Critical speed of a binary superfuid of light

We theoretically study the critical speed for superfluid flow of a two-dimensional (2D) binary superfluid of light past a polarization-sensitive optical obstacle. This speed corresponds to the maximum mean flow velocity below which dissipation is absent. In the weak-obstacle regime, linear-response theory shows that the critical speed is set by Landau’s criterion applied to the density and spin Bogoliubov modes, whose relative ordering can be inverted due to saturation of the optical nonlinearity. For obstacles of arbitrary strength and large spatial extent, we determine the critical speed from the conditions for strong ellipticity of the stationary hydrodynamic equations within the hydraulic and incompressible approximations. Numerical simulations in this regime reveal that the breakdown of superfluidity is initiated by the nucleation of vortex-antivortex pairs for an impenetrable obstacle, and of Jones-Roberts soliton-type structures for a penetrable obstacle. Beyond superfluids of light, our results provide a general framework for the critical speed of 2D binary nonlinear Schrödinger superflows, including Bose-Bose quantum mixtures.

💡 Research Summary

The manuscript presents a comprehensive theoretical investigation of the critical velocity for superfluid flow of a two‑dimensional binary fluid of light past a polarization‑sensitive optical obstacle. The authors first map the paraxial propagation of a monochromatic laser with left‑ and right‑circular polarization components onto a pair of coupled nonlinear Schrödinger equations (NLSE), which are the optical analogue of the two‑component Gross‑Pitaevskii equations describing a Bose‑Bose mixture. By introducing total density, relative (spin) density, center‑of‑mass velocity, and spin velocity fields, the NLSE are recast into a set of hydrodynamic continuity and Bernoulli‑type equations.

In the weak‑obstacle regime (potential amplitude much smaller than the interaction energy μ₀), the authors linearize the hydrodynamic equations around a uniform flow of speed V₀. The resulting linear system yields two Bogoliubov branches: a density (phonon) mode with sound speed c_d and a spin (polarization) mode with sound speed c_s. Applying Landau’s criterion, superfluidity persists as long as V₀ is below the smaller of these two speeds. Crucially, the inclusion of a saturable optical nonlinearity (parameter β) can invert the ordering of c_d and c_s: in the saturated regime (β≫1) the spin sound speed becomes lower than the density sound speed, reversing the usual expectation that the spin channel destabilizes first. This inversion reproduces recent experimental observations of anomalous sound‑speed ordering in binary fluids of light.

For obstacles of arbitrary strength and large spatial extent (radius w much larger than the healing length ξ), the authors go beyond perturbation theory. Assuming the flow is incompressible (∇·V≈0) and using a hydraulic approximation, they derive stationary equations that can be written as a second‑order elliptic partial differential equation for the velocity potential. The condition of strong ellipticity of the coefficient matrix guarantees the existence of a stationary solution; violation of this condition defines the critical velocity V_c. The resulting expression for V_c depends on the total obstacle potential U, the relative (spin‑dependent) potential u, and the interaction parameters α (relative inter‑component coupling) and β (saturation). The analysis shows that a non‑zero u directly excites the spin channel, potentially lowering V_c even when the total potential is modest.

Numerical simulations of the full time‑dependent NLSE confirm the analytical predictions. When V₀ exceeds V_c for an impenetrable obstacle (U≫μ₀), vortex–antivortex pairs are nucleated in both polarization components, leading to a cascade of vortical excitations. For a penetrable obstacle (U comparable to μ₀), the breakdown manifests as the emission of Jones‑Roberts soliton‑like structures that locally suppress the flow in both components. These defect types are the 2D analogues of those known in single‑component superfluids, but their coexistence and coupling are unique to the binary system.

The paper concludes by emphasizing the generality of the framework. Because the governing equations are identical to those of a two‑component Bose‑Einstein condensate, the derived critical‑velocity criteria apply equally to atomic mixtures, with the saturation parameter β corresponding to tunable interaction strengths (e.g., via Feshbach resonances). Moreover, the ability to engineer polarization‑dependent obstacles optically provides a versatile platform for probing spin‑superfluid dynamics at room temperature, opening avenues for cross‑disciplinary studies between nonlinear optics and ultracold‑atom physics.