Study of the Interaction of Static Impurity within a Dipolar Environment*

Information on the relaxation dynamics in quantum systems is essential to understand many-body systems. These dynamics are not only necessary for quantum mechanics but also important to understand several open questions in areas like high-energy physics, cosmology, and quantum data processing [1]. In the present work, we explore these dynamics using a static impurity in a quantum environment as our model. We delve into this by placing a static impurity in a three-dimensional Bose-Einstein Condensate made of dipolar gases. The Hamiltonian of the system was transformed in the frame of impurity, which led to a modified Gross-Pitavskii equation (GPE) [2]. This modified GPE was then solved using both analytical methods and numerical solutions through the split-step Crank-Nicolson method. We then calculated different properties of the static impurity, including its self-energy and density distribution. Additionally, we examined the effects of anisotropic impurities on density results by deforming the impurity. Further, by changing the orientation of the impurity at different deformations, we observed the density profile at several angles, revealing unique shifts due to the impurity's shape changes, emphasizing its complex interaction with the surrounding condensate.

References:

[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).