The soft-core boson system is one of the simplest models of supersolids, which have both off-diagonal long-range order (Bose-Einstein condensation) and diagonal long-range order (crystalline order). Although this model has been studied from various points of view, studies of the stability of current-flowing states are lacking. Solving the Gross-Pitaevskii and Bogoliubov equations, we obtain excitation spectra in superfluid, supersolid, and stripe phases. On the basis of the results of the excitation spectra, we present a stability phase diagram that shows the region of the metastable superflow states for each phase.

We analyze the time evolution of the Bose-Hubbard model after a sudden quantum quench to a weakly interacting regime. Specifically, motivated by a recent experiment at Kyoto University, we numerically simulate redistribution of the kinetic and onsite-interaction energies at an early time, which was observed in non-equilibrium dynamics of ultracold Bose gases in a cubic optical lattice starting with a singly-occupied Mott-insulator state. In order to compute the short-time dynamics corresponding to the experimental situation, we apply the truncated-Wigner approximation (TWA) to the Bose-Hubbard model on a cubic lattice. We show that our semiclassical approach quantitatively reproduces the fast redistribution dynamics. We further analyze spatial spreading of density-density correlations at equal time in the Bose-Hubbard model on a square lattice with a large filling factor. When the system is initially prepared in a coherent state, we find that a propagation velocity of the correlation wave packet in the correlation function strongly depends on the final interaction strength, and it is bounded by twice the maximum group velocity of the elementary excitations. In contrast, when the system is initially in a Mott-insulator state, the propagation velocity of the wave packet is approximately independent of the final interaction strength.

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We investigate dynamic properties of bouncing and penetration in colliding binary and ternary Bose-Einstein condensates comprised of different Zeeman or hyperfine states of 87 Rb. Through the application of magnetic field gradient pulses, two-or three-component condensates in an optical trap are spatially separated and then made to collide. The subsequent evolutions are classified into two categories: repeated bouncing motion and mutual penetration after damped bounces. We experimentally observed mutual penetration for immiscible condensates, bouncing between miscible condensates, and domain formation for miscible condensates. From numerical simulations of the Gross-Pitaevskii equation, we find that the penetration time can be tuned by slightly changing the atomic interaction strengths. Multicomponent Bose-Einstein condensates (BECs) in dilute atomic gases are an attractive system for studying hydrodynamics of multicomponent quantum fluids owing to their unprecedented controllability. One of the significant properties characterizing multicomponent fluid systems is their miscibility; different fluids are either mutually miscible or phase separation occurs. In multicomponent BECs, the miscibility is determined by inter-and intra-species atomic interaction strengths [1] and, importantly, they can be experimentally controlled using Feshbach resonances [2,3] and Rabi coupling [4,5]. Multicomponent BECs with various degrees of miscibility are also available by choosing the internal states [6] or atomic species [7]. Employing such adjustability and selectability, intriguing phenomena that depend on the degree of miscibility have been experimentally observed, e.g., soliton generation in a counterflow of miscible fluids [8,9] The condition for miscibility in multicomponent BECs is determined by linear stability analysis of a static or steady state, and is not naively applicable to dynamical situations. Let us consider a situation in which two wave packets of different BECs collide with each other. One may think that the two wave packets pass through each other without much reflection for miscible BECs, while for immiscible BECs they do not. However, we will show that these simple predictions from the miscibility do not apply to a highly dynamic situation.In this Rapid Communication, we generate multicomponent BECs with various degrees of miscibility by utilizing the rich spin degrees of freedom of the 87 Rb atom, and investigate the dynamical properties of bouncing and penetration in colliding binary and ternary BECs in an optical trap. We observed various dynamics, including bouncing between miscible BECs and mutual penetration of immiscible BECs, which seems counterintuitive at first glance. In miscible and weakly immiscible binary and ternary systems, after a few bounces, BECs mutually penetrate and create the domain structure. In contrast, in the case of a relatively strongly immiscible system, binary BECs continue to bounce. Such repetitive bouncing motion between atoms has been observed only in a Tonks-Girardeau ga...