Critical Speed of Binary Superfluid of Light Achieves 2D Dissipation Limit

Researchers have long sought to understand the limits of dissipationless flow in superfluids, and a new study published this week delves into this phenomenon within binary superfluids of light. Pierre-Élie Larré (Université Paris-Saclay, CNRS, LPTMS), Claire Michel (Université Cote d’Azur, CNRS, INPHYNI) and Nicolas Cherroret (Laboratoire Kastler Brossel, Sorbonne Université, CNRS, ENS-PSL Research University, Collège de France) et al demonstrate a theoretical framework for determining the ‘critical speed’ , the maximum velocity at which this flow remains without energy loss , when a binary superfluid of light encounters an optical obstacle. This research is significant because it not only clarifies the interplay between density, spin modes and optical nonlinearity in defining this critical speed, but also offers a broadly applicable model for understanding superfluidity in diverse two-dimensional nonlinear systems, such as Bose-Bose mixtures, extending beyond the realm of photonics.

Critical Speed for Light Superfluid Obstacle Flow

Scientists have theoretically determined the critical speed for superfluid flow of a two-dimensional binary superfluid of light encountering a polarization-sensitive optical obstacle, representing a significant advance in understanding dissipationless flow. This critical speed defines the maximum flow velocity below which the superfluid exhibits no energy loss, a fundamental property of these quantum systems. The research team employed a combination of linear-response theory and analysis of stationary hydrodynamic equations to establish this speed, meticulously accounting for optical nonlinearity and obstacle strength. Their approach reveals a surprising.

This saturation effect fundamentally alters the expected behaviour, potentially allowing dissipationless flow to occur under conditions previously thought impossible. For obstacles of arbitrary strength and large spatial extent, the researchers determined the critical speed by examining the conditions for strong ellipticity within the hydraulic and incompressible approximations, providing a robust method for predicting superfluid breakdown. Numerical simulations then unveiled that the breakdown of superfluidity initiates with the nucleation of vortex-antivortex pairs when encountering an impenetrable obstacle, and Jones-Roberts soliton-type structures for a penetrable one. This breakthrough extends beyond superfluids of light, offering a general framework applicable to two-dimensional binary nonlinear Schrödinger superflows, including Bose-Bose mixtures, broadening the impact of this work across multiple areas of physics.

The team achieved a comprehensive understanding of the critical speed by meticulously analysing the hydrodynamic equations governing the binary superfluid, focusing on the interplay between total and relative densities and velocities. By exploring a wide range of obstacle parameters, the study establishes a detailed picture of how these structures influence superfluid flow and trigger dissipation, providing valuable insights into the fundamental mechanisms at play. Experiments show that the observed optical saturation effects, previously reported in a recent study, are fully accounted for within the analysis, while the weak-saturation regime also applies to Bose-Bose superfluid mixtures realised with ultracold atoms. The research establishes a clear connection between the obstacle’s characteristics and the resulting fluid excitations just above the critical speed, offering a pathway for controlling and manipulating superfluid flows. This work opens exciting possibilities for designing novel optical devices and exploring quantum phenomena in a variety of condensed matter systems, promising further advancements in the field of superfluidity and beyond.

Critical Speed and Dissipation in Binary Superfluids reveal

Scientists investigated the critical speed governing superfluid flow of a two-dimensional binary superfluid of light interacting with a polarization-sensitive optical obstacle. The research focused on identifying the maximum mean flow velocity at which dissipation ceases, a crucial parameter defining superfluidity. To determine this critical speed, the study employed a theoretical framework combining linear-response theory and hydrodynamic equations within hydraulic and incompressible approximations. Initially, in the weak-obstacle regime, researchers applied Landau’s criterion to both density and spin Bogoliubov modes, noting an intriguing inversion of their relative ordering due to saturation of optical nonlinearity.

For obstacles exhibiting arbitrary strength and substantial spatial extent, the team determined the critical speed by analysing the conditions for strong ellipticity within the stationary hydrodynamic equations. Numerical experiments were then conducted to reveal the mechanisms initiating superfluid breakdown: vortex-antivortex pair nucleation for impenetrable obstacles and Jones-Roberts soliton-type structures for penetrable ones. This innovative approach involved solving the continuity equation nonperturbatively using a hodograph transform, allowing for classification of the equations as elliptic and confirming monotonic flow far from the obstacle, a hallmark of superfluid behaviour. The study pioneered a method analysing the hydrodynamic equations in the immediate vicinity of points where energetic instabilities arise, specifically at the obstacle’s poles or within the obstacle itself.

By simplifying the continuity equations under the incompressible approximation, scientists established that the local velocities align approximately with the x-axis, enabling a rewriting of spatial derivatives of density and spin in terms of velocity derivatives. This led to a matrix equation describing the velocity potentials, from which the characteristic curves of the continuity equation were derived and analysed for ellipticity. Researchers obtained the equation for characteristic curves, Adx⁴ + Bdx²dy² + Cdy⁴ = 0, and subsequently solved for characteristic velocities, establishing conditions for strong ellipticity, B 0, C 0, and B² − 4AC 0, which are equivalent to a local-density generalization of the Landau criterion. By assuming incompressible flow and piecewise-constant densities, the team simplified the Bernoulli equations and continuity equations, ultimately linking these local conditions to a single constraint on the incident velocity, thereby defining the critical speed for superfluidity. This work extends beyond superfluids of light, offering a general framework applicable to 2D binary nonlinear Schrödinger superflows, including Bose-Bose mixtures.

Critical Speed and Mode Ordering in Light Superfluidity

Scientists have theoretically determined the critical speed for superfluid flow of a two-dimensional binary superfluid of light interacting with a polarization-sensitive optical obstacle. The research establishes this speed as the maximum mean flow velocity below which dissipation is entirely absent, a crucial parameter for understanding superfluid behaviour. Experiments revealed that in the weak-obstacle regime, linear-response theory dictates the critical speed is governed by Landau’s criterion, applied specifically to the density and spin Bogoliubov modes. Notably, the relative ordering of these modes can be inverted due to saturation of the optical nonlinearity, a surprising finding with significant implications for superfluidity.

The team measured the critical speed by analysing conditions for strong ellipticity within the stationary hydrodynamic equations, utilising hydraulic and incompressible approximations for obstacles of arbitrary strength and large spatial extent. Numerical simulations demonstrated that the breakdown of superfluidity initiates with the nucleation of vortex-antivortex pairs when encountering an impenetrable obstacle. Conversely, for penetrable obstacles, tests prove the formation of Jones-Roberts soliton-type structures marks the onset of dissipation. These results demonstrate a clear link between obstacle properties and the specific mechanisms triggering superfluid breakdown.

Data shows that the research extends beyond superfluids of light, providing a general framework applicable to 2D binary nonlinear Schrödinger superflows, including Bose-Bose mixtures. Scientists achieved a comprehensive understanding of the critical speed by meticulously examining the hydrodynamic equations governing the binary superfluid, focusing on total and relative densities and velocities. The study thoroughly investigates the critical speed below which the system exhibits superfluid flow, also providing a qualitative overview of the obstacle-induced fluid excitations immediately above this threshold. Measurements confirm that the analysis accounts for optical saturation effects, while in the weak-saturation regime, it also applies to Bose-Bose superfluid mixtures realised with ultracold atoms. The breakthrough delivers a robust methodology for determining the critical speed based on Landau’s criterion, applied to the density and spin Bogoliubov modes. This work establishes a foundation for future.