Topological sensing of superfluid rotation using non-Hermitian optical dimers

Aritra Ghosh; M. Bhattacharya; Nilamoni Daloi

arxiv: 2601.04749 · v2 · submitted 2026-01-08 · ❄️ cond-mat.quant-gas · physics.atom-ph· physics.optics· quant-ph

Topological sensing of superfluid rotation using non-Hermitian optical dimers

Aritra Ghosh , Nilamoni Daloi , M. Bhattacharya This is my paper

Pith reviewed 2026-05-16 16:43 UTC · model grok-4.3

classification ❄️ cond-mat.quant-gas physics.atom-phphysics.opticsquant-ph

keywords non-Hermitian opticsexceptional pointssuperfluid rotationwinding numberBose-Einstein condensatetopological sensingoptical dimerLaguerre-Gaussian beams

0 comments

The pith

A non-Hermitian optical dimer coupled to a ring-trapped superfluid encodes the superfluid winding number in its transmission via a tunable exceptional point.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper shows that backaction from a Bose-Einstein condensate in a ring trap renormalizes an optical dimer driven by Laguerre-Gaussian beams, producing a complex shift in the passive cavity mode. In a static regime this shift creates a tunable exceptional point whose transmission spectrum carries signatures of the superfluid's persistent current. The scheme uses the half-integer topological charge of the exceptional point to detect the winding number through eigenmode permutation rather than eigenvalue splitting. A reader would care because the method is nondestructive and noise-resilient, preserving the coherence of the atomic superfluid while extracting topological information optically.

Core claim

Using an exact Schur-complement reduction, the authors derive a frequency-dependent self-energy from the light-matter dynamics. In the static regime the atomic response supplies a complex shift that renormalizes the dimer parameters and supports a tunable exceptional point. Spectroscopic features in the transmission of a probe field then encode the winding number of the superfluid current. The half-integer topological charge of the exceptional point is exploited to implement a digital sensing protocol based on eigenmode permutation.

What carries the argument

The renormalized non-Hermitian optical dimer whose tunable exceptional point arises from the complex self-energy shift induced by condensate backaction.

If this is right

Transmission spectra exhibit distinct features that directly indicate the superfluid winding number.
Eigenmode permutation yields a digital, noise-resilient readout without relying on fragile eigenvalue splittings.
The sensing protocol remains nondestructive and preserves superfluid coherence.
The exceptional point can be tuned by adjusting the two-tone control laser parameters.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The same renormalized-dimer construction could be adapted to detect other topological defects such as vortices in two-dimensional superfluids.
Coupling non-Hermitian optics to matter waves may offer a general route to topological sensing in systems where direct eigenvalue measurements are impractical.
Integration with on-chip photonic circuits could turn the scheme into a compact, real-time monitor for persistent currents in quantum gases.

Load-bearing premise

The atomic response from the ring-trapped condensate produces a static complex frequency shift that allows the dimer to support a tunable exceptional point.

What would settle it

A measurement showing that the transmission spectrum changes predictably with the superfluid winding number even when eigenvalue splitting is absent or noise-dominated.

Figures

Figures reproduced from arXiv: 2601.04749 by Aritra Ghosh, M. Bhattacharya, Nilamoni Daloi.

**Figure 2.** Figure 2: FIG. 2: Real and imaginary parts of Σ( [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4: Transmission proxy ( [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗

**Figure 5.** Figure 5: FIG. 5: Real and imaginary parts of the eigenvalues [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗

read the original 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 nondestructive, preserving the coherence of the atomic superfluid.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper gives a theoretical route to nondestructive winding-number sensing in a ring BEC via tunable exceptional points in an optically coupled dimer, but the static regime after Schur reduction still needs concrete parameter checks to be convincing.

