Quantum-Limited Optical Vector Analysis

TL;DR

This work introduces a quantum-limited Optical Vector Analysers (OVA) using a free-running balanced-heterodyne interferometer to achieve high-sensitivity, wideband measurements without sacrificing practicality. By mitigating phase noise in hardware and correcting residual noise in software, the approach reaches near-SQL sensitivity over a 20 THz span and enables coherent vector measurements at the single-photon level, characterized by an efficiency of about $\eta \approx 0.64$. Application to thin-film Lithium Niobate microring resonators yields internal quality factors $Q_{int} > 5\times 10^{6}$, demonstrating low internal losses and high fabrication quality. The method offers a practical, scalable pathway for high-sensitivity metrology of photonic components, with potential impact on integrated photonics, quantum information processing, and advanced sensing.

Abstract

Optical Vector Analysers (OVA) are critical for emerging technologies such as integrated photonics and optical positioning. Achieving a sensitivity near the Standard Quantum Limit (SQL) while acquiring a wide spectrum allows an accurate measurement of targets that are fragile, non-linear, or that scatter most of the probe light away. Existing OVAs operate with a sensitivity orders of magnitude below the SQL. In this paper, we use a free-running interferometer with a frequency range of 20 THz as an OVA. We introduce novel methods to mitigate the phase noise and obtain a unit signal-to-noise ratio for powers at the fW level. We apply this technique towards quantifying the fabrication quality of microring resonators in thin-film Lithium Niobate. Our characterisation yields a signal-to-noise ratio above 1 with much less than 1 circulating photon and reveals a quality factor above 5 millions, unambiguously attributed to low internal losses.

Figures (11)

• Figure 1: Schematic of the measurement setup and illustrative results. (a) The Device Under Test (DUT) is characterised with a balanced heterodyne measurement, performed with a free-running Mach-Zehnder Interferometer (MZI) comprising a scanning laser, a Polarisation Controller, an Acousto-Optic Modulator (AOM), a beamsplitter (BS) and a Balanced Photo-Detector (BPD). The free-running MZI is sensitive to vibrations and thermal expansion, represented by the grey lines in the LO path. (b) The amplitude and phase responses of thin-film Lithium Niobate (TFLN) ring resonators are plotted for the over-coupled (black, left), critically coupled (red, middle) and undercoupled (yellow, right) regimes.
• Figure 2: Excess classical phase-noise. (a) Fourier transform of 3 signal traces, acquired at 200 nm/s, with interferometer length mismatch of about 5, 2 and 0 meters. The delay introduces a frequency offset, and the peaks are broadened. (b) Power Spectral Density (PSD) of the phase-noise calculated with the Welch method. The 1/f noise dominates at low frequency (red background, left) and the quantum noise dominates after a few kHz (blue background, right). The level of quantum noise is consistent with expectation from a coherent-state (light blue dashed line, bottom), and our measured efficiency (dark blue dashed line, top). The 1/f noise is attenuated with length matching. (c) Overlapping Allan Deviation, displaying a 1/f averaging in the white noise region (blue, left), and a saturation where the phase drift of the interferometer dominates (red, right).
• Figure 3: Quantum efficiency and minimum power detectable. (a) Amplitude mean (squares) and standard deviation (diamonds) of the signal during frequency sweep, as a function of signal power. The mean and standard deviations are simultaneously fitted to a Rice distribution (solid and dashed lines) to extract the efficiency $\eta=0.64$. (b) Scatter plots of IQ values during scan for signal powers 11pW, 4.4pW, 1.1pW and 0W. The calibration of the IQ space accounts for the responsivity and gain of the detectors, obtained from the fits in Fig. \ref{['fig3']}a. Two disks represent the standard deviation of a coherent-state for a measurement efficiency of 1 (grey) and our measured efficiency (black). (c, d) Minimum average number of photons and power detected with an SNR of at least 1 as a function of IBW. The SNR is calculated for the amplitude only (circles) or including the phase noise via the Error-Vector Magnitude (EVM, squares). The data is plotted for sweep speeds 1 nm/s (purple), 20 nm/s (light blue) and 200 nm/s (dark blue).
• Figure 4: Low-power characterisation of TFLN microring resonators without prior information. The IQ-space trajectory is normalised to the maximum transmission of the fit curve. I and Q display a constant amplitude and a large phase-roll for the over-coupled ring (a), while I and Q simultaneously go through 0 for the critically ring (b). The data is taken for moderate power (10 pW) and low power (20 fW), at a sweep speed of 1 nm/s and an IBW of 20 kHz. The I and Q quadratures are simultaneously fitted to the complex response of a harmonic oscillator, from which we extract the internal and external quality factors ($\mathrm{Q_{int}}$ and $\mathrm{Q_{ext}}$ respectively).
• Figure S1: Visualization of the signal band $\boldsymbol{a_s}(t_k)$ and image band $\boldsymbol{a_i}(t_k)$ modes