Exponentially enhanced sensing through nonreciprocal light propagation

TL;DR

This work addresses the fundamental reciprocity limitations of photonic sensing by realizing a non-Hermitian sensor based on two coupled Hatano-Nelson lattices encoded in an electro-optic frequency comb. Through simultaneous phase and intensity modulation in a fiber-loop cavity, they implement nonreciprocal frequency-space hopping and couple two HN chains via a small perturbation, achieving an output signal that scales as $e^{2AN}$ while the noise scales as $e^{AN}$, yielding an exponential improvement in SNR with system size. The authors validate the scaling experimentally for up to ~70 modes per chain and corroborate it with Langevin-based numerical simulations, also analyzing robustness to additional perturbations such as $3^{rd}$ nearest-neighbor couplings. This work establishes a new non-Hermitian sensing paradigm with potential for remote sensing and optical readout of superconducting circuits, enabling highly sensitive measurements with distributed frequency-domain architectures.

Abstract

Non-reciprocity is a key resource for pushing the performance of photonic devices beyond the fundamental limits imposed by Lorentz reciprocity. Here, we report on the realization of an optical sensor where non-reciprocal light propagation allows detecting small perturbations with a signal-to-noise ratio (SNR) that scales exponentially with system size. Our approach is based on encoding two Hatano-Nelson (HN) chains, which is equivalent to the bosonic Kitaev model, within the resonant modes of an electro-optics frequency comb. Non-reciprocal light propagation in the frequency domain is realized through simultaneous phase and amplitude modulation of the circulating field inside the optical fiber cavity. We demonstrate the sensing of a small modulating tone coupling the two HN chains with a SNR that scales exponentially with the lattice size, formed from up to 70 frequency modes per chain. Our results open a new paradigm in non-Hermitian sensing, with potential applications in remote sensing including the optical readout of superconducting circuits.

Figures (11)

• Figure 1: Optical sensing with a BKC. (a) Schematic depiction of a basic optical sensors transforming an input field $a_{in}$ into an output field $a_{out}$ whose properties depend on an external perturbation $\epsilon$. Mitigating the sensitivity to external noise ($b_i$), which leads to a noisy output field ($B_{out}$), is the key challenge of optical sensors. (b) Depiction of a BKC where every lattice site is coupled to its nearest-neighbor through one-($w$) and two-($\Delta$) photon processes. (c) The BKC is equivalently described by the chiral propagation of light's quadrature ($x$ and $p$) with hopping amplitudes $Je^{\pm A}$. (d) Two coupled HN lattices where each simulates a given quadrature.
• Figure 2: Non-Hermitian skin effect in frequency space. (a) Schematic representation of our photonic platform formed from a main optical fiber loop with FSR $\Omega$ coupled to a smaller loop with a FSR $N\Omega$. An erbium-doped optical amplifier (EDFA) is added to the cavity to mitigate losses. (b) The resulting frequency spectrum consists of a succession of $N$ resonant modes separated by $\Omega$; we only consider two of these arrays to form HN lattices. The circulating field is modulated in phase (PM) and intensity (IM) at frequency $\Omega$ to induce non-reciprocal light propagation in frequency space. The driven and probed modes are depicted in red, each belonging to a distinct HN chain coupled by a perturbation $\epsilon$. The perturbation consists of a reciprocal $3^{rd}$ nearest-neighbor coupling term; the solid lines depict those that couple the two chains. (c)-(d) Time-resolved transmission measurements allows measuring the effective band structure for the reciprocal ($\beta=0$) and non-reciprocal ($\alpha=\beta$) propagation. (e) Heterodyne spectrum (for the non-reciprocal case with $\epsilon=0$) allowing to probe the distribution of the field in frequency space. A clear exponential accumulation associated to the NHSE is observed in the driven lattice; there is no significant emission in the $2^{nd}$ lattice.
• Figure 3: Exponential enhancement of the SNR. (a) Heterodyne spectra, normalized by the input field amplitude $|a_{in}|^{2}$, for different lengths of the main optical fiber loop leading to HN lattice sizes of $N=10,24,34,54,74$. Each measurement is taken with a coupling perturbation $\epsilon=0.1\alpha$. The inset is a close-up to the case $N=54$ that shows a clear amplification $e^{AN}$ (dark dashed lines) in both HN chains separated by the gray dotted lines. The frequency of the driving field and probed modes are indicated by red arrows. (b) Similar measurement when the laser is not resonant with the main loop to obtain noise spectra. Panel (c) summarizes the scaling of the readout signal and noise exhibiting a clear distinction between the scaling of the signal ($e^{2AN}$, blue dashed line) and noise ($e^{AN}$, orange dashed line). The steady-state solution of the Langevin equation is shown by shaded areas whose width indicates the experimental uncertainty and inherent fluctuations. The gray area depicts the photodiode's electrical noise limit.
• Figure 4: Scaling of the SNR as a function of $\epsilon$. Output signal (a, blue curve) and noise (b, orange curve) as a function of the perturbation strength $\epsilon$ for a given chain length $N=54$. The vertical axis of Panel (b) is two orders of magnitude smaller than that in (a). The shaded lines indicate the steady-state solutions of the Langevin equation with their width indicating the uncertainty.
• Figure S1: Schematic representation of the experimental setup.