A quantum electronics fridge

July 28, 2016

A week and few days back, we put a new paper out on the arXiv: https://arxiv.org/abs/1607.05218. I was travelling, so didn’t get around to writing anything before now (I’m getting behind on writing these things… with Rafael Chaves, we have another one out today, but it’ll have to wait).

This one proposes to build a teeny tiny fridge using fancy quantum electronics involving superconductors and Josephson junctions. Sounds crazy, but we think this is actually something experimentalists can do (at least pretty soon) :).

A fridge is a thermal machine – in this case a tiny, quantum one, so the context of this work is quantum thermodynamics. I’ve written about that before, so let me quote a previous post to give some background:

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.

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. Like previous papers I’ve written about, our new work follows this approach.

The new machine basically consists of three LC circuits that talk to each other and to the surroundings. LC circuits are everywhere in modern electronics. They are what enables a radio to tune in to a desired station and digital watches to keep track of time. An LC circuit is analogous to to a spring or a pendulum: something that vibrates at a particular frequency. Physicist call such systems ‘harmonic oscillators’ and they are our favourite building blocks for… well for everything! In our machine, the whole system is cooled down and the oscillators enter the quantum regime where only a few quanta of vibrations are present at any time. Each oscillator is connected to a thermal bath that it can exchange energy with, at different temeperatures. If nothing else is done, each oscillator will then be at the temperature of its bath – it vibrates more or less according to how hot or cold the bath is. The goal of the fridge is to cool one of the oscillators below the temperature of the coldest bath. We can think of that oscillator as the ‘beer’.

To make the fridge cool, the oscillators are connected to each other through something called a Josephson junction. It is basically a weak link between two parts of a superconducting electronic circuit. The physics of what goes on there is a whole topic by itself, but in this case it just enables energy to hop between the oscillators in a very specific way: it can flow from the hottest and coldest oscillators into the one of intermediate temperature, and vice versa. This is exactly what one needs for cooling. Thermodynamics tells us that heat never flows from cold to hot by itself (if you put a beer in a warm room, it never suddenly gets colder, right?). But by taking energy from the hottest oscillator too, we can make heat go from the cold oscillator into the intermediate one, thereby cooling the cold oscillator below its bath temperature. Viola – the beer gets colder!

So, it works. The machine has a couple of nice features too – once everything is connected, it runs all by itself without any external control. And the cooling can be switched on and off in a simple way. But perhaps the nicest thing is that experimentalists have gotten very good with superconducting electronics, and it looks like the machine can work with feasible parameters, so it should be doable in the lab. Let’s see… :).

Thanks to Patrick Hofer and Martí Perarnau Llobet who were the main forces behind this work!

Published paper: https://journals.aps.org/prb/abstract/10.1103/PhysRevB.94.235420