Topological sensing of superfluid rotation using non-Hermitian optical dimers

TL;DR

This work develops a non-Hermitian optical-dimer framework renormalized by a ring-trapped Bose-Einstein condensate, where a two-tone Laguerre-Gaussian drive imprints an optical lattice that couples to Bragg sidemodes. By performing an exact Schur-complement reduction, the authors derive a frequency-dependent self-energy and, in the static regime, a complex detuning shift that yields a tunable exceptional point in the optical dimer. The exceptional point governs a measurable signature in the probe transmission and provides a means to estimate the superfluid winding number $L_p$ via the EP location, while a half-integer topological charge enables a digital, robust sensing protocol based on eigenmode permutation. The proposed topological-sensing scheme is intrinsically non-destructive, preserving the atomic coherence and offering potential for unit-resolution rotation sensing in large-$L_p$ regimes, with broad implications for reconfigurable non-Hermitian photonic–atom platforms.

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.

Figures (5)

• Figure 1: Schematic setup showing the two optical cavities coupled evanescently. The cavity on the left side is the passive cavity with loss rate $\gamma_0$ that contains the ring-trapped BEC and is controlled by a two-tone control laser where each tone is in a coherent superposition of Laguerre-Gaussian modes carrying OAM $\pm \ell \hbar$. The active cavity on the right admits a net gain rate $\Gamma = g_0 - \gamma'$, where $\gamma'$ is the intrinsic loss rate of this cavity and $g_0$ is the gain rate due to the active medium. A probe field is later included for spectroscopic readout.
• Figure 2: Real and imaginary parts of $\Sigma(\bar{\Delta})$. The parameters are $\omega_c = 40.04\gamma_{0}$, $\omega_d = 19.83\gamma_{0}$, $\tilde{G} = 2\gamma_{0}$, and $\gamma_m = 1.7\times 10^{-5}\gamma_{0}$, with $\gamma_{0}=2\pi~{\rm kHz}$. The sidemode frequencies are obtained by putting $m = 23$ amu, $R_0 = 10~\mu$m, $L_p = 115$, and $\ell = 10$ in $\omega_{c(d)} = \frac{\hbar[L_p + (-) 2\ell]^2}{2mR_0^2}$. The dashed vertical line corresponds to $\bar{\Delta}_{0}=-(\omega_c+\omega_d)/2\simeq-29.94\gamma_{0}$, where the real part changes sign.
• Figure 3: Transmission proxy $(\gamma_{0}^{2}/|D(\delta)|)^{2}$ as a function of the probe detuning $\delta/\gamma_{0}$, calculated from the effective non-Hermitian optical dimer including atomic backaction, for two different values of $\tilde{G}$. The remaining parameters are fixed to $\bar{\Delta}=-27\gamma_{0}$, $J=\gamma_{0}$, $\Gamma=\gamma_{0}$, $\gamma_{m}=1.7\times 10^{-5}\gamma_{0}$, and atomic-sidemode frequencies $\omega_{c}=40.04\gamma_{0}$ and $\omega_{d}=19.83\gamma_{0}$.
• Figure 4: Transmission proxy $(\gamma_{0}^{2}/|D(\delta)|)^{2}$ as a function of the probe detuning $\delta/\gamma_{0}$ at the exceptional point. The parameters are $\tilde{G}=3\gamma_{0}$, $\Gamma=\gamma_{0}$, $\gamma_{m}=1.7\times 10^{-5}\gamma_{0}$, $\omega_{c}=40.04\gamma_{0}$, $\omega_{d}=19.83\gamma_{0}$, and $J=J_{\rm EP}$. Both the transmission peaks have coalesced into a single enhanced peak at $\delta \simeq -29.94\gamma_0$.
• Figure 5: Real and imaginary parts of the eigenvalues $\lambda_\pm$ of $M_{\rm eff}(\bar{\Delta})$. The parameters are $\tilde{G}=2\gamma_{0}$, $\Gamma=\gamma_{0}$, $\gamma_{m}=1.7\times 10^{-5}\gamma_{0}$, $\omega_{c}=40.04\gamma_{0}$, $\omega_{d}=19.83\gamma_{0}$, and $J=J_{\rm EP}$ as given by expression (\ref{['JEP_condition_physical']}). The exceptional point is seen to occur at $\bar{\Delta} = - \frac{\omega_c + \omega_d}{2} \simeq -29.94\gamma_0$ (black-dashed line).