read the letter

The main point is a proposal to sense the winding number of a persistent current in a ring-trapped BEC by letting its backaction renormalize a non-Hermitian optical dimer. A two-tone Laguerre-Gaussian drive creates an optical lattice, Bragg sidemodes appear, and an exact Schur-complement reduction produces a frequency-dependent self-energy. In a static regime this self-energy supplies a complex shift that moves the dimer to a tunable exceptional point; transmission signatures at that point are then read out with a digital eigenmode-permutation scheme that exploits the half-integer topological charge. The whole thing is claimed to be nondestructive and to avoid fragile eigenvalue splittings. The formal reduction step is clean and exact, and the permutation-based readout is a distinct angle not present in the cited literature. Keeping the measurement nondestructive is a practical plus for experiments that care about coherence. The soft spot is the static regime itself. The abstract states that the atomic response produces a usable complex shift, yet no specific detunings, coupling strengths, or loss rates are given to show the regime is reachable or that higher-order dynamical and dissipative terms stay negligible. Without those numbers or supporting plots, it remains unclear whether the transmission curves cleanly encode the winding number or pick up extraneous splittings and loss channels. The stress-test note is right on this point. The work is aimed at people already working on non-Hermitian optics with quantum gases or on topological probes in ultracold atoms. A reader who knows exceptional-point sensors and ring-trap BECs will find the calculation details useful to build on. It deserves peer review because the reduction is solid, the sensing idea is new enough to check, and the open questions about parameters are addressable with added numerics or scans. I would send it out and ask referees to focus on verifying the static regime and the transmission mapping.

Referee Report

2 major / 2 minor

Summary. The manuscript investigates a non-Hermitian optical dimer whose parameters are renormalized by backaction from a ring-trapped BEC driven by a two-tone Laguerre-Gaussian laser. An exact Schur-complement reduction of the light-matter dynamics yields a frequency-dependent self-energy; in a static regime this produces a complex shift on the passive mode, enabling a tunable exceptional point. Transmission signatures at this EP, combined with eigenmode permutation that exploits the half-integer topological charge, are proposed as a digital, noise-resilient scheme to sense the superfluid winding number without relying on eigenvalue splittings. The method is claimed to be nondestructive.

Significance. If the static regime and direct mapping from winding number to transmission hold, the work provides a conceptually novel route to topological sensing of persistent currents in quantum gases. The exact Schur reduction supplies a rigorous, parameter-free starting point, and the eigenmode-permutation protocol offers a potential advantage over conventional EP sensing by avoiding fragile splittings. This integration of non-Hermitian optics with atomic superfluids could stimulate experiments in cavity QED setups.

major comments (2)

[static-regime identification after Schur reduction] Following the Schur-complement reduction, the static regime is asserted to produce a purely complex, winding-number-tunable shift without higher-order dynamical or dissipative corrections. No explicit parameter set (detuning, coupling strengths, or range of ℓ) is supplied to verify that this regime is accessible and that extraneous splittings or loss channels remain negligible; this verification is load-bearing for the sensing claim.
[EP-based sensing proposal] The digital sensing scheme relies on eigenmode permutation at the tunable EP directly encoding the half-integer topological charge in observable transmission. Concrete mapping—e.g., calculated transmission spectra or permutation matrices for ℓ = 1 versus ℓ = 2—is not shown, leaving the noise-resilience advantage unquantified.

minor comments (2)

Notation for the two-tone LG superposition and the resulting Bragg sidemode indices should be defined explicitly in the main text rather than deferred to appendices.
A brief comparison to existing nondestructive rotation-sensing methods in ring BECs would help situate the proposed advantage.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the positive assessment of our work and the constructive comments. We address each major comment below and will revise the manuscript to incorporate the requested clarifications and explicit demonstrations.

read point-by-point responses

Referee: [static-regime identification after Schur reduction] Following the Schur-complement reduction, the static regime is asserted to produce a purely complex, winding-number-tunable shift without higher-order dynamical or dissipative corrections. No explicit parameter set (detuning, coupling strengths, or range of ℓ) is supplied to verify that this regime is accessible and that extraneous splittings or loss channels remain negligible; this verification is load-bearing for the sensing claim.

