Operational models of temperature superpositions

An interacting quantum system and thermal bath can reach thermal equilibrium, resulting in the system and bath acquiring the same temperature. But how does a delocalized quantum system thermalize with a bath whose local temperature varies as, for example, in the Tolman effect? Here, we formulate two scenarios in which the notion of a “superposition of temperatures” may arise: first, a probe interaction with two different baths dependent on the state of another quantum system (a control); and second, a probe interaction with a single bath whose purified state is a superposition of states that each correspond to different temperatures. We show that the two scenarios are fundamentally different and can be operationally distinguished. Moreover, we show that the final probe state is sensitive to the specific realization of the thermalizing channels, and that our results hold for partial and prethermalization cases. Our models may be applied to scenarios involving joint quantum and relativistic phenomena, and explain some recent results found in quantum interference of relativistic probes thermalizing with Unruh or Hawking radiation.