BEC Vortex Lattice in a Rotating Trap

What you are seeing: a 2D Bose-Einstein condensate in a harmonic trap, rotated at $\Omega / \omega_{\rm trap}$ . The cyan-magenta cloud is the Thomas-Fermi density; the black holes are singly-quantized vortices on an Abrikosov triangular lattice. Each vortex carries one quantum of circulation $h/m$ . Vortex area density is $n_v = m \Omega / (\pi \hbar)$

Figure 1. 2D BEC in a rotating harmonic trap. Density profile is Thomas-Fermi; phase is encoded as hue rings around each quantized vortex; cores form a triangular Abrikosov lattice. Method: kinematic Gross-Pitaevskii ansatz, density n_TF * Prod tanh^2(|r-r_v|/xi).

Omega / omega_trap0.78

interaction (N a_s / a_ho)2500

phase overlay0.50

resolution220

WHAT TO TRY

Spin the trap faster (Omega/omega_trap toward 1): the condensate cannot rotate as a rigid body, so it threads itself with quantized vortices that arrange into a triangular Abrikosov lattice. The vortex count climbs.
Raise the interaction strength: the Thomas-Fermi cloud swells (R_TF grows) and the healing length xi shrinks, setting the vortex core size. Stronger repulsion means a bigger, flatter condensate.
Toggle the phase overlay: each vortex is a 2-pi winding of the condensate phase, the topological defect that carries the angular momentum L_z in fixed quanta of h-bar.