arXiv subjects

Jing-Yi Liu

Publications and source records attributed to Jing-Yi Liu.

4 recordsLinked to original sources

arXiv2026

Quantum Wave-Particle Duality in Free-Electron--Free-Electron Entanglement

Point-particle descriptions of electron-electron interaction omit the coherent longitudinal extent of a free-electron quantum wave packet (QEW). A relativistic two-electron wave-packet theory identifies the longitudinal QEW size as a direct control parameter for entanglement generated by mutual electromagnetic coupling. For two electrons in spatially separated paths, the quadratic interaction phase gives a dimensionless entangling parameter $\Gee$ and the logarithmic negativity $\EN=\operatorname{arsinh}(\Gee)/\ln2$. Full time-dependent Schrödinger equation calculations confirm the scaling for narrow QEWs and reveal higher-order Coulomb effects at larger spatial extent. Free drift increases the interaction-point QEW width while preserving the momentum probability distribution, thereby enhancing the subsequently generated entanglement. The results establish a direct connection between free-electron wave-particle duality and bipartite entanglement.

quant-ph↗

arXiv2026

Heralded Generation of Multipartite Free-Electron W-State Entanglement

We propose a heralded protocol for generating multipartite free-electron entanglement from atomic $W_N$ resources in a sideband-resolved interaction regime. The scheme consists of $N$ independent electron--atom interaction arms, where each free electron couples locally to one two-level system. For uniform couplings and common detuning, the dynamics is solved analytically within the rotating-wave approximation. Projecting the atoms onto the all-ground state maps the initial atomic excitation manifold onto the electronic upper-sideband manifold and prepares an exact $N$-electron $W_N$-type state. The heralding probability is obtained in closed form for resonant and detuned regimes. At resonance, the optimal success probability obeys the large-$N$ scaling $P_{G_N}^{\max}\sim e^{-1}/N$. The heralded state retains the multipartite entanglement structure of the atomic resource, as shown for arbitrary $N$ and illustrated explicitly for $N=3$. Detuning, weak symmetry breaking, beyond-rotating-wave corrections, and Gaussian coupling envelopes are discussed. The protocol provides a scalable route toward multipartite free-electron entanglement generation from localized atomic resources within quantum electron optics.

quant-ph↗

arXiv2018

Combinatorial proofs of some properties of tangent and Genocchi numbers

The tangent number $T_{2n+1}$ is equal to the number of increasing labelled complete binary trees with $2n+1$ vertices. This combinatorial interpretation immediately proves that $T_{2n+1}$ is divisible by $2^n$. However, a stronger divisibility property is known in the studies of Bernoulli and Genocchi numbers, namely, the divisibility of $(n+1)T_{2n+1}$ by $2^{2n}$. The traditional proofs of this fact need significant calculations. In the present paper, we provide a combinatorial proof of the latter divisibility by using the hook length formula for trees. Furthermore, our method is extended to $k$-ary trees, leading to a new generalization of the Genocchi numbers.

math.CO↗

arXiv2015

Controlling photon transport in the single-photon weak-coupling regime of cavity optomechanics

We study the photon statistics properties of few-photon transport in an optomechanical system where an optomechanical cavity couples to two empty cavities. By analytically deriving the one- and two-photon currents in terms of a zero-time-delayed two-order correlation function, we show that a photon blockade can be achieved in both the single-photon strong-coupling regime and the single-photon weak-coupling regime due to the nonlinear interacting and multipath interference. Furthermore, our systems can be applied as a quantum optical diode, a single-photon source, and a quantum optical capacitor. It is shown that this the photon transport controlling devices based on photon antibunching does not require the stringent single-photon strong-coupling condition. Our results provide a promising platform for the coherent manipulation of optomechanics, which has potential applications for quantum information processing and quantum circuit realization.

quant-ph↗