Multi-stable quantum droplets in optical lattices
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ORIGINAL PAPER
Multi-stable quantum droplets in optical lattices Liangwei Dong · Wei Qi · Ping Peng · Linxue Wang · Hui Zhou · Changming Huang
Received: 10 June 2020 / Accepted: 16 September 2020 © Springer Nature B.V. 2020
Abstract We address the nonlinear dynamics of binary Bose-Einstein condensates with mutually symmetric spinor components trapped in an optical lattice. The interaction between the repulsive Lee–Huang– Yang nonlinearity and the intercomponent attraction as well as Bragg scattering of an optical lattice results in formation of multi-peaked quantum droplets. Evenand odd-symmetric droplets can bifurcate from Bloch modes of the corresponding periodic systems. Linear stability analysis corroborated by direct evolution simulations reveals that even-symmetric droplets with different norms and different number of peaks can evolve stably at the same chemical potential, i.e., multi-stable droplets are possible in the present scheme. Besides the droplets in the semi-infinite gap, the properties of droplets in the first finite bandgap are also discussed. Both even- and odd-symmetric droplets are stable in almost their whole existence domains. We reveal that optical lattice plays an important role for the stabilization of droplets, in sharp contrast to the nonlinear system without a lattice modulation. We, thus, furL. Dong (B)· W. Qi · P. Peng · L. Wang · H. Zhou Department of Physics, Shaanxi University of Science & Technology, Xi’an 710021, China e-mail: [email protected] L. Dong · W. Qi · P. Peng · L. Wang · H. Zhou Institute of Theoretical Physics, Shaanxi University of Science & Technology, Xi’an 710021, China C. Huang Department of Electronic Information and Physics, Changzhi University, Changzhi, Shanxi 046011, China
nish a paradigmatic example of multi-stable quantum droplets held in optical lattices. Keywords Quantum droplets · Stability · Optical lattice · Bifurcation
1 Introduction In the past few years, following the theoretical predictions by Petrov et al. [1,2], peoples observed two kinds of quantum droplets (QDs) in dipolar bosonic gases of dysprosium [3,4], as well as in a mixture of BoseEinstein condensates (BECs) of 39 K with contact interactions [5]. Such droplets are more than two orders of magnitude larger and eight orders of magnitude more dilute than liquid helium [3–5], and thus constitute the most dilute liquid in the world. Ultradilute droplets can find important applications in matter-wave interferometry [6] and manipulations of quantum information [7]. According to the mean-field theory, a binary BoseBose mixture will collapse if the interspecies attraction is stronger than the average of the intraspecies repulsions. However, Petrov et al. found that quantum fluctuations can stabilize the mixture and lead to the formation of dilute droplet state due to beyond-mean-field (BMF) effects [1]. They also calculated the energy of one- and two-dimensional (1D and 2D) weakly interacting Bose-Bose mixtures in the Bogoliubov approximation analytically and by using the diffusion Monte Carlo t
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