Polariton Superfluid Velocity Field (2D)

Polariton Fluid Controls

Flow velocity v 1.00

Interaction strength g 0.40

Obstacle potential V₀ 6.0

Pump amplitude F₀ 1.60

Live State

warming up…

Background density n₀

–

Sound speed c_s

–

Mach number v/c_s

–

Vortex pairs

How it works

This is the 2D companion to the 3D height-field version of this simulation: the same driven-dissipative Gross-Pitaevskii equation, integrated completely independently, but read out in a genuinely 2D-native way — as a superfluid current (velocity) field rather than a rendered 3D density mesh. The condensate wavefunction ψ = u + iv is still evolved on a 2D grid,

iħ ∂ψ/∂t = [ -ħ²/2m* ∇² + g|ψ|² + V(r) - iħγ/2 ]ψ + F₀e^(ikx)

but instead of mapping density to a 3D mesh height, the local probability current is computed directly from the field, j = Im(ψ*∇ψ), and the superfluid velocity v_s = j/n is drawn as a live arrow (quiver) field on top of a density/phase colour map — the same quantity a real polariton-fluid experiment extracts from interferometric phase imaging. This sidesteps phase branch-cut issues that a naive phase-difference plot would hit near a vortex core.

The Landau criterion for superfluidity is the same as in the 3D version: Bogoliubov sound speed c_s = √(g·n₀) sets the threshold. Below it the arrows point smoothly around the obstacle with no wake — frictionless flow. Above it (Mach number v/c_s > ~1) the current field visibly tears into a turbulent wake, and small closed circulation loops appear in the arrows exactly where the phase-winding detector finds a quantized vortex (± marker, full 2π phase wind around the core).

Flow velocity v — pump wavevector k = v/ħ (ħ=m*=1 here); raising it pushes Mach number M = v/c_s past 1.
Interaction strength g — sets c_s = √(g·n₀); stronger interactions make the fluid stiffer.
Obstacle potential V₀ — defect scattering strength; taller obstacles nucleate vortices at lower Mach number.
Pump amplitude F₀ — sets the steady background density n₀ (and hence c_s) via the driven-dissipative balance g²n₀³ + (γ/2)²n₀ = F₀².

This superfluid-to-turbulent transition around a defect was observed experimentally in GaAs microcavities by Amo et al. (Nature Physics, 2009).

Color = phase, brightness = density Arrows = superfluid velocity v_s Grey disc = obstacle / markers = ± vortex cores