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Physical review. B, Condensed matter

Reexamination of magnetic effects in the Bose gas

T. A. Arias, John D. Joannopoulos

Published Mar 1, 1989• 9 citations
Publisher

Abstract

The breakdown of the Meissner-Ochsenfeld effect in the three-dimensional Bose gas as the applied field passes through its critical value is an entropy-driven weakly first-order transition, rather than the second-order transition usually ascribed to the system. The transition is second order at the usual Bose condensation temperature ${T}_{c}$ as well as at T=0, with a line of first-order transitions connecting these critical points. The first-order transitions make the Bose gas resemble familiar superconductors, and a Landau-Ginzburg analysis indicates that the Bose gas is always a type-I superconductor.

DOI
10.1103/physrevb.39.4071

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The breakdown of the Meissner-Ochsenfeld effect in the three-dimensional Bose gas as the applied field passes through its critical value is an entropy-driven weakly first-order transition, rather than the second-order transition usually ascribed to the system. The transition is second order at the usual Bose condensation temperature Tc{T}_{c}Tc​ as well as at T=0, with a line of first-order transitions connecting these critical points. The first-order transitions make the Bose gas resemble familiar superconductors, and a Landau-Ginzburg analysis indicates that the Bose gas is always a type-I superconductor.
It is well-known that the 2-dimensional Bose gas does not condense, and that no transition occurs in its thermodynamic behavior. Despite this, we find that in a magnetic field a 2-dimensional gas of charged, ideal bosons has a nearly sharp transition temperature, below which it displays an "imperfect" Meissner-Ochsenfeld effect, practically indistinguishable from the perfect London one. This fact is relevant to the application of the Bose gas model of superconductivity to thin films.The main interest of the model is, however, that it exhibits an (essentially perfect) Meissner-Ochsenfeld effect without any irregularity in CV(T){C}_{V}(T)CV​(T).
It is shown that an ideal gas of charged bosons exhibits the essential equilibrium features of a superconductor. The onset of Bose-Einstein condensation marks the transition temperature Tc{T}_{c}Tc​. Below Tc{T}_{c}Tc​ a Meissner-Ochsenfeld effect is exhibited which is described in a very good approximation by London's equation.The singular nature of the condensed ideal Bose gas exhibits itself in a space dependence of the London constant $\ensuremath{\lambda}$, determined by the boundary conditions on the wave function. It is shown that the electrostatic repulsion between the bosons compensates this effect and leads to a spatially constant $\ensuremath{\lambda}$, independently of the boundary conditions.The critical field Hc(T){H}_{c}(T)Hc​(T) is determined and found to be related to the penetration depth d(T)d(T)d(T) by ${H}_{c}=\frac{\ensuremath{\hbar}c}{2e{d}^{2}}$ (eee being the boson charge).The B(H)B(H)B(H) law is different from the one usually assumed for actual superconductors. Corresponding changes occur in the thermodynamical relation.A comparison with superconducting metals is made. The main conclusion is that if superconductivity in metals is due to the concurrence of bosons, then the number of these bosons must be strongly temperaturedependent below Tc{T}_{c}Tc​.
The strongly ferromagnetic spin-1 Bose-Einstein condensate has recently been realized with atomic Li7 . It was predicted that a strong ferromagnetic interaction can drive the normal gas into a magnetized phase at a temperature above the superfluid transition, and Li7 likely satisfies the criterion. We reexamine this theoretical proposal employing the two-particle-irreducible effective potential, and conclude that there exists no stable normal magnetized phase for a dilute ferromagnetic Bose gas. For Li7 , we predict that the normal gas undergoes a joint first-order transition and jumps directly into a state with finite condensate density and magnetization. We estimate the size of the first-order jump and examine how a partial spin polarization in the initial sample affects the first-order transition. We propose a qualitative phase diagram at fixed temperature for the trapped gas. Published by the American Physical Society 2024
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Bose-Einstein condensation, observed in either strongly interacting liquid helium or weakly interacting atomic Bose gases, is widely known to be a second-order phase transition. Here we predict a first-order Bose-Einstein condensation in a cloud of harmonically trapped bosons interacting with both attractive two-body interaction and repulsive three-body interaction, characterized respectively by an sss-wave scattering length a<0a<0a<0 and a three-body scattering hypervolume D>0D>0D>0. It happens when the harmonic trapping potential is weak, so with increasing temperature the system changes from a low-temperature liquidlike quantum droplet to a normal gas and therefore experiences a first-order liquid-to-gas transition. At large trapping potential, however, the quantum droplet can first turn into a superfluid gas, rendering the condensation transition occurring later from a superfluid gas to a normal gas smooth. We determine a rich phase diagram and show the existence of a tricritical point, where the three phases, i.e., quantum droplet, superfluid gas, and normal gas, meet. We argue that an ensemble of spin-polarized tritium atoms could be a promising candidate to observe the predicted first-order Bose-Einstein condensation, across which the condensate fraction or central condensate density jumps to zero and the surface-mode frequencies diverge.