Abstract
We theoretically investigate the elusive Andreev-Bashkin collisionless drag for a two-component onedimensional Bose-Hubbard model on a ring. By means of tensor network algorithms, we calculate the superfluid stiffness matrix as a function of intra- and interspecies interactions and of the lattice filling. We then focus on the most promising region close to the so-called pair-superfluid phase, where we observe that the drag can become comparable with the total superfluid density. We elucidate the importance of the drag in determining the long-range behavior of the correlation functions and the spin speed of sound. In this way, we are able to provide an expression for the spin Luttinger parameter $K_S$ in terms of drag and the spin susceptibility. Our results are promising in view of implementing the system by using ultracold Bose mixtures trapped in deep optical lattices, where the size of the sample is of the same order of the number of particles we simulate. Importantly, the mesoscopicity of the system, far from being detrimental, appears to favor a large drag, avoiding the Berezinskii-Kosterlitz-Thouless jump at the transition to the pair-superfluid phase which would reduce the region where a large drag can be observed.
Highlights
The dynamics of multi-component superfluids, ranging from neutron stars [1] to superconducting layers [2], is supposed to be crucially influenced by an intercomponent dissipationless drag
Our results are promising in view of implementing the system by using ultra-cold Bose mixtures trapped in deep optical lattices, where the size of the sample is of the same order of the number of particle we simulate
In analogy with Quantum MonteCarlo (QMC) results in the 2D case [10, 12], we expect that the asymmetry between attractive and repulsive regimes is strongly emphasized in the regime where a single superfluid of dimers can be reached for UAB < 0 (PSF phase)
Summary
The dynamics of multi-component superfluids, ranging from neutron stars [1] to superconducting layers [2], is supposed to be crucially influenced by an intercomponent dissipationless drag. In [6], one-dimensional mixtures close to the so-called Tonks-Girardeau regime have been shown to exhibit a large entrainment Another possibility is to consider Hubbard-like models, by putting cold-atoms in deep optical lattices. In this way it is possible to realise strongly interacting superfluids with reduced 3-body losses, and to study new phases that do not appear in continuous systems. We show how finite-size effects might increase the visibility of the collisionless drag, by circumventing the sudden jump that characterises the phase transition to a pair-superfluid phase in the thermodynamic limit This is relevant for typical 1D cold atomic setups, where the particle number is comparable to our numerical simulations.
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