Operational Models of Temperature Superpositions RQI North 2024

Abstract

An interacting quantum system and thermal bath can reach thermal equilibrium, resulting in each acquiring the same temperature. But how does a quantum probe, with inherent uncertainty in its position, thermalise with a bath with a locally-varying temperature, or which is itself in some superposition of thermal states? Can temperature itself exhibit characteristics such as superposition or quantum coherence? Such abstract ideas are highly relevant in certain scenarios at the intersection of quantum theory, thermodynamics, and relativity. For example, a system probing a gas in thermal equilibrium in a gravitational field would encounter a bath with a temperature that varies with position, according to the Tolman-Ehrenfest effect. Similarly, a quantum system in non-inertial motion, according to the Unruh effect, thermalises to a temperature proportional to its acceleration. In both cases, the delocalised nature of a quantum system has it interacting with baths of differing temperatures, or baths in superposition.

In this work, we identify a general approach to addressing the points raised above, and identify 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 an additional control system. 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 state of the probe is sensitive to the specific dilation of the thermalising channels. These results are further reproduced in our analysis of partial and pre-thermalisation processes. Finally, we identify how our models may be applied to scenarios involving joint quantum, gravitational, and thermodynamic phenomena, and how the second of the two models in particular resolves a formerly-outstanding problem for relativistic quantum systems in superpositions of accelerations.

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.