Quantum Mechanical Stabilization of a Collapsing Bose-Bose Mixture

Abstract

According to the mean-field theory a condensed Bose-Bose mixture collapses when the interspecies attraction becomes stronger than the geometrical average of the intraspecies repulsions, g 2 12 > g11g22. We show that instead of collapsing such a mixture gets into a dilute liquid-like droplet state stabilized by quantum fluctuations thus providing a direct manifestation of beyond mean-field effects. We study various properties of the droplet and find, in particular, that in a wide range of parameters its excitation spectrum lies entirely above the particle emission threshold. The droplet thus automatically evaporates itself to zero temperature, the property potentially interesting by itself and from the viewpoint of sympathetic cooling of other systems.PACS numbers: 03.75. Mn,03.75.Kk The mean-field and the first beyond mean-field contribution, the famous Lee-Huang-Yang (LHY) correction, to the ground state energy of a homogeneous weaklyrepulsive Bose gas read [1]where n is the density and a > 0 and g = 4π 2 a/m are, respectively, the scattering length and coupling constant characterizing the interparticle interaction. The LHY correction originates from the zero-point motion of the Bogoliubov excitations and is thus intrinsically quantum. It is also universal in the sense that it depends only on the two-body scattering length and not on other parameters of the two-body or higher-order interactions. Quite naturally the experimental observation of this fundamental beyond mean-field effect came from the field of ultra-cold gases [2][3][4][5][6][7], where the gas parameter na 3 and, therefore, the relative contribution of the LHY term, can be enhanced by using Feshbach resonances [8]. Note however that the effect is perturbative; for na 3 ∼ 1 higher order terms and processes, in particular, three-body decay, come into play. A different situation is predicted for spinor gases where quantum fluctuations lift the degeneracy in the ground-state manifold [9,10] or lead to quantum mass acquisition [11]. In this Letter we point out that in a Bose-Bose mixture the mean-field term and the LHY term depend on the inter-and intraspecies coupling constants in a different manner. Therefore, one can independently control them and make them comparable to each other without ever leaving the weakly-interacting regime. In particular, an interesting situation, impossible in the singlecomponent case, arises when the mean-field term, ∝ n 2 , is negative and the LHY one, ∝ n 5/2 , is positive. Because of its steeper density scaling the quantum LHY repulsion neutralizes the mean-field attraction and stabilizes the system against collapse. The mixture can then exist as a droplet in equilibrium with vacuum without any external trapping [12]. This phenomenon naturally suggests a proof-of-principle experiment for observing the LHY quantum correction. The droplet can be prepared from currently available homo-and heteronuclear atomic mixtures by tuning the inter-and intraspecies scattering lengths into the unstable (from the mean-field viewpoin...

Quantum liquid droplets in a mixture of Bose-Einstein condensates [Dataset]

“…While a single-component attractive condensate collapses [13], quantum fluctuations stabilize a two-component mixture with inter-component attraction and intra-component repulsion [3]. In this case, the repulsion in each component remains large and results in a non-negligible Lee-Huang-Yang energy.…”

“…Given the generality of the stabilization mechanism, droplets should in fact also exist in simpler systems with pure isotropic contact interactions. Even though they were originally predicted in this setting [3], their experimental observation has so far remained elusive.In this work, we observe ultracold atomic droplets in a mixture of two Bose-Einstein condensates with competing contact interactions. While a single-component attractive condensate collapses [13], quantum fluctuations stabilize a two-component mixture with inter-component attraction and intra-component repulsion [3].…”

“…Even though they were originally predicted in this setting [3], their experimental observation has so far remained elusive.…”

An Arrested Implosion

“…A similar stabilization mechanism using quantum fluctuations was proposed for an attractive Bose-Bose mixture in Ref. [4], which leads to the formation of droplets. In this reference liquidlike droplets are defined as the result of a competition between an attractive n 2 and a repulsive n 2þα term in the energy functional.…”

“…The mechanisms at work in the droplets can indeed be further explored by observing their time-of flight expansion in free space. In principle, pure liquid droplets in the absence of trapping should reach an equilibrium with an absence of growth [4,21]. On the other hand, time-of-flight expansion under a dipolar interaction is nontrivial but well studied [32,33], and it is modified by beyond mean-field effects [27]; these effects are isotropic and counteract magnetostriction.…”