Cristalização e superfluidez em um condensado de Bose-Einstein unidimensional com interações do tipo soft-core

Abstract

In a system of many bosons at low temperatures, the particles can all occupy the same ground state, thus forming a Bose-Einstein condensate. In this case, all bosons share a single wave function to describe the system’s state. One way to study this system is through the Gross-Pitaevskii equation (GPE), which has the form of a nonlinear Schrodinger equation, whose solution is a function whose squared modulus represents a particle density throughout space at each instant of time. For the case where the interaction potential between particles is a contact interaction, a constant function is the solution to the GPE. For dipole-dipole interactions in dipolarboson condensates, the equation takes on a more complicated form, with a nonlocal potential, but the constant solution remains valid depending on the boundary conditions. However, a curious situation arises when we consider a soft-core potential, that is, an interaction potential with a finite value V within a range of particle-particle distances from 0 to R; note that, setting V →∞and R→0, this potential falls within the contact interaction potential. In the soft-core potential, a periodic modulation in the particle density is found: in this case, the condensate possesses superfluid properties, as usual, but also a periodic modulation that brings characteristics of a solid, justifying the term "supersolid."In this work, we use an imaginary time evolution method to solve the GPE numerically for a condensate of interacting bosons with a soft-core potential. Thus, we investigate the conditions necessary in the system to obtain supersolid states and discuss the possibility of observing this type of state in real systems in the future.