# A tiny chilly thermometer

March 24, 2017

Two weeks ago, we had a paper out on arXiv: https://arxiv.org/abs/1703.03719. In it, we show how a small quantum thermal machine can be used as a thermometer. And how one could build one with superconducting circuits. Here is a bit of context.

Usual thermometers – like the medical one, showing you’re definitely running up a fever, or the good old mercury-in-a-glass-tube by the window showing that yes, it’s bloody cold outside – are based on the so-called ‘zeroth law of thermodynamics’. The 0th law states that if one object is in thermal equilibrium with two other objects, then these two must also be in equilibrium with each other. From there it follows that there is something which all systems in thermal equilibrium have in common. That something is the temperature. Systems in thermal equilibrium with each other have the same temperature.

So then, to build a universal thermometer, one just needs a well characterised object, where the relation between temperature and some observable property is known – a glass tube with mercury in it, for example, where one knows what temperature corresponds to different heights of the mercury. To measure the temperature of anything – say your body – one just sticks the thermometer in that thing, waits for the two to be in thermal equilibrium, and then reads off the thermometer. Because of the zeroth law, the temperature on the thermometer is the same as the temperature of the thing.

This is very neat, because one doesn’t need to know anything about how the thermometer is coupled to the sample being measured. There could be all kinds of complicated couplings going on, but as long as one wait for thermal equilibrium to set in, there is no need to worry about that. Only the thermometer itself has to be characterised.

However, there could be cases where waiting for equilibrium might screw things up. When we put a thermometer and a sample in contact, they exchange heat until equilibrium is reached. For example, if the thermometer is warmer than the sample, the sample will heat up a bit while the thermometer gets colder, until they are at the same temperature. For everyday uses, like taking your temperature, the thermometer is almost always much much smaller than the thing being measured, and so the heating (or cooling) of the sample is tiny, and can be ignored. In quantum physics experiments though, this is not necessarily the case. There, things often need to be very cold to make the quantum features noticeable, and the sample might be tiny itself. In such cases, experimentalists generally work hard to cool their quantum samples. So then, if we can’t make the thermometer colder than the sample, how can we measure its temperature without heating it up?

In our paper, we show that instead of equilibration, one can construct a thermometer which simultaneously cools the sample and allows its temperature to be estimated. The construction is based on a quantum thermal machine – basically a teeny tiny fridge, like this one I have previously written about. The machine has the same nice feature as an ordinary thermometer – that one doesn’t need to know the details of how the sample and thermometer couple to each other – but without causing any heating (this is achieved by operating close to the Carnot efficiency, which you might have heard about in classical thermodynamics).

It is interesting that this is possible for tiny quantum systems – and we also show that it could be done in superconducting circuits with existing experimental techniques. So who knows, perhaps the idea may turn out to be useful in the lab at some point.