# How to measure temperature of a laser cooled sample at picoKelvin temperatures?

I'm reading about laser cooling.. my question is: how can the temperature of the sample be measured? (using laser cooling we can reach $10^{-12}K...)$

• I would assume it would be by the electromagnetic emissions of the object. – Jimmy360 May 7 '15 at 23:21
• @Jimmy360 In which way? – sunrise May 8 '15 at 21:30

The temperature is not measured in the sense of using a thermometer. Instead it is calculated from the velocities of the particles in the trap.

Temperature is related to the velocity distribution by the Maxwell-Boltzmann equation. Under normal circumstances we are usually starting from a known temperature and calculating the velocity distribution. However it's a perfectly valid procedure to take the velocity distribution and work backwards to find the temperature. This is what is done in the sort of systems you describe.

• so how one measures velocity of particles in such approach? By doppler-like light scattering or something? – aaaaa says reinstate Monica May 8 '15 at 9:44
• @aandreev: yes, I would guess you measure the doppler broadening of light scattered from your laser. Exactly how it's done I don't know, and there may well be several methods. – John Rennie May 8 '15 at 9:46
• Usually what's done is a time of fight measurement. This is a technique where they turn off the trap, allowing the atoms to fly off in all directions. They they flash a laser and measure the scattered light, imaging the spherical cloud. Since you know how long the atoms had to spread out (the "time of flight") you can turn this into a momentum distribution. This is also how they check whether a BEC has been achieved. – zeldredge May 8 '15 at 12:45
• @JohnRennie I'm not sure to have correctly understood. Do you mean that it is used the Doppler FWHM? (en.wikipedia.org/wiki/Doppler_broadening) – sunrise May 8 '15 at 21:32
• @zeldredge A lot of thanks for your comment, it's very interesting! Could you expand it a little so I can undestand it better? Many thanks again – sunrise May 8 '15 at 21:33

I hope someone with more knowledge will pop into thread, but here is my education. There might be number of ways to measure such low temperatures. One I find fascinating is starting with material, namely Bose-Einstein condensate. Reference is this one: Cooling Bose-Einstein Condensates Below 500 Picokelvin, Leanhardt et al. Science, 12 September 2003.

Shortly, you start with notion that Bose-Einstein condensation (BEC) phase transition temperature is directly related to number of particles:

$\omega$ here is frequency of field that is used for trapping condensate. 2500 atoms in condensate carry temperature of 450 pK. Number of particles was measured using optical absorption.

• So many thanks for sharing your knowledge and for the paper that you have suggested to me. I'll read it carefully, because I haven't undestood your sentence: "Number of particles was measured using optical absorption".. the only way that I know is to use Lambert-Beer Law... – sunrise May 8 '15 at 22:11