Experimental Determination of Dynamical Lee-Yang Zeros

TL;DR

This paper experimentally determines dynamical Lee-Yang zeros in non-equilibrium quantum systems, enabling prediction of large-deviation statistics from short-time measurements, advancing the understanding of out-of-equilibrium phase transitions.

Contribution

It introduces a novel experimental scheme to extract dynamical Lee-Yang zeros in non-equilibrium quantum processes, linking short-time zeros to large-deviation statistics.

Findings

Successfully measured dynamical Lee-Yang zeros in a quantum tunneling process.

Predicted large-deviation statistics from short-time behavior of zeros.

Demonstrated the method's potential for studying out-of-equilibrium phase transitions.

Abstract

Statistical physics provides the concepts and methods to explain the phase behavior of interacting many-body systems. Investigations of Lee-Yang zeros --- complex singularities of the free energy in systems of finite size --- have led to a unified understanding of equilibrium phase transitions. The ideas of Lee and Yang, however, are not restricted to equilibrium phenomena. Recently, Lee-Yang zeros have been used to characterize non-equilibrium processes such as dynamical phase transitions in quantum systems after a quench or dynamic order-disorder transitions in glasses. Here, we experimentally realize a scheme for determining Lee-Yang zeros in such non-equilibrium settings. We extract the dynamical Lee-Yang zeros of a stochastic process involving Andreev tunneling between a normal-state island and two superconducting leads from measurements of the dynamical activity along a trajectory. From the short-time behavior of the Lee-Yang zeros, we predict the large-deviation statistics of the activity which is typically difficult to measure. Our method paves the way for further experiments on the statistical mechanics of many-body systems out of equilibrium.