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Xiaogang Liu

Publications and source records attributed to Xiaogang Liu.

At least 37 records · Page 2Linked to original sources
arXiv2024

Robust Nuclear Spin Polarization via Ground-State Level Anti-Crossing of Boron Vacancy Defects in Hexagonal Boron Nitride

Nuclear spin polarization plays a crucial role in quantum information processing and quantum sensing. In this work, we demonstrate a robust and efficient method for nuclear spin polarization with boron vacancy ($\mathrm{V_B^-}$) defects in hexagonal boron nitride (h-BN) using ground-state level anti-crossing (GSLAC). We show that GSLAC-assisted nuclear polarization can be achieved with significantly lower laser power than excited-state level anti-crossing, making the process experimentally more viable. Furthermore, we have demonstrated direct optical readout of nuclear spins for $\mathrm{V_B^-}$ in h-BN. Our findings suggest that GSLAC is a promising technique for the precise control and manipulation of nuclear spins in $\mathrm{V_B^-}$ defects in h-BN.

quant-ph↗
arXiv2024

So's conjecture for integral circulant graphs of $4$ types

In [Discrete Mathematics 306 (2005) 153-158], So proposed a conjecture saying that integral circulant graphs with different connection sets have different spectra. This conjecture is still open. We prove that this conjecture holds for integral circulant graphs whose orders have prime factorization of $4$ types.

math.CO↗
arXiv2024

Fractional revival on Cayley graphs over abelian groups

In this paper, we investigate the existence of fractional revival on Cayley graphs over finite abelian groups. We give a necessary and sufficient condition for Cayley graphs over finite abelian groups to have fractional revival. As applications, the existence of fractional revival on circulant graphs and cubelike graphs are characterized.

math.CO↗
arXiv2024

Integral Cayley graphs over a group of order $6n$

In this paper, we study the integral Cayley graphs over a non-abelian group $U_{6n}=\langle a,b\mid a^{2n}=b^3=1, a^{-1}ba=b^{-1}\rangle$ of order $6n$. We give a necessary and sufficient condition for the integrality of Cayley graphs over $U_{6n}$. We also study relationships between the integrality of Cayley graphs over $U_{6n}$ and the Boolean algebra of cyclic groups. As applications, we construct some infinite families of connected integral Cayley graphs over $U_{6n}$.

math.CO↗
arXiv2024

Algebraic degrees of $n$-Cayley digraphs over abelian groups

A digraph is called an $n$-Cayley digraph if its automorphism group has an $n$-orbit semiregular subgroup. We determine the splitting fields of $n$-Cayley digraphs over abelian groups and compute a bound on their algebraic degrees, before applying our results on Cayley digraphs over non-abelian groups.

math.CO↗
arXiv2023

Pretty good fractional revival on Cayley graphs over dicyclic groups

In this paper, we investigate the existence of pretty good fractional revival on Cayley graphs over dicyclic groups. We first give a necessary and sufficient description for Cayley graphs over dicyclic groups admitting pretty good fractional revival. By this description, we give some sufficient conditions for Cayley graphs over dicyclic groups admitting or not admitting pretty good fractional revival.

math.CO↗
arXiv2023

Fractional revival on semi-Cayley graphs over abelian groups

In this paper, we investigate the existence of fractional revival on semi-Cayley graphs over finite abelian groups. We give some necessary and sufficient conditions for semi-Cayley graphs over finite abelian groups admitting fractional revival. We also show that integrality is necessary for some semi-Cayley graphs admitting fractional revival. Moreover, we characterize the minimum time when semi-Cayley graphs admit fractional revival. As applications, we give examples of certain Cayley graphs over the generalized dihedral groups and generalized dicyclic groups admitting fractional revival.

math.CO↗
arXiv2023

Interlayer donor-acceptor pair excitons in MoSe2/WSe2 moiré heterobilayer

Localized interlayer excitons (LIXs) in two-dimensional moiré superlattices exhibit sharp and dense emission peaks, making them promising as highly tunable single-photon sources. However, the fundamental nature of these LIXs is still elusive. Here, we show the donor-acceptor pair (DAP) mechanism as one of the origins of these excitonic peaks. Numerical simulation results of the DAP model agree with the experimental photoluminescence spectra of LIX in the moiré MoSe2/WSe2 heterobilayer. In particular, we find that the emission energy-lifetime correlation and the nonmonotonic power dependence of the lifetime agree well with the DAP IX model. Our results provide insight into the physical mechanism of LIX formation in moiré heterostructures and pave new directions for engineering interlayer exciton properties in moiré superlattices.

cond-mat.mes-hall↗
arXiv2022

Excited-state optically detected magnetic resonance of spin defects in hexagonal boron nitride

