A liquid-gas transition for bosons with attractive interaction in one dimension

Abstract

We consider a one dimensional system of $N$ bosons interacting via an attractive Dirac delta function potential. We place the bosonic quantum particles at thermal equilibrium in a box of length $L$ with periodic boundary conditions. At large $N$ and for $L$ much larger than the diameter of a two particle bound state, we predict by numerical and analytical studies of a simple model derived from first principles that the system exhibits a first order phase transition in a high temperature, non-degenerate regime. The higher temperature phase is an almost pure atomic gas, with a small fraction of dimers, a smaller fraction of trimers, etc. The lower temperature phase is a mesoscopic or macroscopic bound state that collects all the particles of the system with the exception of a small gaseous fraction composed mainly of atoms. We term this phase, which is the quantum equivalent of the classical bright soliton, a liquid.---Nous considerons, en dimension un, une assemblee de $N$ particules quantiques bosoniques interagissant par un potentiel de Dirac attractif, a l'equilibre thermique dans une boite de quantification de longueur L avec des conditions aux limites periodiques. Pour de grandes valeurs de N, et lorsque L est bien superieur au diametre de l'etat dimere dans l'espace reel, nous predisons, par etude numerique et analytique d'un modele simple mais deduit des premiers principes, que le systeme presente, a haute temperature c'est-a-dire dans le regime non degenere, une transition du premier ordre entre deux phases. La phase privilegiee a haute temperature est un gaz presque pur d'atomes, avec une faible fraction de dimeres, et des fractions encore plus faibles de trimeres, etc. La phase qui la supplante a moins haute temperature est un etat lie mesoscopique ou macroscopique que nous qualifions de liquide, equivalent quantique du soliton brillant de la theorie de champ classique, et qui renferme toutes les particules du systeme, a l'exception d'une petite fraction gazeuse composee essentiellement d'atomes.

augmented english (14 pages) and french (15 pages) versions: with respect to published version, appendix A added to improve upper bound (28)

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• Quantum unbinding near a zero temperature liquid-gas transition
• Temperatures are not useful to characterise bright-soliton experiments for ultra-cold atoms
• Fragmentation Temperature of 1D and 3D Quantum Droplets in a BEC Mixture