Study of the Interaction of Static Impurity within a Dipolar Environment

Relaxation dynamics in isolated quantum systems contribute to some of the most challenging problems in the study of many-body systems. These dynamics are not only pivotal for grasping quantum statistical mechanics but also have unanswered questions in diverse fields such as high- energy physics, cosmology, and quantum informatics [1]. To understand these relaxation dynamics in closed quantum systems, the ideal model could be an impurity interacting with the quantum environment. In this work, we study these interaction dynamics by introducing a static impurity into a three-dimensional Bose-Einstein condensate composed of dipolar gases. To model this, we transformed the Hamiltonian of the system in the frame of impurity which leads to modified Gross- Pitavskii equation (GPE) [2]. We solve the modified GPE using both analytical techniques and numerical solutions via the split-step Crank-Nicolson approach. Thereafter, we calculated various properties of impurity such as its self-energy, density distribution, and root mean square deviation. Further, we explore how an asymmetrically shaped impurity influences the density outcomes by altering its form. By varying the orientation of the impurity at different deformation ratios, we obtain density profiles at multiple angles. These profiles reveal intriguing, non-uniform shifts in response to the morphological changes in the impurity, highlighting its intricate interaction with the surrounding dipolar Bose-Einstein condensate.

References:

1. [1] T. Langen, R. Geiger, and J. Schmiedmayer, Ultracold Atoms out of Equilibrium, Annu. Rev. Condens. Matter Phys. 6, 201 (2015).
   
   [2] R. K. Kumar, L. E. Young-S., D. Vudragović, A. Balaž, P. Muruganandam, and S. K. Adhikari, Fortran and C Programs for the Time-Dependent Dipolar Gross-Pitaevskii Equation in an Anisotropic Trap, Comput. Phys. Commun. 195, 117 (2015).