Quantum droplets in one-dimensional Bose-Bose mixtures: beyond the Lee-Huang-Yang description

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.

Self-bound droplets with uncorrelated disordered potentials

“…From the theoretical point of view, quantum liquid droplets with their fascinating properties have been investigated extensively such as collective modes [1], soliton to droplet transition [6], droplet-droplet collision [9], low-dimensional properties [10][11][12][13], self-bound vortices [14,15], finite-temperature effects [16][17][18][19] and so on (see recent reviews [20][21][22] and references therein). Furthermore, recent numerical results based on quantum and diffusion Monte Carlo simulations [10, 23, * Author to whom any correspondence should be addressed.…”

Self-bound liquid droplets in one-dimensional optical speckle potentials

“…Early studies in 1D quantum droplets focused on stability, structure and on the dynamics [6,7]. More recently, several aspects of 1D quantum liquids have been explored including collective excitations [8], quantum Monte-Carlo simulations [9], the impact of discreteness in the form of semidiscrete droplets [10,11], thermal effects and evaporation [12][13][14], effects of higher-order corrections [15][16][17][18], phase diagram in 1D optical lattices [19], and universality classes [20]. What is intriguing in such 1D quantum droplets is that quantum fluctuations play a crucial role and three-body losses are suppressed compared to higher dimensions counterparts.…”

“…We investigate in addition the equilibrium and the dynamics of such a disordered droplet in both Gaussian-like and flat-top regimes. To this end, we use the generalized disorder-dependent Gross-Pitaevskii equation (GGPE) which we derive self-consistently in the frame of the Hartree-Fock-Bogoliubov formalism [18]. The numerical simulation of the GGPE points out that the disorder tends to significantly affect the droplet profiles and its width.…”