# How cold can you go?

What is absolute zero?
11 June 2019

## Interview with

Nigel Cooper, University of Cambridge

## Cold_thermometer.png

When it comes to cold, not even the Antarctic can out-compete the right physics lab. Chris Smith spoke to Nigel Cooper, from the Cavendish Laboratory in Cambridge, about the coldest temperatures possible…

Nigel - Okay. To think about that, first it's helpful to understand what we mean by temperature. So temperature, to a physicist, is a measure of the thermal energy in a material due to all the random jostling of its components. So if we have a gas of atoms in a box that is largely carried by the kinetic energy, the motion and velocity of the particles, and so as we cool it down that kinetic energy is removed and the atoms move slower.

And what we understand from the laws of thermodynamics is that there is a limit where, at least in principle, where we can remove all of this thermal energy and the system has just reached its lowest energy state, and this is a state that we refer to as absolute zero.

Chris - If I took a, based on your analogy and your pointing out the particles are moving around jostling, and when I stick a thermometer in a cup of tea, the hot water molecules are hitting the molecules in the thermometer and giving them energy which is why the thermometer registers the temperature. So if I took my thermometer out of my tea and took it into space, because there's no molecules to hit it what would it say then?

Nigel - Well actually, out in space there is still some energy around which is the microwave background radiation left over from the Big Bang which is now, after expansion of the universe, has cooled down to about 2 degrees above absolute zero.

So we understand that there, there will be radiation hitting the thermometer and that radiation will give it a temperature of 2 degrees. Now whether you're thermometer actually registers 2 degrees above absolute zero is another question but, in principle, there is some temperature there.

Chris - And how do we know that there is this theoretical minimum which coincides with what we are calling absolute zero, and what value of temperature is that?

Nigel - Well, we know about the existence of this limit through the consistency of the laws of thermodynamics and many tests that have been done. And the temperature itself has been established to be -273 degrees Celsius, so that's extraordinarily cold of course, and this is why from the perspective of a physicist we typically want to work with an absolute temperature scale where we start at zero, at this absolute zero, and then count upwards. So the freezing point of water, zero degrees on the Celsius scale is +270 degrees of kelvin, this absolute temperature scale, and room temperature's about 300 kelvin. So outer space is about a hundred times colder than room temperature.

But from the low-temperature physics that can be done now, there are different techniques that you can use to cool down to much lower temperatures. So if you take a fridge that is working off liquid helium, then you can reduce the temperature to about 1,000th of a degree above absolute zero, so that's a thousand times colder than outer space. Or if you are willing to work with dilute atomic gases, then the techniques that have been developed over the last 20 or 30 years allow you to cool that system down to about 1 billionth of a degree above absolute zero.

Chris - Why not absolute zero itself? Is there no way of getting all the energy out? Why can't we actually get there?

Nigel - Well, there is a theorem established from thermodynamics in the 19th century by Kelvin and others who worked on it then, that if you have a refrigerator, there's an efficiency of the refrigerator which depends on the ratio of the two temperatures on this absolute temperature scale. And in fact that efficiency tells you how much heat can you pump out by a certain amount of work that you perform on the refrigerating cycle, and that efficiency goes to zero as the cold side of the fridge goes to zero.

Chris - So you get close but you never get there?

Nigel - You never quite get there.

Chris - And when you get very, very close, do you begin to get some insights into what might happen were you to get there? Do things behave in a bizarre way because I would be thinking if you've got particles, and we know that everything is made of atoms - they say never believe an atom because it makes up everything - but if you get to absolute zero would everything just stop moving then?

Nigel - Well no, because the laws of quantum mechanics kick in, and in fact they kicked in at a much higher temperature. So some of these, depending on the gas or the system that you're looking at, as you cool it down and the particles move more and more slowly, then we understand from quantum mechanics that the wavelike nature of that particle starts to become more important. The wavelength of a particle increases as you make it more slow and so there is a point that one reaches for a gas at a certain density at which the quantum wavelength of each individual atom stretches across to its neighbour.

At that point the system is said to be quantum degenerate and then there's a completely new form of behaviour that comes in where the gas behaves in a way that's completely unrelated to what we're familiar with at room temperature, and you get certain collective quantum phenomena appearing such as superconductivity or Bose-Einstein condensation, certain collective phenomena that appear that are completely unfamiliar at room temperature.

Chris  - Could one think of it as though everything sort of locks together then and you get everything behaving as one? So instead of just being one atom that bumps into another atom here and there, you end up with everything behaving as one at the same time because there those wavelengths have all locked together?

Nigel - That's it. Depending on the particular phase, so in a Bose-Einstein condensate, you can think there of a situation where all the atoms are behaving in an identical manner. In other situations, where there are stronger interactions, you have everything locks together but it can form some sort of collective fluid where the particles are dancing around each other in some very complex way.

They can't quite come to rest because quantum mechanics prevents them from actually stopping completely, but the collective zero temperature state that you would have is some many particle collective state which shows interesting long-distance behaviour.