Excitations of dipolar Bose-Einstein condensates

Abstract

In the present project we wish to investigate the excitations in dipolar Bose-Einstein condensates (BECs). In dipolar BECs, the atomic interaction has a long-range dipolar counterpart in addition to the usual contact interaction. The resulting Gross-Pitaevskii (GP) equation in this case is a partial integro-differential equation and special algorithms are required for its numerical solution. We develop a numerical program for solving three-dimensional GP equation for dipolar BECs. We use split-step Crank-Nicolson scheme for the nondipolar part and the dipolar term is treated by Fourier transformation in x,y and z variables. We also develop the numerical program for quasi-one- and quasi-two- dimensions appropriate for a cigar- and disk-shaped dipolar BEC under tight radial and axial trapping, respectively. In all cases, the dipoles are assumed to be polarized along the axial z- direction. By solving the GP equation, we propose to analyse the superfluid properties of the single and multi-component dipolar BECs. An interesting property of Bose-Einstein condensates is the creation of quantized vortices due to excitation. No attempt has been made so far to explore the influence of dipolar interaction on three-dimensional simulations on vortex structures and its phase transition. During the formation of vortices the condensate undergoes a shape deformation, strongly turbulent stage, ripple formation and the penetrating vortex lines. The full 3D simulations reveal these unknown dynamical features of the vortex nucleation process. Moreover, we aim to observe the vortex structure phase transition due to anisotropic effect of dipolar BECs. To analyse the stable vortex structures, we solve the 3D dipolar GP equation with angular momentum term using imaginary-time propagation. Then the stability of the vortex structure investigate by evolving it in real-time propagation. The vortex lattice structures may exhibits a rich variety of structures depending on the dipolar strength. Already we have noticed such phase transitions in the vortex structures due to the dipolar strengths and witnessed a regular pentagon structure with one vortex at center in chromium, square and triangular vortex lattice structures with slight distortion in erbium and dysprosium condensates, respectively. Dipolar BECs in annular trap has investigated by Karabulut et al., Their studies are based on quasi two-dimensional model and correspondingly they have considered the radially quartic potential. Motivated by this progress on the study of rotational properties of dipolar BECs in quartic potential, we wish to analyse the vortex formation and structure using full three-dimensional model. Moreover we aim to consider the quartic traps along the axial- and radial- directions independently. In further we plan to calculate the critical rotation frequency in this set-up with respect to dipolar strengths. The full three dimensional simulations may disclose the dynamical features on the vortex nucleation and bending of vortex core. By using the quasi two-dimensional model for dipolar BECs, we desire to exploit the nucleation of vortices indouble well potential. We anticipate the diverse vortex dynamics and critical rotation frequency. Also, we study the vortex nucleation in the two-component mixture of dipolar and non-dipolar BECs. This study disclose the effect of long range interaction on vortices more distinctly. The observation of vortex dipoles in two-component mixture will be more supportive to investigate the interface effects during thepenetration of vortex dipoles between the mixture of dipolar and non-dipolar BECs. In further, also we wish to observe the dispersive shock waves in dipolar BECs. Apart from the above, we further plan to analyse the collapse dynamics oftwo-component dipolar BECs by numerically solving the GP equation in three-dimensions with the inclusion of three body loss.