The modified perturbation scheme for superfluid Bose systems

Abdelâali Boudjemâa, Karima Abbas

We study the properties of a homogeneous dilute Bose-Bose gas in a weak-disorder potential at zero temperature. By using the perturbation theory, we calculate the disorder corrections to the condensate density, the equation of state, the compressibility, and the superfluid density as a function of density, strength of disorder, and miscibility parameter. It is found that the disorder potential may lead to modifying the miscibility-immiscibility condition and a full miscible phase turns out to be impossible in the presence of the disorder. We show that the intriguing interplay of the disorder and intra- and interspecies interactions may strongly influence the localization of each component, the quantum fluctuations, and the compressibility, as well as the superfluidity of the system.

Красильников Владимир Владимирович, S. V. Peletminskiǐ

Shinji Koshida, Yusuke Kato

A perturbative way to investigate superfluid properties of various systems under nonuniform potential is presented. We derive the perturbation expansion of the superfluid fraction, which indicates how liquid exhibits nonclassical rotational inertia, in terms of the strength of nonuniform potential and find that the coefficient of the leading term reflects the density fluctuation of the system. Our formulation does not assume anything about Bose-Einstein condensation and thus is applicable to wide variety of systems. Superfluid properties of some examples including (non-)interacting Bose systems, especially Bose gas in the mean field limit, (non-)interacting Fermi sytems, Tomonaga-Luttinger liquid and spinless chiral $p$-wave superfluid are investigated.

Victor Nikolaevich Popov

Oladunjoye A. Awoga

Mott insulator to superfluid phase transitions and unconventional superfluid phases in spin-orbit coupled Bose-Einstein condensate in one dimensional, square and hexagonal optical lattices are investigated using decoupling approximation and variational Gutzwiller wave function. We considered a system with two components. In the first part, we used decoupling approximation along side perturbation to chart the phase diagrams of the system in the absence of spin-orbit coupling. Our results show that the occupation number of the species, interspecies interaction and the ratio of the hopping matrix of the species dictate the critical point and the separation of the insulating phases. Applying decoupling approximation to spin-orbit coupled Bose-Einstein condensate in one dimensional optical we find that spin-orbit coupling reduces the phase boundary of Mott insulator-superfluid transition and also modifies the critical point in a way that the critical point reduces as the coupling strength increases. In the second part, we applied the variational Gutzwiller wave function to spin-orbit coupled Bose-Einstein condensate in square and hexagonal lattice. Our results show that the geometry of the optical lattice plays a role in the transition. We find that the mean-field Mott insulator-superfluid phase transition boundary of hexagonal lattice is smaller than that of square lattice for the same system. Finally, we showed that the Gutzwiller variational approach gives us access to the twisted superfluid phase realized in the system. The nonuniformity of the superfluid phase is different for the two lattices.

Victor Nikolaevich Popov, Vladimir Sergeevich Yarunin