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As a bridge connecting the matching polynomial and the Laplacian matching polynomial of graphs, the subdivision method is expected to be useful for investigating the Laplacian matching polynomial. In this paper, we study applications of the method from three aspects. We prove that the zero sequence of the Laplacian matching polynomial of a graph majorizes its degree sequence, establishing a dual relation between the Laplacian matching polynomial and the characteristic polynomial of the signless Laplacian matrix of graphs. In addition, from different viewpoints, we give a new combinatorial interpretations for the coefficients of the Laplacian matching polynomial.

We propose an experimental scheme to realize non-Abelian dynamical gauge field for ultracold fermions, which induces a novel pairing mechanism of topological superfluidity. The dynamical gauge fields arise from nontrivial interplay effect between the strong Zeeman splitting and Hubbard interaction in a two-dimensional (2D) optical Raman lattice. The spin-flip transitions are forbidden by the large Zeeman detuning, but are restored when the Zeeman splitting is compensated by Hubbard interaction. This scheme allows to generate a dynamical non-Abelian gauge field that leads to a Dirac type correlated 2D spin-orbit interaction depending on local state configurations. The topological superfluid from a novel pairing driven by 2D dynamical gauge fields is reached, with analytic and numerical results being obtained. Our work may open up a door to emulate non-Abelian dynamical gauge fields and correlated topological phases with experimental feasibility., Comment: 5+7 pages, 4+6 figures

The non-Hermitian skin effect (NHSE) refers to that an extensive number of eigenstates of a non-Hermitian system are localized in open boundaries. Here we predict a universal phenomenon that with local particle-hole(-like) symmetry (PHS) the skin modes must be equally distributed on different boundaries, manifesting a novel nonlocalization of the local PHS, which is unique to non-Hermitian systems. We develop a generic theory for the emergent nonlocal symmetry-protected NHSE by connecting the non-Hermitian system to an extended Hermitian Hamiltonian in a quadruplicate Hilbert space, which maps the skin modes to the topological zero modes and the PHS to an emergent nonlocal symmetry in the perspective of many body physics. The predicted NHSE is robust against perturbations. We propose optical Raman lattice models to observe the predicted phenomena in all physical dimensions, which are accessible with cold-atom experiments., Comment: 5+9 pages, 3+4 figures

We study the anomalous Hall effect (AHE) in tilted Weyl metals with weak Gaussian disorder under the Kubo-Streda formalism in this work. To separate the three different contributions, namely the intrinsic, side jump and skew scattering contribution, it is usually considered necessary to go to the eigenstate (chiral) basis of the Kubo-Streda formula. However, it is more straight-forward to compute the total Hall current in the spin basis. For the reason, we develop a systematic and transparent scheme to separate the three different contributions in the spin basis for relativistic systems by building a one-to-one correspondence between the Feynman diagrams of the different mechanisms in the chiral basis and the products of the symmetric and anti-symmetric part of the polarization operator in the spin basis. We obtain the three contributions of the AHE in tilted Weyl metals by this scheme and found that the side jump contribution exceeds both the intrinsic and skew scattering contribution for the low-energy effective Hamiltonian. We compared the anomalous Hall current obtained from our scheme with the results from the semi-classical Boltzmann equation approach under the relaxation time approximation and found that the results from the two approaches agree with each other in the leading order of the tilting velocity.

We perform quantum logic spectroscopy (QLS) on $^{27}$Al$^+$ ion $^1$S$_0$ - $^3$P$_1$ transition, which is an important step toward the QLS based $^{27}$Al$^+$ ion optical clock. As a precondition of QLS, both the stretch (STR) mode and the common (COM) mode of the $^{27}$Al$^+$ and $^{25}$Mg$^+$ ions pair are cooled to the vibrational ground state by Raman sideband cooling. The mean phonon number is measured to be 0.10(1) for the STR mode and 0.01(1) for the COM mode, respectively. The heating rate is evaluated to be 13(3) phonons/s for the STR mode and 5.5(1) phonons/s for the COM mode., Comment: 5 pages,4 figures

The third-generation gravitational wave detectors are under development by operating the detector in cryogenic temperature to reduce the thermal noise. Silicon and sapphire are promising candidate materials for the test masses and suspension elements due to their remarkable mechanical and thermal properties at cryogenic temperature. Here we present the performances of the cryogenic thermal cycling and strength testing on hydroxide catalysis bonding between sapphire and silicon. Our results suggest that although these two materials have very different coefficients of thermal expansion, but if the flatness and the thermally grown $\mathrm{SiO_2}$ oxidation layer on the silicon surface are controlled well, the bonded samples can still survive thermal cycling from room temperature to 5.5 K. A breaking strength of 3.6$\pm 0.6$ MPa is measured for the bonds between sapphire and silicon with a 190 nm silicon oxidation thickness after cooling cycle. We construct a hybrid sapphire-silicon Fabry-Perot cavity with the developing bonding technique in our lab. The measurement results reveal that the cavity can survive repeated thermal cycling while maintaining a good finesse.