arXiv subjects

Ziqi Niu

Publications and source records attributed to Ziqi Niu.

6 recordsLinked to original sources

arXiv2026

Smoothness of Inertial Manifold for the Burgers Equation

This paper establishes a ${C^{n,\varepsilon }}$-smooth extension of the inertial manifold for the one-dimensional Burgers equation, which demonstrates that its long-time behavior can be completely determined by explicit smooth first-order ODEs. We first devise a new framework for an abstract equation with two nonlinear terms, where one preserves regularity and the other reduces regularity, and derive sufficient conditions for constructing the ${C^{n,\varepsilon}}$-smooth extension of the IM by treating these two nonlinear terms separately.

math.DS↗

arXiv2025

Engineering nonlinear activation functions for all-optical neural networks via quantum interference

All-optical neural networks (AONNs) promise transformative gains in speed and energy efficiency for artificial intelligence (AI) by leveraging the intrinsic parallelism and wave nature of light. However, their scalability has been fundamentally limited by the high power requirements of conventional nonlinear optical elements. Here, we present a low-power nonlinear activation scheme based on a three-level quantum system driven by dual laser fields. This platform introduces a two-channel nonlinear activation matrix with both self- and cross-nonlinearities, enabling true multi-input, multi-output optical processing. The system supports tunable activation behaviors, including sigmoid and ReLU functions, at ultralow power levels (17 uW per neuron). We validate our approach through theoretical modeling and experimental demonstration in rubidium vapor cells, showing the feasibility of scaling to deep AONNs with millions of neurons operating under 20 W of total optical power. Crucially, we also demonstrate the all-optical generation of gradient-like signals with backpropagation, paving the way for all optical training. These results mark a major advance toward scalable, high-speed, and energy-efficient optical AI hardware.

physics.optics↗

arXiv2023

Four-wave mixing with anti-parity-time symmetry in hot $^{85}$Rb vapor

We report an experimental demonstration of anti-parity-time (anti-PT) symmetric optical four-wave mixing in thermal Rubidium vapor, where the propagation of two conjugate optical fields in a double-$Λ$ scheme is governed by a non-Hermitian Hamiltonian. We are particularly interested in studying quantum intensity correlations between the two conjugate fields near the exceptional point, taking into account loss and accompanied Langevin noise. Our experimental measurements of classical four-wave mixing gain and the associated two-mode relative-intensity squeezing are in reasonable agreement with the theoretical predictions.

quant-ph↗

arXiv2022

Weak Thermal State Quadrature-Noise Shadow Imaging

In this work, we theoretically and experimentally demonstrate the possibility to create an image of an opaque object using a few-photon thermal optical field. We utilize the Quadrature-Noise Shadow Imaging (QSI) technique that detects the changes in the quadrature-noise statistics of the probe beam after its interaction with an object. We show that such thermal QSI scheme has an advantage over the classical differential imaging when the effect of dark counts is considered. At the same time, the easy availability of thermal sources for any wavelength makes the method practical for broad range of applications, not accessible with, e.g. quantum squeezed light. As a proof of principle, we implement this scheme by two different light sources: a pseudo-thermal beam generated by rotating ground glass (RGG) method and a thermal beam generated by Four-Wave Mixing (FWM) method. The RGG method shows simplicity and robustness of QSI scheme while the FWM method validates theoretical signal-to-noise ratio predictions. Finally, we demonstrate low-light imaging abilities with QSI by imaging a biological specimen on a CCD camera, detecting as low as 0.03 photons on average per pixel per 1.7 microseconds exposure.

quant-ph↗

arXiv2022

Wave-Front Reconstruction via Single-Pixel Homodyne Imaging

We combine single-pixel imaging and homodyne detection to perform full object recovery (phase and amplitude). Our method does not require any prior information about the object or the illuminating fields. As a demonstration, we reconstruct the optical properties of several semi-transparent objects and find that the reconstructed complex transmission has a phase precision of 0.02 radians and a relative amplitude precision of 0.01.

physics.optics↗

arXiv2020

Quantum-Enhanced Two-Photon Spectroscopy Using Two-mode Squeezed Light

We investigate the prospects of using two-mode intensity squeezed twin-beams, generated in Rb vapor, to improve the sensitivity of spectroscopic measurements by engaging two-photon Raman transitions. As a proof of principle demonstration, we demonstrated the quantum-enhanced measurements of the Rb $5D_{3/2}$ hyperfine structure with reduced requirements for the Raman pump laser power and Rb vapor number density.

physics.atom-ph↗