arXiv subjects

Wenhua He

Publications and source records attributed to Wenhua He.

11 recordsLinked to original sources

arXiv2026

Programmable pixel-mode linear interferometers using multi-plane light conversion

Programmable linear optical interferometers are a core primitive in optical signal processing, quantum information processing, and photonic computing. Existing photonic-integrated implementations realize arbitrary $M$-mode unitaries using Mach--Zehnder-interferometer meshes whose footprint and accumulated loss scale with $O(M^2)$ optical components. Here we analyze and experimentally demonstrate a programmable architecture for implementing linear optical transformations directly on spatially tiled free-space {\em pixel modes} using multi-plane light conversion (MPLC). In this architecture, $M$ spatial modes arranged on a transverse lattice undergo a unitary transformation and are mapped to $M$ output modes of identical geometry through a sequence of programmable phase masks separated by free-space propagation segments. Numerical simulations show that arbitrary $M$-mode unitaries can be compiled to a desired high fidelity using a number of phase planes that scales approximately linearly with $M$. Using a spatial-light-modulator-based MPLC, we experimentally demonstrate programmable interferometers acting on up to $16$ spatial pixel modes, including tunable beamsplitters, Hadamard unitaries, spatial permutations, and partial unitaries on select subsets of modes. These results establish MPLC-based pixel-mode interferometers as a promising architecture for programmable linear optics with applications in classical and quantum optical interconnects, photonic switching, and quantum information processing.

physics.optics↗

arXiv2026

Ultra-low loss piezo-optomechanical low-confinement silicon nitride platform for visible wavelength quantum photonic circuits

Realizing photonic quantum computing at scale requires integrated circuits that combine ultra-low loss with fast, low-power, low-hysteresis, and low-crosstalk reconfiguration. These requirements are particularly challenging at visible wavelengths, where many quantum resource-state generators, including single-photon sources and quantum memories, naturally operate. Low-confinement silicon nitride waveguides offer the requisite loss performance, but conventional thermo-optic modulators dissipate significant static power, driving thermal crosstalk and precluding cryogenic operation. Visible-wavelength piezo-optomechanical circuits avoid these drawbacks, but existing demonstrations rely either on high-confinement waveguides with propagation losses of 35-100 dB/m, or on low-confinement platforms using foundry-incompatible PZT. Here we combine piezo-optomechanical actuation with a CMOS-foundry-fabricated, low-confinement silicon nitride platform, achieving 2.6 dB/m propagation loss at 780 nm, megahertz-scale modulation bandwidth, a half-wave voltage-length product of 2.8 Vm, and negligible hysteresis. We demonstrate reconfigurable Mach-Zehnder interferometers with 0.63 dB loss per spiral phase shifter, enabling deep, actively reconfigurable visible-wavelength quantum photonic circuits.

physics.optics↗

arXiv2025

Optimal single-mode squeezing for beam displacement sensing

Estimation of an optical beam's transverse displacement is a canonical imaging problem fundamental to numerous optical imaging and sensing tasks. Quantum enhancements to the measurement precision in this problem have been studied extensively. However, previous studies have neither accounted for diffraction loss in full generality, nor have they addressed how to jointly optimize the spatial mode and the balance between squeezing and coherent amplitude. Here we show that, in the small-displacement limit, the seemingly intractable infinite-spatial-mode problem can be reduced to a compact three-mode interaction framework. We quantify the improvement afforded by an optimized single-spatial-mode Gaussian-state probe over the optimal classical laser probe, and show that a two-spatial-mode homodyne receiver is asymptotically optimal for the former in the limit of high probe energy. Our findings reveal a strategy for identifying quantum-optimal probes in the presence of generic multimode linear probe-target interaction and photon loss.

quant-ph↗

arXiv2025

Symmetry-breaking bifurcation of periodic solutions for a free-boundary tumor model

