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arXiv:2105.04172 · Chinese Physics Letters

Self-Bound Quantum Droplet with Internal Stripe Structure in One-Dimensional Spin-Orbit-Coupled Bose Gas

Yuncheng Xiong, Lan Yin

Published Jul 1, 2021• 13 citations
arXivHTMLPDF

Abstract

We study the quantum-droplet state in a three-dimensional (3D) Bose gas in the presence of 1D spin-orbit coupling and Raman coupling, especially the stripe phase with density modulation, by numerically computing the ground state energy including the mean-field energy and Lee–Huang–Yang correction. In this droplet state, the stripe can exist in a wider range of Raman coupling, compared with the BEC-gas state. More intriguingly, both spin-orbit coupling and Raman coupling strengths can be used to tune the droplet density.

DOI
10.1088/0256-307x/38/7/070301

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We study the quantum-droplet state in a three-dimensional (3D) Bose gas in the presence of 1D spin-orbit coupling and Raman coupling, especially the stripe phase with density modulation, by numerically computing the ground state energy including the mean-field energy and Lee–Huang–Yang correction. In this droplet state, the stripe can exist in a wider range of Raman coupling, compared with the BEC-gas state. More intriguingly, both spin-orbit coupling and Raman coupling strengths can be used to tune the droplet density.
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.
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.
We study spin and density excitations of one-dimensional self-bound Bose-Bose droplets within Bogoliubov theory, and show that spin excitations come alive, especially as the interspecies coupling is made less attractive. We argue that spin excitations are particularly relevant in the one-dimensional droplet regime, where droplets are realized within the mean-field stability regime, as has been confirmed by the quantum Monte Carlo simulations. As the interspecies coupling strength increases within the mean-field stability regime, spin modes ultimately fall below the particle-emission threshold, thus becoming observable in the droplet spectrum. We analyze the Bogoliubov model for both pseudospinor and population-imbalanced scalar mixtures, encompassing both the density and spin sectors. We corroborate our findings through variational analysis of density- and spin-breathing modes, which offers physical insight into the mode structure and independently validates the spectrum, as well as through real-time dynamics. Additionally, we compare our results with both Petrov's original theory, which considers the Lee-Huang-Yang (LHY) correction at the attractive edge of the mean-field stability regime, and a beyond-LHY description of Bose-Bose mixtures.
We theoretically investigate a one-dimensional quantum droplet with spin-orbit (SO) coupling and periodically modulated Raman coupling. Using a Floquet approach, we derive an effective time-independent model that reveals a controlled phase diagram. Crucially, the interplay of quantum fluctuations encoded in the Lee-Huang-Yang correction and SO coupling suppresses the plane-wave phase that is typical of mean-field SO-coupled condensates. The ground state is instead restricted to two distinct phases: a stripe phase, with periodic density modulations, and a zero-momentum phase, with a flat-top density profile. The plane-wave droplet is a metastable state of the system. We demonstrate that the boundary between these phases can be dynamically manipulated by tuning the driving parameters. Furthermore, we explore the system's response to quantum quenches, uncovering a wealth of nonequilibrium phenomena, including the dynamical formation of stable, solitonlike structures. Our work establishes periodic driving as a powerful tool for the dynamical control of self-bound quantum matter and elucidates the fundamental role of quantum fluctuations in shaping the phase diagram of SO-coupled droplets.
Supersolidity---a coexistence of superfluidity and crystalline or amorphous density variations---has been vividly debated ever since its conjecture. While the initial focus was on helium-4, recent experiments uncovered supersolidity in ultracold dipolar quantum gases. Here we propose a self-bound supersolid phase in a binary mixture of Bose gases with short-range interactions, making use of the nontrivial properties of spin-orbit coupling. We find that a first-order phase transition from a self-bound supersolid stripe phase to a zero-minimum droplet state of the Bose gas occurs as a function of the Rabi coupling strength. These phases are characterized using the momentum distribution, the transverse spin polarization, and the superfluid fraction. The critical point of the transition is estimated in an analytical framework. The predicted density-modulated supersolid stripe and zero-minimum droplet phase should be experimentally observable in a binary mixture of 39K^{39}\mathrm{K}39K with spin-orbit coupling.
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.