation approach to simulate time-dependent transport in a Coulomb-interacting quantum wire with modulated contacts, capturing complex wave phenomena.

Findings

Current profiles depend on pulse shape and contact position.

Standing wave patterns influence electron transport, similar to a flute.

Rectangular pulses can cause current to flow against bias temporarily.

Abstract

We use a generalized master equation (GME) formalism to describe the non-equilibrium time-dependent transport of Coulomb interacting electrons through a short quantum wire connected to semi-infinite biased leads. The contact strength between the leads and the wire is modulated by out-of-phase time-dependent potentials which simulate a turnstile device. We explore this setup by keeping the contact with one lead at a fixed location at one end of the wire whereas the contact with the other lead is placed on various sites along the length of the wire. We study the propagation of sinusoidal and rectangular pulses. We find that the current profiles in both leads depend not only on the shape of the pulses, but also on the position of the second contact. The current reflects standing waves created by the contact potentials, like in a wind musical instrument (for example a flute), but occurring on the background of the equilibrium charge distribution. The number of electrons in our quantum "flute" device varies between two and three. We find that for rectangular pulses the currents in the leads may flow against the bias for short time intervals, due to the higher harmonics of the charge response. The GME is solved numerically in small time steps without resorting to the traditional Markov and rotating wave approximations. The Coulomb interaction between the electrons in the sample is included via the exact diagonalization method. The system (leads plus sample wire) is described by a lattice model.