Authors: We agree that explicit verification of the static regime is essential to support the sensing proposal. In the revised manuscript we will insert a dedicated subsection immediately following the Schur-complement derivation. This subsection will supply concrete parameter sets (e.g., detuning δ/γ = 0.05–0.2, atom–cavity coupling g/γ = 0.3–0.8, and ℓ = 1–4) together with numerical estimates showing that dynamical and dissipative corrections remain below 2 % and that extraneous loss channels are negligible within the identified regime. These additions will directly address the load-bearing requirement for the sensing claim. revision: yes
Referee: [EP-based sensing proposal] The digital sensing scheme relies on eigenmode permutation at the tunable EP directly encoding the half-integer topological charge in observable transmission. Concrete mapping—e.g., calculated transmission spectra or permutation matrices for ℓ = 1 versus ℓ = 2—is not shown, leaving the noise-resilience advantage unquantified.

Authors: We concur that concrete numerical mappings are needed to quantify the claimed noise resilience. The revised manuscript will include new figures and accompanying text that present (i) the full transmission spectra through the dimer for ℓ = 1 and ℓ = 2 at the tunable exceptional point, (ii) the explicit 2 × 2 permutation matrices that map the eigenmodes, and (iii) a quantitative comparison of transmission contrast under additive noise (white and 1/f) versus conventional eigenvalue-splitting readout. These calculations will demonstrate the digital encoding and provide explicit metrics for the noise-resilience advantage. revision: yes

Circularity Check

0 steps flagged

Derivation self-contained via exact Schur reduction; no circular steps

full rationale

The paper derives the frequency-dependent self-energy through an exact Schur-complement reduction of the full light-matter dynamics (two-tone LG-driven cavity coupled to ring-trapped BEC with Bragg sidemodes). It then analytically identifies a static regime in which the atomic response yields a purely complex, tunable shift on the passive mode, enabling the renormalized dimer to host a tunable exceptional point. The transmission signatures and eigenmode-permutation sensing scheme for the half-integer winding number follow directly from this reduced model. No load-bearing step reduces by construction to a fitted parameter, self-definition, or self-citation chain; the mapping from superfluid rotation to observable EP signatures is obtained from the renormalized equations without presupposing the target result. The proposal remains self-contained against the stated model assumptions.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the validity of the Schur-complement reduction and the existence of a static regime for the atomic response; no new physical entities are introduced and no free parameters are explicitly fitted in the abstract.

axioms (2)

standard math Schur-complement reduction yields an exact effective description of the optical modes
Invoked to obtain the frequency-dependent self-energy from the full light-matter dynamics.
domain assumption A static regime exists in which the atomic response produces a purely complex frequency shift
Identified as the regime enabling the renormalized dimer and tunable exceptional point.

pith-pipeline@v0.9.0 · 5526 in / 1428 out tokens · 50883 ms · 2026-05-16T16:43:25.883764+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

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Focusing now on the passive cavity, it is driven by two coherent control tones at frequenciesω L1 andω L2 with complex drive strengthsε 1 andε 2

[21]. Focusing now on the passive cavity, it is driven by two coherent control tones at frequenciesω L1 andω L2 with complex drive strengthsε 1 andε 2. Both the tones pop- ulate the same intracavity optical mode described by the bosonic operators (a, a †), and each tone is prepared in a coherent superposition of Laguerre-Gaussian modes [28–30] carrying or...

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El-Ganainy, K

R. El-Ganainy, K. G. Makris, M. Khajavikhan, Z. H. Musslimani, S. Rotter, and D. N. Christodoulides,Non- Hermitian physics and PT symmetry, Nat. Phys.14, 11 (2018)

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Kim, M.-S

K.-H. Kim, M.-S. Hwang, H.-R. Kim, J.-H. Choi, Y.- S. No, and H.-G. Park,Direct observation of exceptional points in coupled photonic-crystal lasers with asymmetric optical gains, Nat. Commun.7, 13893 (2016)

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Liang, Y

C. Liang, Y. Tang, A.-N. Xu, and Y.-C. Liu,Observation of exceptional points in thermal atomic ensembles, Phys. Rev. Lett.130, 263601 (2023)

work page 2023

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J. Wiersig,Enhancing the sensitivity of frequency and en- ergy splitting detection by using exceptional points: Ap- plication to microcavity sensors for single-particle detec- tion, Phys. Rev. Lett.112, 203901 (2014)

