Temperature measurements of a Bose--Einstein condensate by ultra--intense light pulses

Experimentally the temperature in a Bose--Einstein condensate is always deduced resorting to the comparison between the Maxwell--Boltzmann velocity distribution function and the density profile in momentum space. Though a successful method it is an approximation, since it also implies the use of classical statistical mechanics at temperatures close to the condensation temperature where quantal effects play a relevant role. The present work puts forward a new method in which we use an ultra--intense light pulse and a nonlinear optical material as detectors for differences in times--of--flight. This experimental value shall be compared against the result here calculated, using the Bose--Einstein distribution function, which is a temperature--dependent variable, and in this way the temperature of the condensate is obtained.