We demonstrate the existence of quantum droplets in two-component one-dimensional Bose-Hubbard chains. The droplets exist for any strength of repulsive intra-species interactions provided they are balanced by comparable attractive inter-species interactions. The ground-state phase diagram is presented and the different phases are characterized by examining the density profile and off-diagonal one-and two-body correlation functions. A rich variety of phases is found, including atomic superfluid gases, atomic superfluid droplets, pair superfluid droplets, pair superfluid gases and a Mott-insulator phase. A parameter region prone to be experimentally explored is identified, where the average population per site is lower than three atoms, thus avoiding three-body losses. Finally, the bipartite entanglement of the droplets is found to have a non-trivial dependence on the number of particles.

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We study weakly-repulsive Bose-Bose mixtures in two and three dimensions at zero temperature using the functional renormalization group (FRG). We examine the RG flows and the role of density and spin fluctuations. We study the condition for phase separation and find that this occurs at the mean-field point within the range of parameters explored. Finally, we examine the energy per particle and condensation depletion. We obtain that our FRG calculations compare favorably with known results from perturbative approaches for macroscopic properties.

We study the 1D dynamics of dark-dark solitons in the miscible regime of two density-coupled Bose-Einstein condensates having repulsive interparticle interactions within each condensate (g > 0). By using an adiabatic perturbation theory in the parameter g12/g, we show that, contrary to the case of two solitons in scalar condensates, the interactions between solitons are attractive when the interparticle interactions between condensates are repulsive g12 > 0. As a result, the relative motion of dark solitons with equal chemical potential µ is well approximated by harmonic oscillations of angular frequency wr = (µ/ ) (8/15)g12/g. We also show that in finite systems, the resonance of this anomalous excitation mode with the spin density mode of lowest energy gives rise to alternating dynamical instability and stability fringes as a function of the perturbative parameter.In the presence of harmonic trapping (with angular frequency Ω) the solitons are driven by the superposition of two harmonic motions at a frequency given by w 2 = (Ω/ √ 2) 2 + w 2 r . When g12 < 0, these two oscillators compete to give rise to an overall effective potential that can be either single well or double well through a pitchfork bifurcation. All our theoretical results are compared with numerical solutions of the Gross-Pitaevskii equation for the dynamics and the Bogoliubov equations for the linear stability. A good agreement is found between them. arXiv:1801.00309v1 [cond-mat.quant-gas]

We analyze the formation of multi-particle bound states in ladders with frustrated kinetic energy in two component bosonic and two component fermionic systems. We focus on the regime of light doping relative to insulating states at half-filling, spin polarization close to 100 percent, and strong repulsive interactions. A special feature of these systems is that the binding energy scales with single particle tunneling t rather than exchange interactions, since effective attraction arises from alleviating kinetic frustration. For two component Fermi systems on a zigzag ladder we find a bound state between a hole and a flipped spin (magnon) with a binding energy that can be as large as 0.6t. We demonstrate that magnon-hole attraction leads to formation of clusters comprised of several holes and magnons and expound on antiferromagentic correlations for the transverse spin components inside the clusters. We identify several many-body states that result from selforganization of multi-particle bound states, including a Luttinger liquid of hole -magnon pairs and a density wave state of two hole -three magnon composites. We establish a symmetry between the spectra of Bose and Fermi systems and use it to establish the existence of antibound states in two component Bose mixtures with SU(2) symmetric repulsion on a zigzag ladder. We also consider Bose and Fermi systems on a square ladder with flux and demonstrate that both systems support bound states. We discuss experimental signatures of multi-particle bound states in both equilibrium and dynamical experiments. We point out intriguing connections between these systems and the quark bag model in QCD.