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arXiv:2607.08345

Rotation Sensing via Josephson-frequency Splitting in a Toroidal Superfluid

Giulio Nesti, Luca Pezzè

Published Jul 9, 2026• 0 citations
arXivHTMLPDF

Abstract

We show that a toroidal superfluid interrupted by $n$ tunneling barriers realizes a compact Josephson gyroscope with an $n$-enhanced response to rotation. In the small-amplitude regime, we derive analytically the normal mode spectrum of the coupled population-phase oscillations. In the absence of rotation, pairs of modes are degenerate: a finite angular velocity $Ω$ lifts this degeneracy through a Doppler shift, producing a frequency splitting that grows linearly with both $Ω$ and $n$. Full numerical simulations confirm this prediction and reveal long-lived two-frequency beatings, in sharp contrast with the monochromatic Josephson oscillations of the nonrotating system. These beatings provide a direct rotation signal with estimation uncertainty scaling as $ΔΩ\sim n^{-3/2}$, while remaining robust against imperfections and dynamical excitations. These results identify multi-junction toroidal superfluids as scalable, micrometer-size rotation sensors compatible with current experimental platforms.

DOI
10.48550/arxiv.2607.08345

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We show that a toroidal superfluid interrupted by nnn tunneling barriers realizes a compact Josephson gyroscope with an nnn-enhanced response to rotation. In the small-amplitude regime, we derive analytically the normal mode spectrum of the coupled population-phase oscillations. In the absence of rotation, pairs of modes are degenerate: a finite angular velocity ΩΩΩ lifts this degeneracy through a Doppler shift, producing a frequency splitting that grows linearly with both ΩΩΩ and nnn. Full numerical simulations confirm this prediction and reveal long-lived two-frequency beatings, in sharp contrast with the monochromatic Josephson oscillations of the nonrotating system. These beatings provide a direct rotation signal with estimation uncertainty scaling as ΔΩ∼n−3/2ΔΩ\sim n^{-3/2}ΔΩ∼n−3/2, while remaining robust against imperfections and dynamical excitations. These results identify multi-junction toroidal superfluids as scalable, micrometer-size rotation sensors compatible with current experimental platforms.
We study Josephson dynamics in a long atomic Bose-Josephson junction formed by two tunnel-coupled coplanar Bose-Einstein-condensate rings. An in-plane linear acceleration breaks the axial symmetry of the trap and transforms a single Josephson plasma oscillation into a multimode population-imbalance response. Gross-Pitaevskii simulations and Bogoliubov-de Gennes analysis show that the additional spectral components arise from collective modes that acquire finite overlap with the population-imbalance operator under symmetry breaking, with their activation governed by reflection symmetry about the acceleration direction. We also propose a mode-resolved Josephson-spectroscopy protocol based on a weak localized periodic perturbation. Frequency scans reveal resonant amplitude peaks and phase shifts at the eigenfrequencies of active Bogoliubov modes, while angular scans of the drive position provide access to the angular structure of the corresponding mode density perturbations. A dissipative time-dependent Bogoliubov theory yields analytical response functions in quantitative agreement with full Gross-Pitaevskii simulations in the linear regime. Our results demonstrate that accelerated dual-ring condensates provide a controllable platform for symmetry-selected Josephson dynamics and spectroscopic probing of collective modes.
Precise control of topologically protected excitations, such as quantum vortices in atomtronic circuits, opens new possibilities for future quantum technologies. We theoretically investigate the dynamics of Josephson vortices (rotational fluxons) induced by coupled persistent currents in a system of coplanar double-ring atomic Bose-Einstein condensates. We study the Josephson effect in an atomic Josephson junction formed by coaxial ring-shaped condensates. Tunneling superflows, initiated by an imbalance in atomic populations between the rings, are significantly influenced by the persistent currents in the inner and outer rings. This results in pronounced Josephson oscillations in the population imbalance for both corotating and nonrotating states. If a linear acceleration is applied to the system, our analysis reveals peculiar azimuthal tunneling patterns and dynamics of Josephson vortices which leads to nonzero net tunneling current and shows sensitivity to the acceleration magnitude. When multiple Josephson vortices are present, asymmetric vortex displacements that correlate with both the magnitude and direction of acceleration can be measured, offering the potential for quantum sensing applications.
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We report the creation of a pair of Josephson junctions on a toroidal dilute gas Bose-Einstein condensate (BEC), a configuration that is the cold atom analog of the well-known dc superconducting quantum interference device (SQUID). We observe Josephson effects, measure the critical current of the junctions, and find dynamic behavior that is in good agreement with the simple Josephson equations for a tunnel junction with the ideal sinusoidal current-phase relation expected for the parameters of the experiment. The junctions and toroidal trap are created with the painted potential, a time-averaged optical dipole potential technique which will allow scaling to more complex BEC circuit geometries than the single atom-SQUID case reported here. Since rotation plays the same role in the atom SQUID as magnetic field does in the dc SQUID magnetometer, the device has potential as a compact rotation sensor.
We use the Gross-Pitaevskii equation to study Josephson tunneling between two weakly coupled Bose-Einstein condensates, which compose spin-1 bosons. We show that a rotating magnetic field on one side can produce a phase difference across the junction, resulting in an oscillatory tunneling spin current. Besides numerical calculation, we derive analytical results in two extreme cases, namely the low- and high-frequency limits: in the low-frequency limit (magnetic field rotates adiabatically), a non-Abelian geometric phase arises and leads to the oscillatory spin current. By sharp contrast, the physics is intrinsically different in the high-frequency limit, where an average Zeeman energy difference leads to an oscillatory spin current. This proposed apparatus should be promising for the future experimental search of spin superfluidity.
We theoretically investigate a non-Hermitian optical dimer whose parameters are renormalized by dispersive and dissipative backaction from the coupling of the passive cavity with a ring-trapped Bose-Einstein condensate. The passive cavity is driven by a two-tone control laser, where each tone is in a coherent superposition of Laguerre-Gaussian beams carrying orbital angular momenta ±ℓℏ\pm \ell \hbar±ℓℏ. This imprints an optical lattice on the ring trap, leading to Bragg-diffracted sidemode excitations. Using an exact Schur-complement reduction of the full light-matter dynamics, we derive a frequency-dependent self-energy and identify a static regime in which the atomic response produces a complex shift of the passive optical mode. This renormalized dimer supports a tunable exceptional point, enabling spectroscopic signatures in the optical transmission due to a probe field, which can in turn be utilized for estimating the winding number of the persistent current. Exploiting the associated half-integer topological charge, we propose a digital exceptional-point-based sensing scheme based on eigenmode permutation, providing a noise-resilient method to sense superfluid rotation without relying on fragile eigenvalue splittings. Importantly, the sensing proposals are intrinsically nondestructive, preserving the coherence of the atomic superfluid.