Constraining work fluctuations of non-Hermitian dynamics across the exceptional point of a superconducting qubit

TL;DR

This study experimentally verifies that the Jarzynski equality holds for non-Hermitian superconducting qubits, revealing the influence of parity-time symmetry on work fluctuations in non-equilibrium quantum thermodynamics.

Contribution

It demonstrates experimentally that work fluctuations in non-Hermitian quantum systems obey fluctuation theorems, clarifying the role of parity-time symmetry in non-Hermitian thermodynamics.

Findings

Jarzynski equality holds for non-Hermitian qubits with complex eigenvalues

Work distribution depends on parity-time symmetry of the Floquet Hamiltonian

Experimental quantification of work fluctuations in dissipative superconducting circuits

Abstract

Thermodynamics constrains changes to the energy of a system, both deliberate and random, via its first and second laws. When the system is not in equilibrium, fluctuation theorems such as the Jarzynski equality further restrict the distributions of deliberate work done. Such fluctuation theorems have been experimentally verified in small, non-equilibrium quantum systems undergoing unitary or decohering dynamics. Yet, their validity in systems governed by a non-Hermitian Hamiltonian has long been contentious, due to the false premise of the Hamiltonian's dual and equivalent roles in dynamics and energetics. Here we show that work fluctuations in a non-Hermitian qubit obey the Jarzynski equality even if its Hamiltonian has complex or purely imaginary eigenvalues. With post-selection on a dissipative superconducting circuit undergoing a cyclic parameter sweep, we experimentally quantify the work distribution using projective energy measurements and show that the fate of the Jarzynski equality is determined by the parity-time symmetry of, and the energetics that result from, the corresponding non-Hermitian, Floquet Hamiltonian. By distinguishing the energetics from non-Hermitian dynamics, our results provide the recipe for investigating the non-equilibrium quantum thermodynamics of such open systems.