Rotating curved spacetime signatures from a giant quantum vortex

The study aims to realize and probe rotating curved spacetime analogues—such as those associated with Kerr black holes—using a superfluid helium-4 (He II) draining vortex with negligible viscosity. Prior analogue gravity experiments have demonstrated horizon physics (Hawking radiation) in one-dimensional supersonic flows; however, phenomena unique to rotation (for example, Penrose superradiance and black hole ringdown) require two-dimensional rotating geometries. The central research questions are whether a stationary, giant (multiply quantized) quantum vortex can be stabilized in He II and whether its flow can be minimally invasively characterized via interface waves to reveal curved-spacetime signatures like bound states and ringdown. The work is motivated by the need for irrotational, centrally confined vortex flows to emulate effective acoustic metrics, and by the challenge that alike-oriented quantized vortices tend to separate, complicating stabilization of a large, multiply quantized core.

Analogue gravity has established that excitations in fluids can mimic fields on curved spacetimes, enabling studies of Hawking radiation and related effects in classical and quantum media. One-dimensional analogue black holes have yielded stimulated and quantum Hawking signals in water tanks and Bose–Einstein condensates. More complex rotational effects, including superradiance and quasinormal mode oscillations (ringdown), have been demonstrated in classical vortex flows. Multiply quantized vortices are typically dynamically unstable and decay into singly quantized clusters; stabilization strategies in polariton condensates have used draining flows and central density depletion, reaching topological charges up to about 100. In superfluid helium, prior experiments measured macroscopic circulation in suction vortices, second-sound attenuation and vortex line density, but lacked spatial resolution to confirm central confinement or required invasive tracer particles that perturb vortex dynamics. Numerical models capture vortex-line motion coupled to normal and superfluid components but generally do not include dynamic free interfaces, limiting applicability to the present system.

Experimental platform: A cylindrical, optically accessible He II apparatus based on a stationary suction vortex is driven by a spinning propeller that establishes a continuous recirculation loop feeding a central drain. Experiments are conducted at 1.95 K, where the effective kinematic viscosity is ~100 times lower than water and damping is dominated by the viscous normal component comprising roughly half the density. A purpose-built flow conditioner minimizes injected solid-body rotation, promoting formation of a centrally confined vortex cluster. Depending on propeller frequency, two regimes are observed: (i) a solid-core regime at low drive, with a finite depression and parabolic free surface consistent with a compact, polarized cluster of singly quantized vortices; (ii) a hollow-core regime at higher drive, with an open core extending from the surface to the drain, behaving effectively as a multiply quantized object. Measurement technique: To avoid invasive tracers, the team employs adapted Fourier transform profilometry (synthetic Schlieren) to reconstruct free-surface height fluctuations with ~1 µm sensitivity. Waves on the interface are analyzed using spatiotemporal Fourier transforms exploiting cylindrical symmetry, yielding modes labeled by frequency f and azimuthal number m (positive for co-rotating, negative for counter-rotating). Theory and inversion: Interface excitations obey a Doppler-shifted dispersion relation (ω − v·k)^2 = F(|k|), with F the dispersion function. For each radius, solving the dispersion relation identifies a minimum frequency f_min permitting propagation for given m and local background velocity v(r) = (v_r, v_θ). The observed spectral cutoff (absence of excitations below f_min) is used to infer v by scanning (v_r, v_θ) to best match f_min across several m. This is repeated radially to reconstruct v_θ(r) and v_r(r). The reconstructed v_θ is fitted to v_θ(r) = Ω r + C/r, separating solid-body rotation Ω from irrotational circulation C. The number of circulation quanta confined in the core is N_c = 2π C / κ, with κ ≈ 10^−7 m^2 s^−1. Wave dynamics and effective potential: Radial profiles of spectral amplitude for selected azimuthal modes (notably |m| = 8) are examined. The f_min curve acts as an effective potential barrier for wave propagation. With the outer boundary at r = 37.3 mm, this yields bound (standing) states for co-rotating modes where the barrier reflects waves. A simplified vortex model with v = (0, C/r) extends the experimentally accessible potential inward to estimate core dimensions and compare bound-state frequencies with theoretical predictions. Counter-rotating modes probe shallow potential maxima associated with analogue black hole ringdown. Data analysis includes averaging v_θ over 2.5-mm radial bins and comparing Ω to the drive frequency to quantify leakage of rotation.

