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arXiv:2306.12283 · SciPost Physics

Quantum droplets with particle imbalance in one-dimensional optical lattices

Jofre Vallès-Muns, Ivan Morera, G. E. Astrakharchik, Bruno Juliá-Díaz

Published Mar 13, 2024• 14 citations
arXivHTMLPDF

Abstract

We study the formation of particle-imbalanced quantum droplets in a one-dimensional optical lattice containing a binary bosonic mixture at zero temperature. To understand the effects of the imbalance from both the few- and many-body perspectives, we employ density matrix renormalization group (DMRG) simulations and perform the extrapolation to the thermodynamic limit. In contrast to the particle-balanced case, not all bosons are paired, resulting in an interplay between bound states and individual atoms that leads to intriguing phenomena. Quantum droplets manage to sustain a small particle imbalance, resulting in an effective magnetization. However, as the imbalance is further increased, a critical point is eventually crossed, and the droplets start to expel the excess particles while the magnetization in the bulk remains constant. Remarkably, the unpaired particles on top of the quantum droplet effectively form a super Tonks-Girardeau (hard-rod) gas. The expulsion point coincides with the critical density at which the size of the super Tonks-Girardeau gas matches the size of the droplet.

DOI
10.21468/scipostphys.16.3.074

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We study the formation of particle-imbalanced quantum droplets in a one-dimensional optical lattice containing a binary bosonic mixture at zero temperature. To understand the effects of the imbalance from both the few- and many-body perspectives, we employ density matrix renormalization group (DMRG) simulations and perform the extrapolation to the thermodynamic limit. In contrast to the particle-balanced case, not all bosons are paired, resulting in an interplay between bound states and individual atoms that leads to intriguing phenomena. Quantum droplets manage to sustain a small particle imbalance, resulting in an effective magnetization. However, as the imbalance is further increased, a critical point is eventually crossed, and the droplets start to expel the excess particles while the magnetization in the bulk remains constant. Remarkably, the unpaired particles on top of the quantum droplet effectively form a super Tonks-Girardeau (hard-rod) gas. The expulsion point coincides with the critical density at which the size of the super Tonks-Girardeau gas matches the size of the droplet.
The ground-state properties of two-component bosonic mixtures in a one-dimensional optical lattice are studied both from few- and many-body perspectives. We rely directly on a microscopic Hamiltonian with attractive intercomponent and repulsive intracomponent interactions to demonstrate the formation of a quantum liquid. We reveal that its formation and stability can be interpreted in terms of finite-range interactions between dimers. We derive an effective model of composite bosons (dimers) which correctly captures both the few- and many-body properties and validate it against exact results obtained by the density matrix renormalization group method for the full Hamiltonian. The threshold for the formation of the liquid coincides with the appearance of a bound state in the dimer-dimer problem and possesses a universality in terms of the two-body parameters of the dimer-dimer interaction, namely, scattering length and effective range. For sufficiently strong effective dimer-dimer repulsion we observe fermionization of the dimers which form an effective Tonks-Girardeau state and identify conditions for the formation of a solitonic solution. Our predictions are relevant to experiments with dipolar atoms and two-component mixtures.
Quantum droplets are a quantum analog to classical fluid droplets in that they are self-bound and display liquid-like properties---such as incompressibility and surface tension---though their stability is the result of quantum fluctuations. One of the major systems for observing quantum droplets is two-component Bose gases. Two-component droplets are typically considered to be balanced, having a fixed ratio between the densities of the two components. This work goes beyond the fixed density ratio by investigating spherical droplets in imbalanced mixtures. With increasing imbalance, the droplet is able to lower its energy up to a limit, at which point the droplet becomes saturated with the atoms of the majority component and any further atoms added to this component cannot bind to the droplet. Analyzing the breathing mode dynamics of imbalanced droplets indicates that the droplet can emit particles, as in balanced mixtures, but the imbalance leads to an intricate superposition of multiple simultaneously decaying collective oscillations.
While binary atomic Bose-Einstein condensates (BECs) are typically prone to collapse under strong interspecies attraction, it has been shown that higher-order fluctuation corrections, known as Lee-Huang-Yang corrections, can stabilize the mixture. In this work we demonstrate an alternative stabilization mechanism based on kinetic energy. Specifically, we consider a one-dimensional mixture of a quasi-BEC and a Tonks-Girardeau (TG) gas and show that the kinetic energy of the TG component can counteract the interspecies attraction, thereby preventing collapse. This balance leads to the formation of a self-bound quantum droplet, which exhibits two distinct regimes: a low-density droplet and a high-density droplet. We argue that these regimes are smoothly connected by a crossover. Furthermore, an analysis of the derivatives of the ground-state energy and bulk modulus reveals that the transition from a miscible mixture to the droplet phase is of third order. Our findings extend the theoretical understanding of quantum droplets in low-dimensional quantum gases, and the proposed system may be experimentally accessible within current ultracold-atom platforms.
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.
Recent experiments on ultracold atomic alkali gases in a one-dimensional optical lattice have demonstrated the transition from a gas of soft-core bosons to a Tonks-Girardeau gas in the hard-core limit, where one-dimensional bosons behave like fermions in many respects. We have studied the underlying many-body physics through numerical simulations which accommodate both the soft-core and hard-core limits in one single framework. We find that the Tonks-Girardeau gas is reached only at the strongest optical lattice potentials. Results for slightly higher densities, where the gas develops a Mott-like phase already at weaker optical lattice potentials, show that these Mott-like short-range correlations do not enhance the convergence to the hard-core limit.
We investigate the formation of self-bound quantum droplets in a one-dimensional binary mixture of bosonic atoms, applying the method of numerical diagonalization of the full Hamiltonian. The excitation spectra and ground-state pair correlations signal the formation of a few-boson droplet when crossing the region of critical interspecies interactions. The self-binding affects the rotational excitations, displaying a change in the energy dispersion from negative curvature, associated with superfluidity in the many-body limit, to a nearly parabolic curvature indicative of rigid body rotation. We exploit two global symmetries of the system to further analyze the few-body modes in terms of transition matrix elements and breathing mode dynamics. The ground and excited state energies reported here are exact within the respective Hilbert spaces, which have been adapted according to a given set of single-particle basis states and a specific importance threshold of the employed truncation method. We compare these data to the usual ad hoc inclusion of higher-order contributions in the extended Gross-Pitaevskii equation. For the given parameters we find a remarkable agreement between the few-body regime and the thermodynamic limit in one dimension.