Properties of Dipolar Impurities in a Dipolar Medium

Relaxation dynamics in closed quantum systems are responsible for some of the most difficult issues in many-body physics. Understanding these dynamics is crucial for quantum statistical physics, but it is also an open question in many other disciplines, such as cosmology, quantum information, and high-energy physics [1]. An ideal model to answer those problems is an impurity interacting with a quantum environment. A dipole with at least one different property from the medium, such as a distinct hyperfine state, mass, or dipole moment, would be referred to as a dipolar polaron. All the dipole moments are aligned along the z-axis by an external field. The polaron-dipolar gas system could exhibit attractive and repulsive interactions depending on the direction as the dipole-dipole interaction is anisotropic and long-range. As a result, we have investigated and calculated the many characteristics of this impurity in both two (2D) and three (3D) dimensional environments. For this purpose, we used the split-step Crank-Nicolson method to solve the modified Gross-Pitaevskii (GP) equation. In 2D, the calculation has been carried out for two geometries: when the plane is perpendicular and when the plane is parallel to the polarization direction. The properties like self-energy and density of the impurity are calculated in the thermodynamic limit for different numbers of particles and impurity strengths for the stationary states. Additionally, these results are calculated for different angles, i.e., the angle between the system’s dipoles and the dipolar polaron impurity. We also determined the impurity-impurity interaction energy as a function of impurity strengths by adding another impurity to the system. The GP equation incorporating temporal dynamics was then solved in three dimensions using one impurity. We deduced from the results that the system exhibits anisotropic response in quench dynamics after the addition of the impurity.

References:

[1] T. Langen, R. Geiger, and J. Schmiedmayer, Ultracold Atoms out of Equilibrium, Annu. Rev. Condens. Matter Phys. 6, 201 (2015).