Quantum beer coolers

August 11, 2015

Today, with Nicolas Brunner, we have a new paper out on the arXiv: https://arxiv.org/abs/1508.02025 . This one studies the behaviour of a small quantum refrigerator.

Thermal machines – such as the refrigerator which keeps your beer cold and makes ice for your caipirinha, or a steam turbine generating electricity from heat in a power plant – have been studied for a long time. The desire to improve early steam engines led to the development of thermodynamics which is now a very broad physical theory dealing with any process where heat is exchanged or converted into other forms of energy. Thermodynamics now allows us to understand well what goes on in thermal machines.

Quantum mechanics is another very successful theory, which gives us a good description of things on very small scales – the interaction of a few atoms with each other, or of an atom with light and so on. As you may know, on these scales the physics is different from everyday experience, and weird things start to happen. Quantum systems can be in superpositions – the famous Schrödinger’s cat which is neither dead nor alive – and can show correlations that are stronger than in any classical system (as I have written about before, for example here).

Usually, when we think about thermal processes, such as cooling a beer, large systems with many particles are involved (the beer and the refrigerator consist of zillions of atoms). It is natural to ask though, what happens when we make things so small that quantum effects begin to matter? Can we understand thermodynamics at the quantum level? Can we still define quantities such as heat and work? What happens to important concepts in thermodynamics such as the Carnot efficiency or the second law?

There is a lot of work going on at present trying to answer these questions. One approach is to go back to the beginnings of thermodynamics – steam engines and other thermal machines – and make the machines as small as possible. Such quantum thermal machines are a good testing ground where ideas from thermodynamics and quantum mechanics can be combined. Our work follows this approach. We look at a small absorption refrigerator consisting of just three two-level systems (think of three atoms) coupled to thermal baths at different temperatures.

This quantum fridge has already been used to find several interesting results, for example that quantum entanglement can improve cooling, and that quantum machines can reach Carnot efficiency. These results were obtained by looking at the fridge in the ‘steady state’ – i.e. after a long time, when the ‘beer’ in the fridge is already cold. In this paper, we take a look at the ‘transient regime’ of the fridge – i.e. what happens in the time between putting a warm beer in the fridge and taking out a cold one. Our contribution is a bit technical. We map out some details of this process and find the time scales for the ‘beer’ to loose it’s quantum character or approach the steady state. Among other things, we find that the ‘beer’ can sometimes get colder at an intermediate time than in the steady state – i.e. if you want the beer cold you shouldn’t leave in the fridge too long. This is a purely quantum effect and that happens to single-atom beers but definitely not to that tasty IPA you were saving for later!

Published paper: https://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.062101