We study Andreev-Bashkin drag interactions between the superflow of different components in the superfluid phase of a three-component Bose-Hubbard model without component-mixing interactions, relevant for cold atom systems subjected to an optical lattice. By means of directed worm algorithm path integral Monte Carlo simulations we produce the phase diagram of the superfluid drag density as a function of the nearest-neighbor hopping amplitude and the chemical potential in the case of component-symmetric parameters. In both one and two dimensions, we find an expected region of negative drag close to the tip of the first Mott lobe and a generalization of the two-component supercounterfluid phase in parts of this region. In addition, we also find a more trivial positive drag with strongest presence below the Mott lobe. Further, we investigate the dependence of the drag on the details of the intercomponent interactions strengths in the weakly-coupled regime. In accordance with mean-field results obtained by Stian Hartman, we find that, unlike in the two-component case, the drag is no longer independent of the sign of the intercomponent interaction strengths. In particular, the drag between component a and b can either be strengthened or weakened by increasing interaction strength between component a and c, depending on the sign of the interaction strength between b and c.
The superfluid drag coefficient of a weakly interacting three-component Bose-Einstein condensate is computed on a square optical lattice deep in the superfluid phase, starting from a Bose-Hubbard model with component-conserving, on-site interactions and nearest-neighbor hopping. At the mean-field level, Rayleigh-Schr\"odinger perturbation theory is employed to provide an analytic expression for the drag density. In addition, the Hamiltonian is diagonalized numerically to compute the drag within mean-field theory at both zero and finite temperatures to all orders in intercomponent interactions. Moreover, path integral Monte Carlo simulations, providing results beyond mean-field theory, have been performed to support the mean-field results. In the two-component case the drag increases monotonically with the magnitude of the intercomponent interaction ${\ensuremath{\gamma}}_{AB}$ between the two components
A and
B. The increase is independent of the sign of the intercomponent interaction. This no longer holds when an additional third component
C is included. Instead of increasing monotonically, the drag can either be strengthened or weakened depending on the details of the interaction strengths, for weak and moderately strong interactions. The general picture is that the drag coefficient between component
A and
B is a nonmonotonic function of the intercomponent interaction strength ${\ensuremath{\gamma}}_{AC}$ between
A and a third component
C. For weak ${\ensuremath{\gamma}}_{AC}$ compared to the direct interaction ${\ensuremath{\gamma}}_{AB}$ between
A and
B, the drag coefficient between
A and
B can decrease, contrary to what one naively would expect. When ${\ensuremath{\gamma}}_{AC}$ is strong compared to ${\ensuremath{\gamma}}_{AB}$, the drag between
A and
B increases with increasing ${\ensuremath{\gamma}}_{AC}$, as one would naively expect. We attribute the subtle reduction of ${\ensuremath{\rho}}_{d,AB}$ with increasing ${\ensuremath{\gamma}}_{AC}$, which has no counterpart in the two-component case, to a renormalization of the intercomponent scattering vertex ${\ensuremath{\gamma}}_{AB}$ via intermediate excited states of the third condensate
C. We briefly comment on how this generalizes to systems with more than three components.
We study a mixture of two superfluids with density–density and current–current (Andreev–Bashkin) interspecies interactions. The Andreev–Bashkin coupling gives rise to a dissipationless drag (or entrainment) between the two superfluids. Within the quantum hydrodynamics approximation, we study the relations between speeds of sound, susceptibilities and static structure factors, in a generic model in which the density and spin dynamics decouple. Due to translational invariance, the density channel does not feel the drag. The spin channel, instead, does not satisfy the usual Bijl–Feynman relation, since the f-sum rule is not exhausted by the spin phonons. The very same effect on one dimensional Bose mixtures and their Luttinger liquid description is analysed within perturbation theory. Using diffusion quantum Monte Carlo simulations of a system of dipolar gases in a double layer configuration, we confirm the general results. Given the recent advances in measuring the counterflow instability, we also study the effect of the entrainment on the dynamical stability of a superfluid mixture with non-zero relative velocity.
The mutual drag in strongly interacting two-component superfluids in optical lattices is discussed. Two competing drag mechanisms are the vacancy-assisted motion and proximity to a quasimolecular state. In a case of strong drag, the lowest energy topological excitation (vortex or persistent current) can consist of several circulation quanta. In the SQUID-type geometry, the circulation can become fractional. We present both the mean field and Monte Carlo results. The drag effects in optical lattices are drastically different from the Galilean-invariant Andreev-Bashkin effect in liquid helium.
We study the effects of quantum fluctuations in the two-component Bose-Hubbard model generalizing to mixtures the quantum Gutzwiller approach introduced recently in [Phys. Rev. Research 2, 033276 (2020)]. As a basis for our study, we analyze the mean-field ground-state phase diagram and spectrum of elementary excitations, with particular emphasis on the quantum phase transitions of the model. Within the quantum critical regimes, we address both the superfluid transport properties and the linear response dynamics to density and spin probes of direct experimental relevance. Crucially, we find that quantum fluctuations have a dramatic effect on the drag between the superfluid species of the system, particularly in the vicinity of the paired and antipaired phases absent in the usual one-component Bose-Hubbard model. Additionally, we analyse the contributions of quantum corrections to the one-body coherence and density/spin fluctuations from the perspective of the collective modes of the system, providing results for the few-body correlations in all the regimes of the phase diagram.
Strongly interacting many-body quantum systems constitute some of the most challenging problems in physics, and exact analytical solutions are rare. In this thesis, we will investigate the models of two such systems numerically using the unbiased worm-algorithm Monte Carlo method. The first model is the t-J model, which describes strongly correlated lattice electrons and is thought to capture the essential physics of high-temperature superconductors. Of particular interest to us is the emergent magnetic polaron studied in the first two papers. The microscopic pairing mechanism between these quasiparticles remains one of the most outstanding open questions in condensed matter physics. The second model is an extended multi-component Bose--Hubbard model, which describes lattice bosons of multiple species. This model is essential to the third paper, in which we demonstrate a novel superfluid phenomenon in the form of a dissipationless drag effect that couples the different superfluid components of a superfluid mixture in a noncollinear fashion. Dissipationless drag is a fundamental effect present in a diverse set of physical systems. In the fourth paper, we further use the Bose--Hubbard model to study other new superfluid phenomena that arise when the number of superfluid components is increased. A general introduction to the research field is first given in the thesis, after which some prerequisites are refreshed. Then essential concepts are introduced, and the numerical method is outlined and benchmarked. Following that is a summary of the research carried out.