Definition and measurement of global thermodynamic variables for laser-cooled trapped gas

We have used the definition of global thermodynamic variables like pressure and volume for atoms trapped in a nonuniform potential to measure the state equation for a sample of cold Na atoms kept trapped in a quadrupole magnetic field. The results show that, for low atomic density, the system behaves like an ideal gas where pressure and volume are inversely proportional. At high density values (compressed system), the deviation from an ideal gas is clear. A model based on virial expansion shows that the measured deviation is larger than the expected first-order correction. Employing the concept of global variables may be an important procedure to describe the thermodynamic of gases in the ultracold regime eventually crossing the values where critical phenomena like Bose condensation, among others, take place.