Vortex-lattice in a uniform Bose-Einstein condensate in a box trap

Area of Science:

• Quantum physics
• Condensed matter physics
• Atomic physics

Background:

• Bose-Einstein condensates (BECs) are quantum states of matter formed by cooling bosons to near absolute zero.
• Rapid rotation of BECs leads to the formation of quantized vortices.
• Understanding vortex lattice formation is crucial for quantum fluid dynamics.

Purpose of the Study:

• To numerically investigate vortex-lattice formation in rapidly rotating quasi-two-dimensional Bose-Einstein condensates (BECs) within square and circular box traps.
• To compare vortex arrangements in different trap geometries and with theoretical predictions.
• To analyze the dynamical stability of the formed vortex lattices.

Main Methods:

• Numerical simulation using the Gross-Pitaevskii (GP) equation in a rotating frame.
• Imaginary-time propagation to find stationary vortex lattice states.
• Real-time propagation to assess dynamical stability under changes in rotation frequency.

Main Results:

• In square traps, perfect square vortex lattices form when the vortex number is an integer squared; arbitrary numbers cause central deviations.
• In circular traps, vortices arrange in concentric orbits—polygonal near the center and circular near the periphery.
• The number of vortices in both trap types qualitatively agrees with Feynman's universal estimate.

Conclusions:

• The geometry of the trap significantly influences the arrangement of vortices in a rotating BEC.
• The simulated vortex lattices are dynamically stable against small perturbations in rotation frequency.
• Numerical solutions of the GP equation accurately predict vortex lattice formation and stability in confined BECs.