Properties of Dipolar Impurities in a Dipolar Medium

Some of the most challenging problems in many-body physics are due to relaxation dynamics in closed quantum systems. The understanding of these dynamics is not only important in quantum statistical physics but also an open problem in diverse fields including high-energy physics, quantum information, and cosmology [1]. An ideal model to answer those problems is an impurity interacting with a quantum environment. In this work, we study a dipolar polaron, an impurity in a Bose gas of trapped dipoles in an isotropic harmonic trap. The dipolar polaron would be a dipole with at least one different property than the medium, such as a different hyperfine state, mass, or dipole moment. An external field aligns the dipole moments along the z-axis. Since the dipole-dipole interaction is both anisotropic and long-range, the dipole-polaron system would have both attractive and repulsive interactions depending on direction. Thus, we have studied and calculated the various properties of this impurity in two-dimensional (2D) and three-dimensional (3D) spaces. For this purpose, we solved the modified Gross-Pitaevskii (GP) equation by employing the split-step Crank-Nicolson method]. 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. In addition, these results are calculated for different angles, i.e., the angle between the system’s dipoles and the dipolar polaron impurity. Further, by introducing another impurity into the system, we calculated the impurity-impurity interaction energy as a function of impurity strengths. Thereafter, in 3D, we solved the GP equation involving time dynamics with one impurity. We observed from the results that after introducing the impurity into the system it is showing anisotropic response in quench dynamics.



References:

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