[Paper Review] Topological sensing of superfluid rotation using non-Hermitian optical dimers

Aritra Ghosh, Nilamoni Daloi+1 more|arXiv (Cornell University)|Jan 8, 2026

Quantum Mechanics and Non-Hermitian Physics0 citations

TL;DR

The paper theoretically demonstrates a non-Hermitian optical dimer renormalized by a ring-trapped BEC, hosting tunable exceptional points and proposing topological, non-destructive sensing schemes to estimate superfluid rotation.

ABSTRACT

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 $\pm \ell \hbar$. 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 non-destructive, preserving the coherence of the atomic superfluid.

Motivation & Objective

• Motivate non-Hermitian sensing by leveraging exceptional points in a cavity-BEC system.
• Develop an exact Schur-complement reduction to obtain a frequency-dependent self-energy from light-matter backaction.
• Identify static regimes where atomic backaction yields a complex shift of the passive mode.
• Demonstrate how exceptional points enable spectroscopic readout for winding number estimation of persistent currents.
• Propose topologically robust, digital sensing schemes based on eigenmode permutation around exceptional points.

Proposed method

• Model two coupled cavities (one passive with a ring-BEC, one active) forming a non-Hermitian dimer.
• Derive an exact Schur-complement reduction to obtain a frequency-dependent self-energy Sigma(lambda).
• Apply static approximation to replace Sigma(lambda) by Sigma(bar{Delta}) for a closed 2x2 optical matrix.
• Diagonalize the effective optical matrix to obtain dimer supermodes and their eigenvalues lambda_±.
• Find conditions for exceptional points where the discriminant vanishes and link to gain-loss renormalization (Gamma).
• Propose probe-transmission signatures T_b(delta) ∝ |D(delta)|^{-2} and relate peaks to lambda_±.

Experimental results

Research questions

• RQ1 Can a ring-BEC coupled to a passive cavity renormalize a two-mode optical dimer into a non-Hermitian system with exceptional points?
• RQ2 How can one read out the winding number of a persistent current via transmission spectra and exceptional-point topology?
• RQ3 What are the conditions for an exceptional point in the renormalized dimer, and how can it be used for sensing rotation?
• RQ4 Can a topological, digital sensing scheme based on eigenmode permutation around an EP provide noise-resilient rotation sensing?
• RQ5 Is the proposed sensing non-destructive to the atomic superfluid?

Key findings

• An exact Schur-complement reduction yields a frequency-dependent self-energy that renormalizes the passive cavity mode.
• A static regime exists where the atomic backaction reduces to a complex detuning-dependent shift of the passive mode.
• Exceptional points exist in the renormalized dimer, with a condition linking J_EP to the sum of gain and loss plus backaction.
• The transmission spectrum of the second cavity reveals spectroscopic signatures of the modified eigenvalues and their real/imaginary parts.
• A topological sensing scheme uses half-integer topological charge at the EP to implement a digital, noise-resilient sensor based on eigenmode permutation.
• The proposed EP-based sensing is intrinsically non-destructive, preserving the coherence of the atomic superfluid.