Quench dynamics in superconducting nanojunctions: metastability and dynamical Yang-Lee zeros

TL;DR

This paper investigates the charge transfer dynamics in superconducting nano-junctions using full counting statistics, revealing metastable states, the role of dynamical Yang-Lee zeros, and how initial conditions influence non-equilibrium populations.

Contribution

It introduces a novel method linking dynamical zeros of the generating function to charge transfer statistics, enabling analysis of metastability and state control in superconducting nano-junctions.

Findings

Metastable states depend on initial conditions.

Slower switching rates increase deviation from thermal equilibrium.

Method accurately predicts steady state current and noise.

Abstract

We study the charge transfer dynamics following the formation of a phase or voltage biased su- perconducting nano-junction using a full counting statistics analysis. We demonstrate that the evolution of the zeros of the generating function allows one to identify the population of different many body states much in the same way as the accumulation of Yang-Lee zeros of the partition function in equilibrium statistical mechanics is connected to phase transitions. We give an exact expression connecting the dynamical zeros to the charge transfer cumulants and discuss when an approximation based on "dominant" zeros is valid. We show that, for generic values of the parameters, the system gets trapped into a metastable state characterized by a non-equilibrium population of the many body states which is dependent on the initial conditions. We study in particular the effect of the switching rates in the dynamics showing that, in contrast to intuition, the deviation from thermal equilibrium increases for the slower rates. In the voltage biased case the steady state is reached independently of the initial conditions. Our method allows us to obtain accurate results for the steady state current and noise in quantitative agreement with steady state methods developed to describe the multiple Andreev reflections regime. Finally, we discuss the system dynamics after a sudden voltage drop showing the possibility of tuning the many body states population by an appropriate choice of the initial voltage, providing a feasible experimental way to access the quench dynamics and control the state of the system.