Non-Hermitian quantum gases: a platform for imaginary time crystals

TL;DR

This paper explores non-Hermitian quantum gases as a new platform for realizing imaginary time crystals, revealing temperature and imaginary time oscillations, and linking these to disorder points and measurable Matsubara modes.

Contribution

It introduces non-Hermitian quantum gases as a novel platform for imaginary time crystals and connects their properties to disorder points and experimental observability.

Findings

Non-Hermitian systems exhibit oscillations in temperature and imaginary time.

The Hatano-Nelson model demonstrates the emergence of imaginary time crystal behavior.

Conditions for iTC are linked to the presence of disorder points and oscillating correlation functions.

Abstract

One of the most important applications of quantum mechanics is the thermodynamic description of quantum gases. Despite the fundamental importance of this topic, a comprehensive description of the thermodynamic properties of non-Hermitian quantum gases is still lacking. Here, we investigate the properties of bosonic and fermionic non-Hermitian systems at finite temperatures. We show that non-Hermitian systems exihibit oscillations both in temperature and imaginary time. As such, they can be a possible platform to realize an imaginary time crystal (iTC) phase. The Hatano-Nelson model is identified as a simple lattice model to reveal this effect. In addition, we show that the conditions for the iTC to be manifest are the same as the conditions for the presence of disorder points, where the correlation functions show oscillating behavior. This analysis makes clear that our realization of iTC is effectively a way to filter one specific Matsubara mode. In this realization, the Matsubara frequency, that enters as a mathematical tool to compute correlation functions for finite temperatures, can be measured experimentally.