Quasiparticle states in AC-driven quantum conductors: A scattering theory approach

TL;DR

This paper presents a scattering theory method to extract quasiparticle wave functions in AC-driven quantum conductors, revealing distinct excitation behaviors in quantum contacts and mesoscopic capacitors, with implications for electron quantum optics.

Contribution

The authors introduce a novel scattering theory approach incorporating Bloch-Messiah reduction to analyze quasiparticle states in AC-driven conductors, enabling wave function extraction from the scattering matrix.

Findings

Multiple particle-hole pairs excited in quantum contacts with increasing driving strength.

Single pair excitation with oscillating probability in mesoscopic capacitors.

Phase relationships between quasiparticle components and driving field vary between systems.

Abstract

We introduce a general procedure to extract the wave function of quasiparticles in AC-driven quantum conductors. By incorporating the Bloch-Messiah reduction into the scattering theory approach to quantum transport, we construct the many-body state from the scattering matrix, within which the wave function of quasiparticles can be extracted. We find that two kinds of quasiparticles can be excited, while both of them are superpositions of particle and hole states in the Fermi sea. Due to the electron number conservation, the quasiparticles are always created in pairs, resulting in particle-hole pair excitations in quantum conductors. We apply our approach to compare these particle-hole pairs excited in perfectly transparent quantum contacts and mesoscopic capacitors with single-level quantum dot. For the quantum contacts, multiple pairs can be excited, while the excitation probability of each pair increases as the strength of the driving field increasing. The particle(hole) components are always in phase (180 degrees out of phase) with the driving field. These features agree with the results obtained via the extended Keldysh-Green's function technique. For the mesoscopic capacitors, only one particle-hole pair can be excited, while the corresponding excitation probability undergoes an oscillation as the strength of the driving field increasing. A nonzero phase delay between the particle(hole) component and the driving field exists, which can be tuned via the dot-lead coupling in the mesoscopic capacitor. These features are very distinct from the case of quantum contacts, which can be attributed to the finite dwell time of electrons in the mesoscopic capacitor. We also find that our approach can also offer a general way to extract the wave function of quasiparticles from the Wigner function, making it helpful for the signal processing of relevant experiments in electron quantum optics.