Negatively charged boron vacancy (VB-) centers in hexagonal boron nitride (hBN) are promising spin defects in a van der Waals crystal. Understanding the spin properties of the excited state (ES) is critical for realizing dynamic nuclear polarization. Here, we report zero-field splitting in the ES of DES = 2160 MHz and an optically detected magnetic resonance (ODMR) contrast of 12% at cryogenic temperature. The ES has a g-factor similar to the ground state. The ES photodynamics is further elucidated by measuring the level anti-crossing of the VB- defects under varying external magnetic fields. In contrast to nitrogen vacancy (NV-) centers in diamond, the emission change caused by excited-state level anti-crossing (ESLAC) is more prominent at cryo-temperature than at room temperature. Our results provide important information for utilizing the spin defects of hBN in quantum technology.

cond-mat.mes-hall↗
arXiv2022

Laplacian pretty good edge state transfer in paths

In this paper, we first give a necessary and sufficient condition for a graph to have Laplacian pretty good pair state transfer. As an application of such result, we give a complete characterization of Laplacian pretty good edge state transfer in paths.

math.CO↗
arXiv2022

Tri-Functional Metasurface for Phase, Amplitude, and Luminescence Control

In optical anti-counterfeiting, several distinct optically variable devices (OVDs) are often concurrently employed to compensate for the insufficient security level of constituent OVDs. Alternatively, metasurfaces that exhibit multiple optical responses effectively combine multiple OVDs into one, thus significantly enhancing their security and hindering fraudulent replication. This work demonstrates the simultaneous control of three separate optical responses, i.e., phase, amplitude, and luminescence, using anisotropic gap-plasmon metasurfaces. Due to the incorporated geometric anisotropy, the designed structure exhibits distinct responses under x- and y-polarized light, revealing either a color image, or a holographic projection in the far field. Furthermore, inserting upconversion nanoparticles (UCNPs) into the dielectric gaps of the structures, the designed metasurface is able to generate a third luminescent image upon illumination with the near-infrared light. The stochastic distribution of the UCNPs constitutes a unique fingerprint, achieving a physically unclonable function (PUF) layer. Crucially, our triple-mode metasurface requires only readily attainable equipment such as a macro-lens/camera and a laser pointer to read most of the channels, thus paving the way towards highly secure and easy-to-authenticate metasurface-driven OVDs (mOVDs).

physics.optics↗
arXiv2022

Eigenvalues of Cayley graphs

We survey some of the known results on eigenvalues of Cayley graphs and their applications, together with related results on eigenvalues of Cayley digraphs and generalizations of Cayley graphs.

math.CO↗
arXiv2022

State transfers in vertex complemented coronas

In this paper, we study the existence of perfect state transfer and pretty good state transfer in vertex complemented coronas. We prove that perfect state transfer in vertex complemented coronas is extremely rare. In contrast, we give sufficient conditions for vertex complemented coronas to have pretty good state transfer.

quant-ph↗
arXiv2022

Laplacian state transfer in vertex complemented coronas

In this paper, we investigate the existence of Laplacian perfect state transfer and Laplacian pretty good state transfer in vertex complemented coronas. We prove that there is no Laplacian perfect state transfer in vertex complemented coronas. In contrast, we give a sufficient condition for vertex complemented coronas to have Laplacian pretty good state transfer.

quant-ph↗
arXiv2022

Constructing graphs having Laplacian pair state transfer by an edge perturbation

In this paper, we give some sufficient conditions for graphs with an edge perturbation between twin vertices to have Laplacian perfect pair state transfer as well as Laplacian pretty good pair state transfer. By those sufficient conditions, we also construct many new graphs having Laplacian perfect pair state transfer as well as Laplacian pretty good pair state transfer.

quant-ph↗
arXiv2020

Perfect state transfer in NEPS of complete graphs

Perfect state transfer in graphs is a concept arising from quantum physics and quantum computing. Given a graph $G$ with adjacency matrix $A_G$, the transition matrix of $G$ with respect to $A_G$ is defined as $H_{A_{G}}(t) = \exp(-\mathrm{i}tA_{G})$, $t \in \mathbb{R},\ \mathrm{i}=\sqrt{-1}$. We say that perfect state transfer from vertex $u$ to vertex $v$ occurs in $G$ at time $τ$ if $u \ne v$ and the modulus of the $(u,v)$-entry of $H_{A_G}(τ)$ is equal to $1$. If the moduli of all diagonal entries of $H_{A_G}(τ)$ are equal to $1$ for some $τ$, then $G$ is called periodic with period $τ$. In this paper we give a few sufficient conditions for NEPS of complete graphs to be periodic or exhibit perfect state transfer.

math.CO↗
arXiv2019

Some results about permutation properties of a kind of binomials over finite fields

Permutation polynomials have many applications in finite fields theory, coding theory, cryptography, combinatorial design, communication theory, and so on. Permutation binomials of the form $x^{r}(x^{q-1}+a)$ over $\mathbb{F}_{q^2}$ have been studied before, K. Li, L. Qu and X. Chen proved that they are permutation polynomials if and only if $r=1$ and $a^{q+1}\not=1$. In this paper, we consider the same binomial, but over finite fields $\mathbb{F}_{q^3}$ and $\mathbb{F}_{q^e}$. Two different kinds of methods are employed, and some partial results are obtained for them.

cs.IT↗