Quantum superpositions of different temperatures: is it possible?

We live in a quantum world where physical objects can, in principle, exist in a superposition of very different states. Can a quantum system be in a superposition of two states characterized by different temperatures, for example, ice and boiling water? Most physicists would certainly say “no”. And yet, the tenets of quantum mechanics don’t negate the possibility of this type of superposition. In fact, if one were to randomly select a wave function for any large isolated system, such superpositions are overwhelmingly likely to occur.

Two scientists from Skoltech – Walter Hahn and Boris Fine – recently asked themselves: Why don’t we encounter superpositions or quantum mixtures of different temperatures in everyday life, and what needs to be done to observe such states in the laboratory? Theoretically, the answers to these questions could have an integral impact on the foundations of quantum statistical physics. On a practical level, these answers could have considerable implications for quantum simulator technology, a technology that is currently being pursued by many laboratories across the globe.

In an article published in the journal Physical Review E, Hahn and Fine introduced a novel fundamental principle: physically realizable quantum statistical ensembles must be stable with respect to accidental random measurements. The article presented analytical and quantitative evidence that ensembles representing two or more different temperatures are extremely unstable, while the canonical statistical ensemble corresponding to a single temperature is stable. The study also offered suggestions with respect to how to design a quantum system in the laboratory to maximize the lifetime of the superpositions of different temperatures.

The study’s lead author, Skoltech research scientist Walter Hahn, said, “We think that superpositions of two different temperatures could eventually be realized experimentally, for example, with ultracold atoms. If this happens, one could check our theoretical predictions.”

The project leader, Skoltech professor Boris Fine, said: “Our goal was to clarify the applicability limit of conventional statistical physics associated with the energy width of quantum statistical ensembles. We hope Interesting things will be discovered as one explores the regimes beyond this limit.”

The results of the study were published in the journal Physical Review E.

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