0 Thermodynamics of Bose - Condensed Atomic Hydrogen

We study the thermodynamics of the Bose-condensed atomic hydrogen confined in the Ioffe-Pritchard potential. Such a trapping potential, that models the magnetic trap used in recent experiments with hydrogen, is anharmonic and strongly anisotropic. We calculate the ground-state properties, the condensed and non-condensed fraction and the Bose-Einstein transition temperature. The thermodynamics of the system is strongly affected by the anhar-monicity of this external trap. Finally, we consider the possibility to detect Josephson-like currents by creating a double-well barrier with a laser beam. 1 Few years ago, Bose-Einstein condensation (BEC) has been experimentally observed in clouds of trapped alkali-metal atoms [1]. Recently, BEC has been also achieved with atomic hydrogen confined in a Ioffe-Pritchard trap [2]. That is an important result because hydrogen properties, like interatomic potentials and spin relaxation rates, are well understood theoretically. As stressed by Killian et al. [2], the s-wave scattering length of the hydrogen is very low and, compared with other atomic species, the condensate density is high, even for small condensate fractions. Moreover, due to hydrogen's small mass, the BEC transition occurs at higher temperatures than in those of alkali atoms. In this paper we calculate the thermodynamical properties of the trapped hydrogen gas by using the quasi-classical Hartree-Fock approximation [3]. This approach is justified by the very large number of atoms (about 10 10) in the trap and by the relatively high temperatures involved (order of µK). Due to the anharmonic external trap, the analytical results for BEC thermodynamics obtained by Stringari et. al [3] cannot be used for quantitative predictions. Our detailed theoretical study of the hydrogen thermodynamics can give useful informations for future experiments with a better optical resolution. In the last part of the paper we discuss the criteria for macroscopic quantum tunneling and macroscopic quantum self-trapping by using a laser beam to create a double-well potential. In the experiment reported in Ref. [2], the axially symmetric magnetic trap is modelled by the Ioffe-Pritchard potential U(ρ, z) = (αρ) 2 + (βz 2 + γ) 2 − γ , (1) where ρ and z are cylindrical coordinates and the parameters α, β and γ can be calculated from the magnetic coil geometry. In particular, for small displacements, the radial oscillation frequency is ω ρ = α/ √ mγ = 2π × 3.90 kHz, the axial frequency is ω z = 2β/m = 2π × 10.2 Hz and γ/k B = 35 …