ECAMP 15

We present the study of dilute Bose-Bose mixture of two hyperfine states of $^{39}$K confined by an external harmonic potential in one spatial direction extending the recent research of some of the authors [1] towards the two-dimensional limit, in which the liquid phase is formed whenever the intraspecies interactions are repulsive and the interspecies one is attractive [2].

First, we study the bulk mixture using quantum Monte Carlo methods at T=0 and obtain equations of state for several confinement strengths. Attractive interspecies and repulsive intraspecies interactions are modeled with potentials that include information on s-wave scattering length and effective range. Based on the quantum Monte Carlo equation of state we develop a two-dimensional density functional for each confinement strength and use it together with the local density approximation to determine density profiles of self-bound drops and the formation of vortices. For weaker confinement, droplet profiles obtained using two-dimensional density functional agree well with the profiles previously obtained using three-dimensional functionals [1]. As the confinement strength is increased the number of particles needed to form a droplet with saturated density is significantly decreased. This is accompanied with the decrease of the critical number of atoms needed to form a stable vortex. In selected cases, we compare our results with Lee–Huang–Yang beyond mean-field theory predictions.

Adding the optical lattice in two directions perpendicular to the harmonic confinement, we study the changes in droplet stability and density profiles as the strength of the optical lattice is increased. Additionally, we report the quantum Monte Carlo results of bulk mixture in optical lattices, including the equations of state and the evolution of superfluidity with the increase of lattice depth.

[1] A. Sanuy, et al., PRA 109, 013313 (2024).
[2] D. S. Petrov and G. E. Astrakharchik, Phys. Rev. Lett 117, 100401 (2016).