An exciton-polariton is a hybrid light–matter quasiparticle formed when a cavity photon and a semiconductor exciton couple strongly enough in a microcavity that they periodically exchange energy faster than either decays (vacuum Rabi splitting), producing new "lower polariton" eigenstates. Because the photonic component gives it a tiny effective mass (~10⁻⁴ of a free electron), a gas of polaritons can reach quantum degeneracy — condense into a single macroscopic wavefunction ψ(r,t) — at temperatures far above what atomic Bose-Einstein condensates need.
Polaritons constantly leak out of the cavity as photons, so the condensate must be continuously replenished: it is a driven-dissipative condensate, governed by a generalized Gross-Pitaevskii equation. This simulation coherently pumps the fluid at a fixed flow wavevector k (in a frame co-moving with the pump), so a uniform polariton fluid streams past a static defect:
iħ ∂ψ/∂t = [ -ħ²/2m* ∇² + g|ψ|² + V(r) - iħγ/2 ]ψ + F₀e^(ikx)
m* = polariton effective mass g = polariton-polariton interaction
V(r) = obstacle potential γ = photon escape (decay) rate
The key result is the Landau criterion for superfluidity. A weakly-interacting quantum fluid supports sound-like (Bogoliubov) excitations with speed c_s = √(g·n₀/m*), set by the local density n₀. When the flow speed v is below c_s, the obstacle cannot radiate excitations — the fluid glides past it with no drag and no wake, exactly like a superfluid. Push v above c_s and the flow becomes energetically able to shed excitations: a turbulent wake of quantized vortex–antivortex pairs nucleates downstream of the defect, visible here as small dark cores with a full 2π phase wind (colored dots).
- Flow velocity v — the pump wavevector k = v/ħ (with ħ=m*=1 here); raising it pushes the Mach number M = v/c_s past 1.
- Interaction strength g — sets the Bogoliubov sound speed c_s = √(g·n₀); stronger interactions make the fluid harder to disturb.
- Obstacle potential V₀ — how strongly the defect scatters the flow; a taller obstacle nucleates vortices at a lower Mach number.
- Pump amplitude F₀ — sets the steady-state condensate density n₀, which also sets c_s.
This exact superfluid-to-turbulent transition around a defect was observed experimentally in GaAs microcavities by Amo et al. (Nature Physics, 2009), and polariton condensates are now studied as room-temperature-capable quantum fluids of light for simulating quantum hydrodynamics on a chip.