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arXiv:2502.08392 · SciPost Physics

Multicomponent one-dimensional quantum droplets across the mean-field stability regime

I. A. Englezos, Peter Schmelcher, S. I. Mistakidis

Published Nov 24, 2025• 6 citations
arXivHTMLPDF

Abstract

The Lee-Huang-Yang (LHY) energy correction at the edge of the mean-field stability regime is known to give rise to beyond mean-field structures in a wide variety of systems. In this work, we analytically derive the LHY energy for two-, three- and four-component one-dimensional bosonic short-range interacting mixtures across the mean-field stability regime. For varying intercomponent attraction in the two-component setting, quantitative deviations from the original LHY treatment emerge being imprinted in the droplet saturation density and width. On the other hand, for repulsive interactions an unseen early onset of phase-separation occurs for both homonuclear and heteronuclear mixtures. Closed LHY expressions for the fully-symmetric three- and four-component mixtures, as well as for mixtures comprised of two identical components coupled to a third independent component are provided and found to host a plethora of mixed droplet states. Our results are expected to inspire future investigations in multicomponent systems for unveiling exotic self-bound states of matter and unravel their nonequilibrium quantum dynamics.

DOI
10.21468/scipostphys.19.5.133

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The Lee-Huang-Yang (LHY) energy correction at the edge of the mean-field stability regime is known to give rise to beyond mean-field structures in a wide variety of systems. In this work, we analytically derive the LHY energy for two-, three- and four-component one-dimensional bosonic short-range interacting mixtures across the mean-field stability regime. For varying intercomponent attraction in the two-component setting, quantitative deviations from the original LHY treatment emerge being imprinted in the droplet saturation density and width. On the other hand, for repulsive interactions an unseen early onset of phase-separation occurs for both homonuclear and heteronuclear mixtures. Closed LHY expressions for the fully-symmetric three- and four-component mixtures, as well as for mixtures comprised of two identical components coupled to a third independent component are provided and found to host a plethora of mixed droplet states. Our results are expected to inspire future investigations in multicomponent systems for unveiling exotic self-bound states of matter and unravel their nonequilibrium quantum dynamics.
We study the impact of beyond Lee-Huang-Yang (LHY) physics, especially due to intercomponent correlations, in the ground state and the quench dynamics of one-dimensional quantum droplets with an ab initio nonperturbative approach. It is found that the droplet Gaussian-shaped configuration arising for intercomponent attractive couplings becomes narrower for stronger intracomponent repulsion and transits towards a flat-top structure either for larger particle numbers or weaker intercomponent attraction. Additionally, a harmonic trap prevents the flat-top formation. At the balance point where mean-field interactions cancel out, we show that a correlation hole is present in the few-particle limit of LHY fluids as well as for flat-top droplets. Introducing mass imbalance, droplets experience intercomponent mixing and excitation signatures are identified for larger masses. Monitoring the droplet expansion (breathing motion) upon considering interaction quenches to stronger (weaker) attractions, we explicate that beyond LHY correlations result in a reduced velocity (breathing frequency). Strikingly, the droplets feature two-body anticorrelations (correlations) at the same position (longer distances). Our findings pave the way for probing correlation-induced phenomena of droplet dynamics in current ultracold-atom experiments.
We explore the ground state properties and excitation spectra of one-dimensional three-component bosonic mixtures accommodating a droplet in two of the species and a third minority component. Relying on the suitable Lee-Huang-Yang framework, we reveal a plethora of distinct self-bound droplet phases and their phase transitions through variations of either the particle number of the majority components or the intercomponent coupling. The ensuing phases demonstrate that the minority component is being un-trapped, partially trapped, or fully trapped by the majority droplet species. These states are characterized by their binding energies captured by the chemical potentials and their low-amplitude excitation spectrum, including mode crossings at the particle-emission threshold. We further derive effective reduced models which are valid in the high-imbalance limit, and accurately reproduce the numerically computed ground states, while providing analytical insights into the role of quantum fluctuations. Our results map out the stability and structure of mixed droplet phases offering guidance into forthcoming experimental and theoretical studies of multicomponent quantum droplets.
Quantum droplets (QDs) in weakly interacting ultracold quantum gases are typically characterized by mean-field theories incorporating Lee-Huang-Yang (LHY) quantum fluctuations under simplified zero-range interaction assumptions. However, bridging these models to broader physical regimes like superfluid helium requires precise understanding of short-range interatomic interactions. Here, we investigate how finite-range interactions--next-order corrections to zero-range potentials--significantly alter QDs mechanics. Using a consistent effective theory, we derive an analytical equation of state (EOS) for three-dimensional bosonic mixtures under finite-range interactions at zero temperature. Leveraging the Hubbard-Stratonovich transformation, we demonstrate that interspecies attraction facilitates bosonic pairing across components characterized by the non-perturbative parameter of ΔΔΔ, leading to nonuniversal LHY terms that encode short-range interaction details while recovering previous universal QDs EOS in the zero-range limit. Extending superfluid hydrodynamic equations for two-component systems, we predict fractional frequency shifts in breathing modes induced by these nonuniversal terms. Experimental observation of these shifts would reveal critical insights into QDs dynamics and interatomic potential characteristics.
We exemplify the impact of beyond Lee-Huang-Yang (LHY) physics, especially due to intercomponent correlations, in the ground state and the quench dynamics of one-dimensional so-called quantum droplets using an ab-initio nonperturbative approach. It is found that the droplet Gaussian-shaped configuration arising for intercomponent attractive couplings becomes narrower for stronger intracomponent repulsion and transits towards a flat-top structure either for larger particle numbers or weaker intercomponent attraction. Additionally, a harmonic trap prevents the flat-top formation. At the balance point where mean-field interactions cancel out, we show that quantum fluctuations prevent the collapse of LHY fluids for larger atom numbers and a correlation hole is present in the few particle limit of these fluids as well as for flat-top droplets. Introducing mass-imbalance, droplets experience intercomponent mixing and excitation signatures are identified for larger masses. Monitoring the droplet expansion (breathing motion) upon considering interaction quenches to stronger (weaker) attractions we explicate that beyond LHY correlations result in a reduced velocity (breathing frequency). Strikingly, the droplets feature two-body anti-correlations (correlations) at the same position (longer distances). Our findings pave the way for probing correlation-induced phenomena of droplet dynamics in current ultracold atom experiments.
Abstract The static and dynamic properties of self-bound quantum droplets in a one-dimensional Bose-Bose mixture are discussed in the spirit of the Hartree–Fock-Bogoliubov theory. This latter enables us to provide beyond the Lee-Huang-Yang (LHY) quantum corrections to the equation of state at both zero and finite temperatures. In the uniform case our results for the ground-state energy and the critical temperature are confirmed through comparison with Quantum Monte-Carlo simulation and with available theoretical results. The density profiles are supported by numerical simulations of the generalized Gross-Pitaevskii equation which selfconsistently includes higher-order terms originating from the normal and anomalous fluctuations under the local density approximation. We show that the density exhibits a dip near its center in the flat-top plateau region for large interspecies interactions. We exemplify the impact of the beyond LHY corrections on the spatiotemporal evolution of the self-bound droplet in the presence of excitation induced by periodic density modulation. It is found that higher-order corrections may lead to the formation of a train of small droplets. We then extend our study for the case of inhomogeneous droplets in quasi one-dimensional Bose mixtures.
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.