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arXiv:2105.01277 · Physical Review Research

Lee-Huang-Yang effects in the ultracold mixture of Na 23 and Rb 87 with attractive interspecies interactions

Zhichao Guo, Fan Jia, Lintao Li, Yinfeng Ma, Jeremy M. Hutson, Xiaoling Cui, Dajun Wang

Published Sep 14, 2021• 85 citations
arXivHTMLPDF

Abstract

The beyond-mean-field Lee-Huang-Yang (LHY) correction is ubiquitous in dilute ultracold quantum gases. However, its effects are often elusive due to the typically much larger influence of the mean-field (MF) energy. In this work, we study an ultracold mixture of $^{23}\mathrm{Na}$ and $^{87}\mathrm{Rb}$ with tunable attractive interspecies interactions. The LHY effects manifest in the formation of self-bound quantum liquid droplets and the expansion dynamics of the gas-phase sample. A liquid-to-gas-phase diagram is obtained by measuring the critical atom numbers below which the self-bound behavior disappears. In stark contrast to trapped gas-phase condensates, the gas-phase mixture formed following the liquid-to-gas-phase transition shows an anomalous expansion featuring a larger release energy for increasing MF attractions.

DOI
10.1103/physrevresearch.3.033247

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The beyond-mean-field Lee-Huang-Yang (LHY) correction is ubiquitous in dilute ultracold quantum gases. However, its effects are often elusive due to the typically much larger influence of the mean-field (MF) energy. In this work, we study an ultracold mixture of 23Na^{23}\mathrm{Na}23Na and 87Rb^{87}\mathrm{Rb}87Rb with tunable attractive interspecies interactions. The LHY effects manifest in the formation of self-bound quantum liquid droplets and the expansion dynamics of the gas-phase sample. A liquid-to-gas-phase diagram is obtained by measuring the critical atom numbers below which the self-bound behavior disappears. In stark contrast to trapped gas-phase condensates, the gas-phase mixture formed following the liquid-to-gas-phase transition shows an anomalous expansion featuring a larger release energy for increasing MF attractions.
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.
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 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.
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.
Due to high density and incompressibility, attempts to enter the quantum regime for usual liquids are prohibited. However, incorporating the high-order Lee-Huang-Yang (LHY) correction, a gas-to-liquid phase transition violating the van der Waals model has been observed in two-component mixtures and dipolar condensates when the particle number exceeds a certain threshold. By tuning interatomic interactions, creating dilute self-bound Bose-Einstein quantum droplets (QD) provides strong evidence of phenomena beyond mean-field (MF) effects [1]. In this work, we theoretically investigated the nonlinear effects on the Bloch oscillation (BO) and the Landau-Zener tunneling (LZT) of a QD in an one-dimensional optical lattice (OL) perturbed by an external force.
A quantum liquid in a heterogeneous mixture of 41K^{41}\mathrm{K}41K and 87Rb^{87}\mathrm{Rb}87Rb atoms is studied using the diffusion Monte Carlo method and density-functional theory. The perturbative Lee-Huang-Yang term for a heterogeneous mixture is verified and it is proved to be valid only near the gas-liquid transition. Based on the equations of state of the bulk mixture, calculated with diffusion Monte Carlo, extensions to Lee-Huang-Yang corrected mean-field energy functionals are presented. Using density-functional theory, a systematic comparison between different functionals is performed, focusing on the critical atom number, surface tension, surface width, Tolman length, and compressibility. These results are given as a function of the interspecies interaction strength, within the stability domain of the liquid mixture.