On Temperature Superpositions

Abstract

When a quantum system interacts with a thermal bath it can reach thermal equilibrium with and acquire the same temperature as the bath. But how does a delocalised quantum system thermalise with a bath whose local temperature varies, as, for example, in the Tolman-Ehrenfest effect?

Motivated by such scenarios that arise where quantum physics and thermodynamics intersect with relativity, we formulate two scenarios in which the notion of a “superposition of temperatures” may arise. First: a probe interacting with two different baths dependent on the state of a control. Second: a probe interacting with a single bath whose purified state is itself a superposition of states corresponding to different temperatures. We show that the two scenarios are fundamentally different and operationally distinguishable. Moreover, we show that the probe does not in general thermalise even when the involved temperatures are equal, and that the final probe state is sensitive to the specific realisation of the thermalising channels. These results are further reproduced in partial and pre-thermalisation processes. Our models may be applied to scenarios involving joint quantum, gravitational, and thermodynamic phenomena, and explain some recent results found in quantum interference of relativistic probes thermalising with Unruh or Hawking radiation.

Carolyn Wood

Postdoctoral Scientist

Carolyn Wood is a postdoctoral researcher at the University of Queensland, in Brisbane, Australia focusing on quantum machine learning and physics at the interface between quantum mechanics and general relativity.