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 $10^{-12}K...)$
 A: 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.
A: 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.
