# Cooling down atoms by “truncating the potential”

My professor briefly mentioned a method of cooling down atoms by subjecting them to a potential which is then repeatedly truncated.

He explained something along these lines: say we have $N_0$ atoms trapped in a potential given by $U=0.5mw^2(x^2+y^2+z^2)$, initially in thermal equilibrium, so at some defined temperature $T_0$.

He said we can cool down the atoms by repeatedly "truncating" the potential, i.e at each truncation, during a time period $\Delta t$ we the potential "becomes constant at a height of $\lambda Tk_B$" (not sure what this means, but I guess he means for points $(x,y,z)$ such that $U(x,y,z) \ge \lambda Tk_B$, after truncation we have $U(x,y,z)=\lambda Tk_B$).

His explanation was just in passing, so I'm wondering if there is a name for this technique of cooling down atoms and how it works. Please discuss the relevant physics involved so I can study quantitatively how this works myself.

## 1 Answer

What you describe pretty mutch sounds like the so called Evaporative Cooling It basically is a technique to achieve very low temperatures (enough for atoms to condensate to a Bose-Einstein-condensate, for example.

The basic Idea is that you have many particles in a given potential. The state of all particles is thought to be a state of thermodynamic equillibrium, which of course means that there will be some particles who have higher energies, and others who have lower.

The question how to cool this system, is the question how to remove energy from the system, or in that case, how to remove energy from the many particles inside.

The idea of evaporative cooling is to remove especially the particles with the greatest energies. If you remove one particle whiches energy is over the average energy, the the energy per particle in the system will decrease, and that is exactly the cooling that you want to achieve.

So how do you "remove" the particles with the highest energies? One way would be (as you said) to lower the potential a bit. By that, especially the particles with the most overall energy are able to overcome the potential wall, and escape the system. Afterwards, you let the remaining particles the opportunity to return to a state of thermodynamic equilibrium, and continue the process.

Actually, we know a very intuitive case of evaporative cooling from our daily life: When you blow on a spoon of tea, for example, the wind of your breath will cool down the tea in the exact same way: By removing exactly those particles in the tea-liquid-phase that have the most energy (and are thus the easiest to blow away).

• I see. How might I go about calculating the number of truncations needed to reach a target temperature $T_f$ starting from a temperature $T_0$? I guess I would need to know the distribution of speeds at a given temperature, perhaps I can assume a Boltzmann distribution. – Joshua Benabou Mar 30 '18 at 16:43
• could you give me a hint on how to study this quantitatively? – Joshua Benabou Mar 31 '18 at 7:34
• I'm sorry, I don't have more information on that subject, as well, because in my lectures, calculations were pretty mutch handweaving. – Quantumwhisp Mar 31 '18 at 22:43