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arXiv:2108.00727 · Physical Review Research

Formation and quench of homonuclear and heteronuclear quantum droplets in one dimension

S. I. Mistakidis, Thudiyangal Mithun, P. G. Kevrekidis, H. R. Sadeghpour, Peter Schmelcher

Published Nov 19, 2021• 47 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevresearch.3.043128

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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 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.
We address the existence and dynamics of one-dimensional harmonically confined quantum droplets appearing in two-component mixtures by deploying a nonperturbative approach. We find that, in symmetric homonuclear settings, beyond-Lee-Huang-Yang correlations result in flat-top droplet configurations for either decreasing intercomponent attraction or larger atom number. Asymmetric mixtures feature spatial mixing among the involved components with the more strongly interacting or heavier one exhibiting flat-top structures. Applying quenches on the harmonic trap we trigger the lowest-lying collective droplet excitations. The interaction-dependent breathing frequency, being slightly reduced in the presence of correlations, shows a decreasing trend for stronger attractions. Semianalytical predictions are also obtained within the Lee-Huang-Yang framework. For relatively large quench amplitudes the droplet progressively delocalizes and higher-lying motional excitations develop in its core. Simultaneously, enhanced intercomponent entanglement and long-range two-body intracomponent correlations arise. In sharp contrast, the dipole motion remains robust irrespective of the system parameters. Species-selective quenches lead to a correlation-induced dephasing of the droplet or to irregular dipole patterns due to intercomponent collisions.
We explore the formation of one-dimensional two-component quantum droplets with intercomponent particle imbalance using an ab initio many-body method. It is shown that for moderate particle imbalance each component maintains its droplet flat-top or Gaussian-type character depending on the intercomponent attraction. Importantly, large particle imbalance leads to a flat-top shape of the majority component with the minority exhibiting spatially localized configurations. The latter imprint modulations on the majority component which become more pronounced for increasing interspecies attraction. The same holds for larger mass or increasing repulsion of the minority species. Such structural transitions are also evident in the underlying two-body correlation functions. To interpret the origin and characteristics of these droplet states we derive an effective model based on the established Lee-Huang-Yang theory providing adequate qualitative analytical predictions even away from its expected parametric region of validity. In contrast, the droplet character is found to vanish in the presence of fermionic minority atoms. Our results pave the way for unveiling complex droplet phases of matter.
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.
Significant efforts have been devoted to studying the properties of quantum droplets, an ultra low-temperature phase of bosonic quantum matter that emerges as a consequence of the Lee-Huang-Yang fluctuating correction. However, the temporal dynamics of droplet formation for heteronuclear bosonic mixtures is only partially understood. Here, we numerically analyze the droplet formation process for homonuclear and heteronuclear binary bosonic mixtures in one dimension, using a tight-binding model and real-time evolution with a novel, highly robust integration algorithm. We proceed with a systematic scan of interaction intensities, mass ratios, and initial conditions that allows us to characterize quantitative criteria for droplet formation and equilibrium prospects. Noticeably, most droplets readily form across the entire parameter space, although only a small fraction achieves a stable equilibrium configuration within the simulation horizon. We attribute this equilibrium deficiency to damping from a breathing mode, which we extract directly from the width oscillations at late times. The Lee-Huang-Yang contribution supplies essentially the entire binding energy, while, at late times, the density profile of the equilibrated subset is better described by a soliton-like shape rather than the flat-topped profiles characteristic of larger droplets. Referring to the energy of the free-atom band, the binding energy grows super-extensively with the number of atoms as Ebind∝N1.6E_{\text{bind}} \propto N^{1.6}Ebind​∝N1.6. Heteronuclear droplets bind more strongly as the mass ratio between their components increases and exhibit breathing oscillations that are greater than those of their homonuclear counterparts, which is consistent with the role of mass-imbalanced kinetic terms. Our analysis provides a methodological framework for interpreting real-time quantum droplet simulations.
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.