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

Abstract

AbstractOne of the foremost objectives of statistical mechanics is the description of the thermodynamic properties of quantum gases. Despite the great importance of this topic, such achievement is still lacking in the case of non-Hermitian quantum gases. Here, we investigate the properties of bosonic and fermionic non-Hermitian systems at finite temperatures. We show that non-Hermitian systems exhibit 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 an iTC is effectively a way to filter one specific Matsubara mode. In this realization, the Matsubara frequency, which usually appears as a mathematical tool to compute correlation functions at finite temperatures, can be measured experimentally.