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arXiv:2307.16742 · Physical Review A

Spectrum and quench-induced dynamics of spin-orbit-coupled quantum droplets

Sonali Gangwar, Rajamanickam Ravisankar, S. I. Mistakidis, Paulsamy Muruganandam, Pankaj Kumar Mishra

Published Jan 24, 2024• 25 citations
arXivHTMLPDF

Abstract

We investigate the ground state and dynamics of one-dimensional spin-orbit coupled (SOC) quantum droplets within the extended Gross--Pitaevskii approach. As the SOC wave number increases, stripe droplet patterns emerge, with a flat-top background, for larger particle numbers. The surface energy decays following a power-law with respect to the interactions. At small SOC wave numbers, a transition from Gaussian to flat-top droplets occurs for either a larger number of atoms or reduced intercomponent attraction. The excitation spectrum shows that droplets for relatively small SOC wave numbers are stable, otherwise stripe droplets feature instabilities as a function of the particle number or the interactions. We also witness rich droplet dynamical features using velocity imprinting and abrupt changes in the intercomponent interaction or the SOC parameters. Characteristic responses include breathing oscillations, expansion, symmetric and asymmetric droplet fragmentation, admixtures of single and stripe droplet branches, and erratic spatial distributions suggesting the triggering of relevant instabilities. Our results reveal the controlled dynamical generation and stability properties of stripe droplets that should be detectable in current cold-atom experiments.

DOI
10.1103/physreva.109.013321

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We investigate the ground state and dynamics of one-dimensional spin-orbit coupled (SOC) quantum droplets within the extended Gross--Pitaevskii approach. As the SOC wave number increases, stripe droplet patterns emerge, with a flat-top background, for larger particle numbers. The surface energy decays following a power-law with respect to the interactions. At small SOC wave numbers, a transition from Gaussian to flat-top droplets occurs for either a larger number of atoms or reduced intercomponent attraction. The excitation spectrum shows that droplets for relatively small SOC wave numbers are stable, otherwise stripe droplets feature instabilities as a function of the particle number or the interactions. We also witness rich droplet dynamical features using velocity imprinting and abrupt changes in the intercomponent interaction or the SOC parameters. Characteristic responses include breathing oscillations, expansion, symmetric and asymmetric droplet fragmentation, admixtures of single and stripe droplet branches, and erratic spatial distributions suggesting the triggering of relevant instabilities. Our results reveal the controlled dynamical generation and stability properties of stripe droplets that should be detectable in current cold-atom experiments.
We study the static and traveling droplet phases of spin-orbit coupled, one-dimensional Bose-Bose mixtures with a Lee-Huang-Yang correction. For the static droplets, employing a variational analysis for an infinitely extended mixture, we show that the system can feature two ground-state droplet phases: a stripe droplet phase up to a critical Rabi coupling strength, at which it undergoes a first-order transition to a zero-momentum droplet phase. The variational results for the ground-state properties are shown to be in good agreement with numerical solutions for droplets in the thermodynamic limit as well as finite-size droplets in the "flat-top regime". For finite-size droplets, the stripe phase can feature multiple stationary states with different numbers of peaks in their stripe density patterns. The calculation of the excitation spectrum for these stationary states confirms their stability. To study the moving droplets, we investigate the ground-state phases of the system in the droplet's comoving frame. We show that in the comoving frame, droplets acquire a finite longitudinal magnetization. As a consequence, the phase diagram features two distinct phases: a traveling stripe droplet and a plane-wave droplet. The real-time evolution of these droplets in the space-fixed frame, complemented by the Bogoliubov analysis in the comoving frame, illustrates the stability of these traveling droplet phases.
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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 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 theoretically investigate ground-state properties and collective excitations of one-dimensional quantum droplets in asymmetric Bose-Bose mixtures with unequal intraspin interactions. Using the extended Gross-Pitaevskii equation supported by variational, sum-rule, and linearization methods, we show that the intraspin interaction ratio substantially alters the droplet's density profile, driving a transition from Gaussian-like to flat-top shapes. By examining two experimentally relevant parameter regions, we analyze density profiles, radii, peak densities, and excitation spectra to distinguish quantum phases and to depict phase diagrams in the space of asymmetric interaction ratio and total atom number. We carefully study the frequencies of both well-known dipole and breathing modes and less-explored spin-dipole and spin-breathing modes. The breathing-mode frequency decreases monotonically with interaction ratio, approaching asymptotically the result of a conventional weakly interacting Bose gas. It varies nonmonotonically with total atom number, peaking at a critical point that highlights the crucial role of quantum fluctuations. In contrast, spin modes display distinct temporal spin density distributions and reveal in-phase and out-of-phase relative dynamics between components. Their frequencies depend instead monotonically on the interaction ratio and atom number. Our results provide a comprehensive understanding of asymmetric quantum droplets and link to experimentally accessible regimes in ultracold 39^{39}39K atomic gases.
We analyze the role played by quantum fluctuations on a Raman spin-orbit-coupled system in the stripe phase under attractive interspin interactions. We show that beyond-mean-field effects stabilize the collapse predicted by mean-field theory for attractive enough interspin interactions and induce the emergence of two phases, a gas and a liquid, which also show spatial periodicity along a privileged direction. We show that the energetically favored phase is determined by the Raman coupling and the spin-dependent scattering lengths. We obtain the ground-state solution of the finite system by solving the extended Gross-Pitaevskii equation and find self-bound dropletlike solutions that feature internal structure through a striped pattern. We estimate the critical binding number of these droplets and show that their value is experimentally accessible. We report an approximate energy functional in order to ease the evaluation of the Lee-Huang-Yang correction in practical terms.