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arXiv:1007.4926 · Journal of Low Temperature Physics

Thermodynamic Properties of Ultracold Bose Gas: Transition Exponents and Universality

Sanchari Goswami, Tapan Kumar Das, Anindya Biswas

Published Feb 5, 2013• 5 citations
arXivHTMLPDF
DOI
10.1007/s10909-013-0860-3

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We report the measurement of the global thermal expansion coefficient of a confined Bose gas of 87Rb^{87}\rm Rb87Rb in a harmonic potential around the Bose-Einstein condensation transition temperature. We use the concept of global thermodynamic variable, previously introduced and appropriated for a non homogeneous system. The data show divergence on the thermal expansion coefficient near the transition temperature and analyses of the universality behavior shows a critical exponent α=0.15±0.09\alpha = 0.15\pm 0.09α=0.15±0.09. With this obtained value and the critical exponent for the correlation length recently presented in the literature we analyse the scaling law combining dimension and critical exponents.
Critical exponents characterize the divergent scaling of thermodynamic quantities near phase transitions and allow for the classification of physical systems into universality classes. While quantum gases thermalizing by interparticle interactions fall into the XY model universality class, the ideal Bose gas has been predicted to form a distinct universality class whose signatures have not yet been revealed experimentally. Here, we report the observation of critical scaling in a two-dimensional trapped quantum gas of essentially noninteracting photons, which thermalize by radiative contact to a reservoir of molecules inside a microcavity. By measuring the spatial correlations near the condensation transition, we determine the critical exponent for the correlation length to be ν=0.52(4)ν= 0.52(4)ν=0.52(4). Our results constitute a first experimental test of the long-standing scaling predictions for the Bose gas universality class.
The study of second-order phase transitions is a broad research theme that provides fundamental insights into the physical nature of complex systems. A central aspect deals with the concept of universal behavior. Universality governs, for example, the diverging correlated fluctuations of an order parameter, characterized by a macroscopic correlation length ξ, as well as the divergence of other thermodynamic quantities near the critical point. Extracting the critical exponents associated with these diverging quantities shows that quite different physical systems can exhibit identical scaling behavior, placing them into common universality classes. Bose-Einstein condensation of an ideal (i.e., non-interacting) gas of bosons is a second-order phase transition, and thus provides a valuable platform to investigate universal critical behavior in the quantum gas regime, driven purely by quantum statistics rather than inter-particle interactions. While historically studied in ultracold atomic and molecular gases, Bose-Einstein condensation can now be realized in a two-dimensional photonic gas at room temperature using dye-filled microcavities. The microcavity imposes a low-energy cutoff, providing a non-vanishing ground state and an effective mass for the intracavity photons, which thermalize via repeated absorption and emission processes with the dye reservoir rather than inter-particle interactions. Consequently, this platform establishes an almost perfectly ideal, two-dimensional quantum gas of light. In combination with versatile trapping techniques, it provides a highly tunable platform to explore the thermodynamics of quantum gases. This thesis presents a quantitative study of spatial correlations in a uniformly trapped two-dimensional photon gas. The uniform confinement is achieved by a custom mirror-structuring technique, resulting in box-like trapping potentials. The temporal and spatial coherence properties of the gas are validated in both the thermal and condensed regimes using an interferometric measurement technique. Because the applicability of scanning interferometry limits measurements of critical scaling behavior, an alternative method is introduced to extract the first-order spatial coherence directly from the far-field angular distribution of the cavity emission in a single experimental shot. This technique enables the extraction of the spatial correlation length ξ and a precise evaluation of its scaling behavior in the vicinity of the critical point Nc. The measurements presented here demonstrate, for the first time, the determination of a critical exponent in the (ideal) Bose gas universality class. The obtained critical exponent of ν = 0.52 ± 0.04 for the two-dimensional ideal Bose gas is consistent with theoretical expectations. Crucially, this critical exponent is found to be robust and independent of the system size within experimental uncertainties, demonstrating the universality of the scaling behavior. Finally, the limits of this universal behavior are explored by demonstrating the breakdown of critical scaling when the thermalizing coupling between the photons and dye molecules in the cavity is reduced, driving the photon gas out of thermal equilibrium.