Essential, but largely unaddressed effect is the impact of strong interaction on properties of superfluid phases where each component has its finite expectation value. In a one-component superfluids, the strong interaction causes large depletion of the condensate. The same is expected in two-component superfluids. Besides depletion, another interesting manifestation of the strong interaction is the inter-component drag similar to the Andreev-Bashkin effect in helium isotope mixtures. In general, the drag effect between non-convertible species at zero temperature is represented by the cross-terms in the expansion of the ground state energy in terms of small gradients of the superfluid phases.

This project is dedicated to the mutual drag in strongly interacting two-component superfluids in optical lattices. The results were reported in [1]. The drag effect in optical lattices is drastically different from the Galilean invariant Andreev-Bashkin effect. There are two competing drag mechanisms: 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. Both the mean field and Monte Carlo methods are employed and results are compared. It is important to note that in optical lattices regime of strong interaction is readily achievable, and in this case the drag effect becomes crucial. There are two main mechanisms of the strong drag effect in optical lattices. They are induced, respectively, by proximity to quasi-molecular states (formed due to strong enough attractive as well as repulsive inter-atomic interaction) and by vacancy assisted transport. These mechanisms in optical lattices are drastically different from the Galilean-invariant Andreev-Bashkin drag effect in liquid helium, where the drag is controlled by particle effective masses. The simplest mean field approximation does not adequately describe the strong drag in optical lattices. In the proximity induced drag, the phases of the separate superfluid components and the phase of the molecular superfluid are locked. This leads to formation of vortices with **1** circulation of one component (say, A) and **q = 1, 2, 3, …** circulations of the other (say, B), if the quasi-molecular state is given by the formula **A-qB**. In the case of the attractive interaction, the drag coefficient is positive. In the case of the supercounterfluid – bound states of atoms of one sort and holes of the other (repulsive interaction) – the components flow predominantly in the opposite directions, resulting in negative drag coefficient. In the vacancy assisted drag, since a vacancy does not have an association with particular component, motion of a vacancy induces flow of both components in the same direction, which results in positive drag coefficient similarly to the case of the proximity to the quasi-molecular state **A-qB**. This effect increases as the vacancy density decreases. However, no bound vortex complexes can form in this regime because the drag coefficient is found to be always below the threshold for formation of such complexes. Different drag mechanisms compete in the case of repulsive interaction. Hence the result of this competition can be vanishing drag. The microscopic arguments explaining drag effect in different cases were supported by Monte-Carlo numerical simulation based on the Worm Algorithm developed for two-color J-current model. The drag was identified through the nonvanishing off-diagonal (inter-component) terms of the superfluid stiffness obtained from the statistics of winding numbers. Monte-Carlo simulations showed that **q+1** topological structures with **q = 1** can exist in a wide range of the system parameters. In some cases fractional phase circulation **q** can be observed when persistent current is interrupted by a Josephson junction which lifts the requirement of the integer of 2? windings by creating a phase jump across the junction. The **q+1** vortex complexes can be observed by absorptive imaging technique similar to imaging of vortices in one-component Bose-Einstein condensates. A typical pattern should include extra **q** fringes in one component.

#### References

1. Drag Effect and Topological Complexes in Strongly Interacting Two-Component Lattice Superfluids, V. M. Kaurov, A. B. Kuklov, and A. E. Meyerovich, Phys. Rev. Lett. 95, 090403 (2005)