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arXiv:2308.13608

Generalized stability conditions for binary bose mixtures

Mohamed Benarous, Hocine Ahmed, Atika MEHEDI

Published Aug 25, 2023• 0 citations
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Abstract

Considering both interspecies and intraspecies fluctuations in ultracold bose-bose mixtures, we derive generalized stability conditions against collapse and phase separation. Furthermore, by examining the energy density of the system, we show that new LHY-like effects may enforce or destroy the stability according to the excitation branch, therefore, permitting or prohibiting the existence of droplet states.

DOI
10.48550/arxiv.2308.13608

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Considering both interspecies and intraspecies fluctuations in ultracold bose-bose mixtures, we derive generalized stability conditions against collapse and phase separation. Furthermore, by examining the energy density of the system, we show that new LHY-like effects may enforce or destroy the stability according to the excitation branch, therefore, permitting or prohibiting the existence of droplet states.
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_{12}^{2}>g_{11}g_{22}. We show that instead of collapsing such a mixture gets into a dilute liquidlike 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.
In a binary quantum droplet, the interspecies attraction dominates over the intraspecies repulsions and the mean-field energy is unstable. The mechanical stability is restored by the repulsive Lee-Huang-Yang (LHY) energy [D. S. Petrov, Phys. Rev. Lett. 115, 155302 (2015)]. In the Bogoliubov theory of the binary quantum droplet, there are two branches of gapless excitations. The lower branch describes the phonon excitation and its energy is imaginary in the long-wavelength limit, implying dynamical instability. Recently, it was found that the phonon energy is renormalized by higher-order quantum fluctuations and the dynamical instability is removed [Q. Gu and L. Yin, Phys. Rev. B 102, 220503(R) (2020)]. In this paper, we study a binary quantum droplet in the path-integral formalism to construct an effective model with the correct phonon energy. By integrating out the upper excitation branch, we obtain an effective single-mode model describing density fluctuations, and derive the extended Gross-Pitaevskii equation (EGPE). In this approach, the LHY energy in the EGPE is purely positive without any assumption of neglecting the imaginary part. This effective single-mode model can be also used outside and close to the quantum droplet region such as in the LHY gas. Based on this effective model, we obtain the phase diagram of a uniform binary Bose system near the mean-field unstable point, which can be tested in experiments.
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, g122>g11g22g_{12}^2>g_{11} g_{22}g122​>g11​g22​. 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.
Motivated by recent experimental advances in bubble traps which confine atoms on a thin shell, we investigate the stabilization of droplet states of a Bose-Bose mixture on a spherical surface due to quantum fluctuations. We analytically calculate the energy of a weakly interacting Bose-Bose mixture on a spherical surface with attractive interspecies and repulsive intraspecies interactions using the Bogoliubov approximation. Our findings show that the energy per particle has a minimum at a finite density in the presence of the Lee-Huang-Yang (LHY) term, which indicates the presence of liquidlike droplet state stabilized by quantum fluctuations. We also numerically solve the extended Gross-Pitaevskii equation, incorporating both bubble traps and an additional repulsive LHY correction derived from the Bogoliubov spectrum of a three-dimensional homogeneous mixture. Our calculations show that, due to the size limitations of the sphere, droplet states can only exist within specific parameter ranges. We also verify the transition between droplet states and uniform condensates in spherical confinement potentials, as well as the coexistence of the two. Our results pave the way for future exploration of quantum droplets in curved geometries with nontrivial real-space topologies.
The existence and stability of domain walls (DWs) and bubble-droplet (BD) states in binary mixtures of quasi-one-dimensional ultracold Bose gases with inter- and intraspecies repulsive interactions is considered. Previously, DWs were studied by means of coupled systems of Gross-Pitaevskii equations (GPEs) with cubic terms, which model immiscible binary Bose-Einstein condensates (BECs). We address immiscible BECs with two- and three-body repulsive interactions, as well as binary Tonks--Girardeau (TG) gases, using systems of GPEs with cubic and quintic nonlinearities for the binary BEC, and coupled nonlinear Schr\"odinger equations with quintic terms for the TG gases. Exact DW solutions are found for the symmetric BEC mixture, with equal intraspecies scattering lengths. Stable asymmetric DWs in the BEC mixtures with dissimilar interactions in the two components, as well as of symmetric and asymmetric DWs in the binary TG gas, are found by means of numerical and approximate analytical methods. In the BEC system, DWs can be easily put in motion by phase imprinting. Combining a DW and anti-DW on a ring, we construct BD states for both the BEC and TG models. These consist of a dark soliton in one component (the ``bubble''), and a bright soliton (the ``droplet'') in the other. In the BEC system, these composite states are mobile, too.
We investigate an ultracold Bose-Fermi mixture with a Feshbach resonance between two hyperfine states of fermions. Using a functional integral method, we calculate collective modes associated with fermion pairs and bosons in the superfluid phase. We derive a stability condition of the mixtures that is valid in the entire region of the BCS-BEC crossover. This stability condition, which smoothly connects the well-known results obtained in both the BCS and Bose-Einstein Condensate (BEC) limits, shows that sufficiently strong fermion-boson (FB) interactions destabilize the mixtures. In order to investigate the consequence of this instability, we study the ground-state energy of both the uniformly mixed and the phase-separated states. We find that FB repulsion induces a phase separation, whereas FB attraction should cause a collapse of the mixture. The possibilities for the experimental observation of such instabilities are also discussed.