A supersolid simultaneously breaks U(1) gauge symmetry (superfluidity) and translational symmetry (crystal order). The stripe phase emerges in spin-orbit coupled BECs: ψ(x) = A cos(k₀x)e^{iφ} — both a superfluid and a density wave coexist.
λ = 40
δ = 0
g↑↓/g = 0.80
T = 10
Superfluid (plane wave)
Supersolid (stripe)
Normal fluid
Mott insulator
Stripe phase: ψ ≈ (ψ₊e^{ik₀x} + ψ₋e^{-ik₀x}) · e^{iφ(t)}
U(1) broken → superfluid; translational sym broken → crystal order
Coexistence is the hallmark of supersolidity