A parallel framework for the numerical simulation of Bose–Einstein condensates

Mary Ann Leung, William P. Reinhardt

Weizhu Bao, Hanquan Wang

Huang Zhao-Hui, Desheng Wang

We employ the parallel computing technology to study numerically the three-dimensional structure of quantized vortices of Bose–Einstein condensates. For anisotropic cases, the bending process of vortices is described in detail by the decrease of Gross–Pitaevskii energy. A completely straight vortex and the steady and symmetrical multiple-vortex configurations are obtained. We analyse the effect of initial conditions and angular velocity on the number and shape of vortices.

Abel Beregi, Jean-Baptiste Gérent, Nathan E. Lundblad

Bubble-shaped Bose-Einstein condensates (BECs) constitute a unique class of quantum fluids with a hollow, thin-shell geometry that supports a wide variety of phenomena distinct from those of compact condensates. Numerical simulation of such systems is particularly challenging due to their inherently three-dimensional structure and extreme aspect ratios. We present an efficient finite-difference simulation framework for solving partial differential equations in nontrivial topologies, with a focus on the static and dynamical modeling of bubble-shaped BECs. By employing selective spatial sampling on a semistructured grid, our method substantially reduces memory usage and achieves more than an order-of-magnitude improvement in computational performance compared with conventional split-step Fourier solvers. The algorithm is naturally extendable to highly parallel execution on graphics processing units (GPUs), enabling large-scale, time-dependent simulations of thin-shell condensates. We apply this framework to simulate the formation of bubble BECs through a controlled hollowing-out protocol using trapping potentials relevant to the Cold Atom Laboratory aboard the International Space Station. From these simulations, we identify characteristic timescales and parameter ramps required to achieve adiabatic evolution, thereby assessing the feasibility of experimentally realizing bubble-shaped condensates in microgravity environments.

Weizhu Bao, Yongyong Cai, Hanquan Wang

Stephen U. S. Choi, Vladimir Chernyak, Shaul Mukamel

Using the Liouville space framework developed in nonlinear optics, we calculate the linear response functions and susceptibilities of Bose-Einstein condensates (BEC) subject to an arbitrary mechanical force. Distinct signatures of the dynamics of finite-temperature BEC are obtained by solving the Hartree-Fock-Bogoliubov theory. Numerical simulations of the position-dependent linear response functions of one-dimensional trapped BEC in the time and the frequency domains are presented.