Measuring The Heat Capacity in a Bose-Einstein Condensation using Global Variables

Abstract

Phase transitions are well understood and generally followed by the behavior of the associated thermodynamic quantities, such as in the case of the $\lambda$ point superfluid transition of liquid helium, which is observed in its heat capacity. In the case of a trapped Bose-Einstein condensate (BEC), the heat capacity cannot be directly measured. In this work, we present a technique able to determine the global heat capacity from the density distribution of a weakly interacting gas trapped in an inhomogeneous potential. This approach represents an alternative to models based on local density approximation. By defining a pair of global conjugate variables, we determine the total internal energy and its temperature derivative, the heat capacity. We then apply the technique to a trapped ${}^{87}$Rb BEC a $\lambda$-type transition dependent on the atom number is observed, and the deviations from the non-interacting, ideal gas case are discussed. Finally we discuss the chances of using this method to study the heat capacity at $T\to 0$.

arXiv comment9 pages, 4 figures

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• Many-Body Physics with Ultracold Gases
• Revealing the Superfluid Lambda Transition in the Universal Thermodynamics of a Unitary Fermi Gas
• Exploring the Thermodynamics of a Universal Fermi Gas
• Evolution of a Bose-condensed gas under variations of the confining potential
• A more accurate analysis of Bose-Einstein condensation in harmonic traps
• Nonlinear Dynamics of a Bose Condensed Gas
• Criticality in Trapped Atomic Systems
• Thermodynamics of ultracold trapped gases. Generalized mechanical variables, equation of state and heat capacity

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• Calorimetry of a harmonically trapped Bose gas
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• Characterizing Real-space Topology in Rice-Mele Model by Thermodynamics