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arXiv:2103.16044 · Physical Review A

First-order Bose-Einstein condensation with three-body interacting bosons

Hui Hu, Zeng-Qiang Yu, Jia Wang, Xia-Ji Liu

Published Oct 4, 2021• 11 citations
arXivHTMLPDF

Abstract

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 $s$-wave scattering length $a<0$ and a three-body scattering hypervolume $D>0$. 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.

DOI
10.1103/physreva.104.043301

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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.
We address the possibility of realizing Bose-Einstein condensation as a first-order phase transition by admixture of particles of different species. To this aim we perform a comprehensive analysis of phase diagrams of two-component mixtures of bosons at finite temperatures. As a prototype model, we analyze a binary mixture of Bose particles interacting via an infinite-range (Kac-scaled) two-body potential. We obtain a rich phase diagram, where the transition between the normal and Bose-Einstein-condensed phases may be either continuous or first order. The phase diagram hosts lines of triple points, tricritical points, and quadruple points. We address the structure of the phase diagram depending on the relative magnitudes of the inter- and intraspecies interaction couplings. In addition, even for purely repulsive interactions, we identify a first-order liquid-gas-type transition between noncondensed phases characterized by different particle concentrations. In the obtained phase diagram, a surface of such first-order transitions terminates with a line of critical points.
The stability of a Bose–Einstein condensed state of trapped ultra-cold atoms is investigated under the assumption of an attractive two-body and a repulsive three-body interaction. The Ginzburg–Pitaevskii–Gross (GPG) nonlinear Schrödinger equation is extended to include an effective potential dependent on the square of the density and solved numerically for the s-wave. The lowest collective mode excitations are determined and their dependences on the number of atoms and on the strength of the three-body force are studied. The addition of three-body dynamics can allow the number of condensed atoms to increase considerably, even when the strength of the three-body force is very small compared with the strength of the two-body force. We study in detail the first-order liquid–gas phase transition for the condensed state, which can happen in a critical range of the effective three-body force parameter. 1.
The stability of a Bose-Einstein condensed state of trapped ultra-cold atoms is investigated under the assumption of an attractive two-body and a repulsive three-body interaction. The Ginzburg-Pitaevskii-Gross (GPG) nonlinear Schrödinger equation is extended to include an effective potential dependent on the square of the density and solved numerically for the s-wave. The lowest collective mode excitations are determined and their dependences on the number of atoms and on the strength of the three-body force are studied. The addition of three-body dynamics can allow the number of condensed atoms to increase considerably, even when the strength of the three-body force is very small compared with the strength of the two-body force. We study in detail the first-order liquid-gas phase transition for the condensed state, which can happen in a critical range of the effective three-body force parameter.
We study the effects of a repulsive three-body interaction on a system of trapped ultra-cold atoms in a Bose-Einstein condensed state. The corresponding s−s-s−wave non-linear Schrödinger equation is solved numerically and also by a variational approach. A first-order liquid-gas phase transition is observed for the condensed state up to a critical strength of the effective three-body force.
This thesis is devoted to the rigorous study of dilute Bose gases with two-body and three-body interactions at zero temperature in two and three dimensions. Bose gases are many-body quantum systems composed of bosons, which notably do not obey the Pauli exclusion principle. As a consequence, at extremely low temperatures, a macroscopic fraction of the particles can occupy the same one-body quantum state. This phenomenon, known as Bose–Einstein condensation, was predicted in the 1920s by Bose and Einstein for noninteracting Bose gases, and first realised experimentally by the groups of Cornell and Wieman, and Ketterle, earning them the Nobel Prize for Physics in 2001. However, proving the occurrence of Bose–Einstein condensation in general interacting bosonic systems remains a major open problem and constitutes a central theme in this thesis. Another important property of bosonic matter is that it is generally more unstable than fermionic matter. In particular, for systems interacting via the Coulomb force, the Pauli exclusion principle is essential for explaining the stability of the second kind, which states that the energy and volume scale linearly with the number of particles. Nonetheless, bosonic systems with attractive but less singular interactions can also be stable, and the rigorous proof of this fact forms a second focus of this thesis. In three dimensions, we consider predominantly repulsive interactions. Firstly, we prove a leading order upper bound on the thermodynamic ground state energy of Bose gases with hard-core three-body interactions, which matches an existing lower bound. In addition, we obtain a simpler proof for integrable potentials. Secondly, we derive the leading order of the thermodynamic ground state energy of Bose gases with combined two-body and three-body interactions. More specifically, we show that, at the leading order, the ground state energy is entirely characterised by the scattering length of the two-body potential and the scattering hypervolume of the three-body potential. Thirdly, we study the time evolution of Bose–Einstein condensates with three-body interactions in the so-called Gross–Pitaevskii regime. We show that Bose–Einstein condensation is preserved under many-body evolution and that the condensate wavefunction evolves according to the quintic Gross–Pitaevskii equation. In particular, we show that the effective coupling constant is universal in the sense that it depends only on the scattering hypervolume of the interaction potential. As a by-product of our proof, we derive a stability of the second kind result for Bose gases with attractive two-body interactions and repulsive three-body interactions. In two dimensions, we consider trapped Bose gases with mean-field-type interactions, including the purely attractive case. We prove the stability of the second kind of the system and the convergence of the ground state energy per particle to that of a non-linear Schrödinger energy functional. As a consequence of the stability of the second kind, we also obtain Bose–Einstein condensation for the many-body ground states.
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