In this paper, we consider a free boundary multi-layer tumor model that incorporates a $T-$periodic provision of external nutrients $\Phi(t)$. The simplified model contains three parameters: the mean of periodic external nutrients $\Phi(t)$, the threshold concentration $\widetilde{\sigma}$ for proliferation and the cell to cell adhesiveness coefficient $\gamma$. We first study the flat solution and give a complete classification about $\frac{1}{T} \int_0^T \Phi(t) d t$ and $\widetilde{\sigma}$ according to global stability of zero equilibrium solution or global stability of the positive periodic solution. Precisely, (i) a zero flat solution is globally stable under the flat perturbations if and only if $\widetilde{\sigma} \geqslant \frac{1}{T} \int_0^T \Phi(t) d t$; (ii) If $\widetilde{\sigma}<\frac{1}{T} \int_0^T \Phi(t) d t$, then there exists a unique positive flat solution $\left(\sigma_*(y, t), p_*(y, t), { \rho_*(t)}\right)$ with period $T$ and it is a global attractor of all positive flat solutions for all $\gamma>0$. We further investigate periodic solutions bifurcating from the flat periodic solution $\left(\sigma_*(y, t), p_*(y, t), { \rho_*(t)}\right)$. By periodicity and symmetry, we not only give symmetry-breaking periodic solutions for all positive parameter $\gamma_j$, but also show the existence of a plethora of periodic bifurcations. For the free boundary tumor problem, this is the first result of the existence of periodic bifurcations.

math.AP↗

arXiv2025

Imaging-based Quantum Optomechanics

In active imaging protocols, information about an object is encoded into the spatial mode of a scattered photon. Recently the quantum limits of active imaging have been explored with levitated nanoparticles, which experience a multimode radiation pressure backaction (the photon recoil force) due to radiative scattering of the probe field. Here we extend the analysis of multimode backaction to compliant surfaces, accessing a broad class of mechanical resonators and fruitful analogies to quantum imaging. As an example, we consider imaging of the flexural modes of a membrane by sorting the spatial modes of a laser reflected from its surface. We show that backaction in this setting can be understood to arise from spatiotemporal photon shot noise, an effect that cannot be observed in single-mode optomechanics. We also derive the imprecision-backaction product in the limit of purely spatial (intermodal) coupling, revealing it to be equivalent to the standard quantum limit for single-mode optomechanical coupling. Finally, we show that optomechanical correlations due to spatiotemporal backaction can give rise to two-mode entangled light, providing a mechanism for entangling desired pairs of spatial modes. In conjunction with high-Q nanomechanics, our findings point to new opportunities at the interface of quantum imaging and optomechanics, including sensors and networks enhanced by spatial mode entanglement.

quant-ph↗

arXiv2024

Quantum limited imaging of a nanomechanical resonator with a spatial mode sorter

We explore the use of a spatial mode sorter to image a nanomechanical resonator, with the goal of studying the quantum limits of active imaging and extending the toolbox for optomechanical force sensing. In our experiment, we reflect a Gaussian laser beam from a vibrating nanoribbon and pass the reflected beam through a commercial spatial mode demultiplexer (Cailabs Proteus). The intensity in each demultiplexed channel depends on the mechanical mode shapes and encodes information about their displacement amplitudes. As a concrete demonstration, we monitor the angular displacement of the ribbon's fundamental torsion mode by illuminating in the fundamental Hermite-Gauss mode (HG$_{00}$) and reading out in the HG$_{01}$ mode. We show that this technique permits readout of the ribbon's torsional vibration with a precision near the quantum limit. Our results highlight new opportunities at the interface of quantum imaging and quantum optomechanics.

quant-ph↗

arXiv2024

Optimum classical beam position sensing

Beam displacement measurements are widely used in optical sensing and communications; however, their performance is affected by numerous intrinsic and extrinsic factors including beam profile, propagation loss, and receiver architecture. Here we present a framework for designing a classically optimal beam displacement transceiver, using quantum estimation theory. We consider the canonical task of estimating the position of a diffraction-limited laser beam after passing through an apertured volume characterized by Fresnel-number product DF. As a rule of thumb, higher-order Gaussian modes provide more information about beam displacement, but are more sensitive to loss. Applying quantum Fisher information, we design mode combinations that optimally leverage this trade-off, and show that a greater than 10-fold improvement in precision is possible, relative to the fundamental mode, for a practically relevant DF = 100. We also show that this improvement is realizable with a variety of practical receiver architectures. Our findings extend previous works on lossless transceivers, may have immediate impact on applications such as atomic force microscopy and near-field optical communication, and pave the way towards globally optimal transceivers using non-classical laser fields.