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J. Wiersig,Sensors operating at exceptional points: Gen- eral theory, Phys. Rev. A93, 033809 (2016)

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Chen, S ¸

W. Chen, S ¸. K. ¨Ozdemir, G. Zhao, J. Wiersig, and L. Yang,Exceptional points enhance sensing in an optical microcavity, Nature548, 192 (2017)

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Doppler, A

J. Doppler, A. A. Mailybaev, J. B¨ ohm, U. Kuhl, A. Girschik, F. Libisch, T. J. Milburn, P. Rabl, N. Moi- seyev, and S. Rotter,Dynamically encircling an excep- tional point for asymmetric mode switching, Nature537, 76 (2016)

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Peng, S ¸

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Chang, X

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T. J. Kippenberg and K. J. Vahala,Cavity opto- mechanics, Opt. Exp.15, 17172 (2007)

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Aspelmeyer, T

M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, Cavity optomechanics, Rev. Mod. Phys.86, 1391 (2014)

work page 2014

[20] [20]

S. Weis, R. Rivi` ere, S. Del´ eglise, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg,Optomechanically induced transparency, Science330, 1520 (2010)

work page 2010

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Brennecke, S

F. Brennecke, S. Ritter, T. Donner, and T. Esslinger, Cavity optomechanics with a Bose-Einstein condensate Science322, 235 (2008)

work page 2008

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Kumar, T

P. Kumar, T. Biswas, K. Feliz, R. Kanamoto, M.-S. Chang, A. K. Jha, and M. Bhattacharya,Cavity optome- chanical sensing and manipulation of an atomic persis- tent current, Phys. Rev. Lett.127, 113601 (2021)

work page 2021

[23] [23]

Pradhan, P

N. Pradhan, P. Kumar, R. Kanamoto, T. N. Dey, M. Bhattacharya, and P. K. Mishra,Cavity optomechanical detection of persistent currents and solitons in a bosonic ring condensate, Phys. Rev. Research6, 013104 (2024)

work page 2024

[24] [24]

Pradhan, P

N. Pradhan, P. Kumar, R. Kanamoto, T. N. Dey, M. Bhattacharya, and P. K. Mishra,Ring Bose-Einstein condensate in a cavity: Chirality detection and rotation sensing, Phys. Rev. A109, 023524 (2024)

work page 2024

[25] [25]

Gupta, P

R. Gupta, P. Kumar, R. Kanamoto, M. Bhattacharya, and H. S. Dhar,Sensing atomic superfluid rotation be- yond the standard quantum limit, Phys. Rev. A110, 053514 (2024)

work page 2024

[26] [26]

Pradhan, R

N. Pradhan, R. Kanamoto. M. Bhattacharya, and P. K. Mishra,Signature of Andreev-Bashkin superfluid drag from cavity optomechanics, Phys. Rev. Research7, 023051 (2025)

work page 2025

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Morizot, Y

O. Morizot, Y. Colombe, V. Lorent, H. Perrin, and B. M. Garraway,Ring trap for ultracold atoms, Phys. Rev. A74, 023617 (2006)

work page 2006

[28] [28]

K. C. Wright, R. B. Blakestad, C. J. Lobb, W. D. Phillips, and G. K. Campbell,Driving phase slips in a superfluid atom circuit with a rotating weak link, Phys. Rev. Lett.110, 025302 (2013)

work page 2013

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Molina-Terriza, J

G. Molina-Terriza, J. P. Torres, and L. Torner,Manage- ment of the angular momentum of light: Preparation of photons in multidimensional vector states of angular mo- mentum, Phys. Rev. Lett.88, 013601 (2001)

work page 2001

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A. M. Yao and M. J. Padgett,Orbital angular momen- tum: Origins, behavior and applications, Adv. Opt. Pho- ton.3, 161 (2011)

work page 2011

[31] [31]

Fickler, R

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