Spatiotemporal evolution of polaronic states in finite quantum systems

TL;DR

This paper investigates the real-time quantum dynamics of polaron formation and transport in finite one-dimensional systems using advanced numerical methods, revealing how initial states and parameters influence polaron behavior and phonon fluctuations.

Contribution

It introduces a combined Lanczos and Chebyshev approach to study polaron dynamics in finite quantum structures, highlighting the role of initial states and interaction parameters.

Findings

Polaron decay depends on energy, momentum, and coupling strength.

Bound polaron-phonon states can form in strong coupling regimes.

Polaron tunneling involves significant phonon number fluctuations.

Abstract

We study the quantum dynamics of small polaron formation and polaron transport through finite quantum structures in the framework of the one-dimensional Holstein model with site-dependent potentials and interactions. Combining Lanczos diagonalization with Chebyshev moment expansion of the time evolution operator, we determine how different initial states, representing stationary ground states or injected wave packets, after an electron-phonon interaction quench, develop in real space and time. Thereby, the full quantum nature and dynamics of electrons and phonons is preserved. We find that the decay out of the initial state sensitively depends on the energy and momentum of the incoming particle, the electron-phonon coupling strength, and the phonon frequency, whereupon bound polaron-phonon excited states may emerge in the strong-coupling regime. The tunneling of a Holstein polaron through a quantum wall/dot is generally accompanied by strong phonon number fluctuations due to phonon emission and re-absorption processes.