Low-Temperature Behaviour of the Ideal Bose Gas Confined to Restricted Geometries.

H. R. Pajkowski

Tao Wen, Ji-Ping Ye, Su-Qiao An +3 more

Quantum confinement shifts quantum phase transitions like the λ-point of liquid helium. This effect is calculated here for ideal Bose–Einstein condensates (BECs) using thermodynamic mapping (TM). TM is a procedure to obtain low temperature behaviour from high temperature information via elementary transformations. We report here a series of TM relations for thermodynamic quantities and the resulting transition properties for ideal BECs.

L. S. Campana, Alvaro Caramico D’Auria, L. De Cesare +1 more

Giulia De Rosi

Ultracold atoms are exceptional tools to explore the physics of quantum matter. In fact, the high degree of tunability of ultracold Bose and Fermi gases makes them ideal systems for quantum simulation and for investigating macroscopic manifestations of quantum effects, such as superfluidity. In ultracold gas research, a central role is played by collective oscillations. They can be used to study different dynamical regimes, such as superfluid, collisional, or collisionless limits or to test the equation of state of the system. In this thesis, we present a unified description of collective oscillations in low dimensions covering both Bose and Fermi statistics, different trap geometries and zero as well as finite temperature, based on the formalism of hydrodynamics and sum rules. We discuss the different behaviour exhibited by the second excited breathing mode in the collisional regime at low temperature and in the collisionless limit at high temperature in a 1D trapped Bose gas with repulsive contact interaction. We show how this mode exhibits a single-valued excitation spectrum in the collisional regime and two different frequencies in the collisionless limit. Our predictions could be important for future research related to the thermalization and damping phenomena in this low-dimensional system. We show that 1D uniform Bose gases exhibit a non-monotonic temperature dependence of the chemical potential characterized by an increasing-with-temperature behaviour at low temperature. This is due to the thermal excitation of phonons and reveals an interesting analogy with the behaviour of superfluids. Finally, we investigate a gas with a finite number N of atoms in a ring geometry at T = 0. We discuss explicitly the deviations of the thermodynamic behaviour in the ring from the one in the large N limit.

Rémi Desbuquois, Lauriane Chomaz, Tarik Yefsah +4 more

C. S. Zasada, Raj K. Pathria

The low-temperature internal energy and specific heat of a hard sphere Bose gas confined to a general cuboidal enclosure are calculated under periodic boundary conditions. The special cases of a film and a channel geometry are considered in some detail. It is shown that, in the appropriate limits, one recovers the recent results of Pajkowski and Pathria, and of Zasada and Pathria, for a system of phonons confined to different geometries. Systematic applications of the Poisson summation formula enable us to obtain strongly convergent expansions, in both λ/L≪1 and λ/L≫1 regimes, and to see how the magnitude of the finite size corrections in the asymptotic limit (L/λ≫1) is directly linked with the dimensionality of the system. Special attention is paid to examining the combined influence of the dispersion in the phonon spectrum of the system and the finiteness of the enclosure.