Thermal expansion coefficient for a trapped Bose gas during phase transition - Gutierrez, Emmanuel David Mercado (2016)
Ultra cold quantum gas is a convenient system to study fundamental questions of modern physics, such as phase transitions and critical phenomena. This master thesis is devoted to experimental investigation of the thermodynamics susceptibilities, such as the isothermal compressibility and the thermal expansion coefficient of a trapped Bose-Einstein condensate (BEC) of 87Rb atoms. The critical phenomena and the critical exponents across the transition can explain the behavior of the isothermal compressibility and the thermal expansion coefficient near the critical temperature TC. By employing the developed formalism of global thermodynamics variables, we carry out a statistical treatment of Bose gas in a 3D harmonic potential. After that, comparison of obtained results reveals the most appropriate state variables describing the system, namely volume and pressure parameter V and Π respectively. The both are related with the confining frequencies and BEC density distribution. We apply this approach to define the set of new thermodynamic variables of BEC, and also to construct the isobaric phase diagram V T. Its allows us to extract the compressibility κT and the thermal expansion coefficient βΠ. The behavior of the isothermal compressibility corresponds to the second-order phase transition, while the thermal expansion coefficient around the critical point behaves as β ∼ tr-α, where tr is reduced temperature of the system and α is the critical exponent on the basic of these. Results we have obtained the critical exponent α = 0.15±0.09, which allows us to determine the system dimensionality by means of the scaling theory, relating the critical exponents with the dimensionality. As a result, we found out that the dimensionality of the system to be d ∼ 3, one is in agreement with the real dimension of the system.