1. Stabilization of a stationary giant quantum vortex in He II: Both solid-core (compact cluster) and hollow-core (multiply quantized) regimes were realized. The reconstructed azimuthal velocity profiles are well described by v_θ(r) = Ω r + C/r, with v_r ≈ 0 within resolution.
2. Dominance of irrotational flow: The ratio Ω/Ω_drive is below 2.5% across all configurations, indicating minimal solid-body rotation leakage; the velocity field is dominated by the irrotational vortex term C/r.
3. Record circulation quanta: The inferred topological charge corresponds to N_c on the order of 10^6 circulation quanta, far exceeding prior quantum-fluid realisations. In the solid-core regime N_c approximates the number of concentrated singly quantized vortices; in the hollow-core regime it represents the core’s topological charge. The core radius is constrained to ≈4 mm (solid-core) and ≈6 mm (hollow-core).
4. Minimally invasive velocimetry: By matching spectral cutoffs f_min from interface-wave spectra to theory, the background velocity distribution was reconstructed without seeding particles.
5. Bound states (standing waves): Co-rotating m = 8 modes exhibit distinct radial standing-wave patterns up to ~40 Hz, bounded by the outer wall and the effective potential barrier; bound-state frequencies show excellent agreement with predictions from the extended potential model.
6. Ringdown signatures: In counter-rotating m = −8 waves for the hollow-core regime, no bound states occur. Instead, dominant excitations cluster near a shallow potential maximum (~8.25 Hz), consistent with analogue black hole ringdown modes. The radius where the potential crosses zero frequency relates to an analogue ergoregion.
7. Quantum-to-classical transition: Achieving circulation far above κ (by ~10^4–10^6) allows circulation quantization to be effectively neglected at macroscopic scales, realizing a quantum-to-classical vortex-flow transition.

The findings directly address the core goals of realizing rotating curved-spacetime analogues in a quantum fluid and diagnosing them minimally invasively. Stabilizing a giant vortex with centrally confined rotation provides the irrotational velocity profile required for effective acoustic metrics. The observed bound states validate the effective potential framework and enable precise characterization of the flow geometry. The counter-rotating wave dynamics in the hollow-core regime reveal ringdown-like excitations, marking the first indications of analogue black hole ringdown in a quantum liquid and bridging classical-fluid analogue gravity experiments with quantum-fluid systems. The minimal solid-body rotation leakage (Ω/Ω_drive < 2.5%) confirms that the measured signatures predominantly arise from the desired irrotational flow. The excellent agreement between observed bound-state spectra and the extended C/r model supports extrapolations that constrain core size beyond direct optical access. These results underscore He II’s advantages as a finite-temperature, non-equilibrium quantum field theory simulator: tunable dissipation via temperature, macroscopic system sizes enabling large winding numbers, and the ability to explore regimes complementary to cold-atom and polariton platforms. Mutual friction with the normal component likely aids stabilization of dense vortex clusters, consistent with recent theoretical work. The prospects include direct observation of ergoregions and superradiance, and controlled studies of ringdown, with modest adjustments to drive speed and/or geometry.

The work demonstrates a stationary giant quantum vortex in superfluid 4He and introduces a minimally invasive wave-based method to reconstruct the underlying velocity field. The flow is dominated by an irrotational C/r profile with negligible radial component, and supports co-rotating bound states and counter-rotating ringdown-like excitations, providing rotating curved-spacetime signatures in a quantum liquid. Achieving effective circulation of order 10^6 quanta realizes a quantum-to-classical vortex transition at macroscopic scale. These advances position He II as a versatile simulator for finite-temperature quantum field theory in rotating curved spacetimes. Future directions include: direct observation of ergoregions and Penrose superradiance; systematic excitation and characterization of analogue black hole ringdown; enhanced spatial resolution nearer the core to map individual vortex distributions; refined models coupling vortex-line dynamics with a dynamic free surface; exploration across temperatures (including below 1 K) to tune dissipation; and time-dependent protocols (e.g., modulating first/second sound) to study non-equilibrium field dynamics and wave turbulence.

The spatial distribution and dynamics of individual vortex lines within the core are not resolved; current numerical models lack dynamic free-surface coupling relevant to this system. The inversion assumes near-equality of normal and superfluid velocities, justified by suppressed rotation but not directly verified throughout. Mechanical vibrations imprint signatures (notably m = ±1) in spectra and may contribute to stochastic wave driving. The effective potential model (v = C/r) must break down near the core, and inferences about core size rely on extrapolation. The accessible radial range excludes the innermost core, limiting direct observation of ergoregions at present; higher azimuthal velocities or closer probing are required. High-frequency dispersion limits the strict applicability of the acoustic metric description. Residual solid-body rotation, though small, is nonzero. Results pertain to 1.95 K and may vary with temperature-dependent mutual friction and normal-fluid fraction.