physics.optics↗

arXiv2021

The existence of periodic solution and asymptotic behavior of solutions for a multi-layer tumor model with a periodic provision of external nutrients

In this paper, we consider a multi-layer tumor model with a periodic provision of external nutrients. The domain occupied by tumor has a different shape (flat shape) than spherical shape which has been studied widely. The important parameters are periodic external nutrients $Φ(t)$ and threshold concentration for proliferation $\widetildeσ$. In this paper, we give a complete classification about $Φ(t)$ and $\widetildeσ$ according to global stability of zero equilibrium solution or global stability of the positive periodic solution. Precisely, if $\frac{1}{T} \int_{0}^{T} Φ(t)d t\leqslant\widetildeσ$, then the zero equilibrium solution is globally stable while if $\frac{1}{T} \int_{0}^{T} Φ(t)d t>\widetildeσ$, then there exists a unique positive T-periodic solution and it is globally stable.

math.AP↗

arXiv2021

The linear stability for a free boundary problem modeling multi-layer tumor growth with time delay

We study a free boundary problem modeling multi-layer tumor growth with a small time delay $τ$, representing the time needed for the cell to complete the replication process. The model consists of two elliptic equations which describe the concentration of nutrient and the tumor tissue pressure, respectively, an ordinary differential equation describing the cell location characterizing the time delay and a partial differential equation for the free boundary. In this paper we establish the well-posedness of the problem, namely, first we prove that there exists a unique flat stationary solution $(σ_*, p_*, ρ_*, ξ_* )$ for all $μ>0$. The stability of this stationary solution should depend on the tumor aggressiveness constant $μ$. It is also unrealistic to expect the perturbation to be flat. We show that, under non-flat perturbations, there exists a threshold $μ_*>0$ such that $(σ_*, p_*, ρ_*, ξ_*)$ is linearly stable if $μ<μ_*$ and linearly unstable if $μ>μ_*$. Furthermore, the time delay increases the stationary tumor size. These are interesting results with mathematical and biological implications.

math.AP↗

arXiv2021

Performance Analysis of Free-space Quantum Key Distribution Using Multiple Spatial Modes

In the diffraction-limited near-field propagation regime, free-space optical quantum key distribution (QKD) systems can employ multiple spatial modes to improve their key rate. Here, we analyze QKD using the non-orthogonal flat-top focused beams. Although they suffer from a rate penalty, their ease of implementation makes them an attractive alternative to the well-studied orthonormal Laguerre-Gauss (LG) modes. Indeed, in the presence of turbulence, the non-orthogonal modes may achieve higher QKD rate than the LG modes.

quant-ph↗

arXiv2020

The existence and linear stability of periodic solution for a free boundary problem modeling tumor growth with a periodic supply of external nutrients

We study a free boundary problem modeling tumor growth with a T-periodic supply $Φ(t)$ of external nutrients. The model contains two parameters $μ$ and $\widetildeσ$. We first show that (i) zero radially symmetric solution is globally stable if and only if $\widetildeσ\ge \frac{1}{T} \int_{0}^{T} Φ(t) d t$; (ii) If $\widetildeσ<\frac{1}{T} \int_{0}^{T} Φ(t) d t$, then there exists a unique radially symmetric positive solution $\left(σ_{*}(r, t), p_{*}(r, t), R_{*}(t)\right)$ with period $T$ and it is a global attractor of all positive radially symmetric solutions for all $μ>0$. These results are a perfect answer to open problems in Bai and Xu [Pac. J. Appl. Math. 2013(5), 217-223]. Then, considering non-radially symmetric perturbations, we prove that there exists a constant $μ_{\ast}>0$ such that $\left(σ_{*}(r, t), p_{*}(r, t), R_{*}(t)\right)$ is linearly stable for $μ<μ_{\ast}$ and linearly unstable for $μ>μ_{\ast}$.

math.AP↗