arXiv subjects

Long Tian

Publications and source records attributed to Long Tian.

43 records · Page 3Linked to original sources

arXiv2017

Critical points of solutions for mean curvature equation in strictly convex and nonconvex domains

In this paper, we mainly investigate the set of critical points associated to solutions of mean curvature equation with zero Dirichlet boundary condition in a strictly convex domain and a nonconvex domain respectively. Firstly, we deduce that mean curvature equation has exactly one nondegenerate critical point in a smooth, bounded and strictly convex domain of $\mathbb{R}^{n}(n\geq2)$. Secondly, we study the geometric structure about the critical set $K$ of solutions $u$ for the constant mean curvature equation in a concentric (respectively an eccentric) spherical annulus domain of $\mathbb{R}^{n}(n\geq3)$, and deduce that $K$ exists (respectively does not exist) a rotationally symmetric critical closed surface $S$. In fact, in an eccentric spherical annulus domain, $K$ is made up of finitely many isolated critical points ($p_1,p_2,\cdots,p_l$) on an axis and finitely many rotationally symmetric critical Jordan curves ($C_1,C_2,\cdots,C_k$) with respect to an axis.

math.AP↗

arXiv2017

Spatial multiplexing of atom-photon entanglement sources using feed-forward controls and switching networks

The light-matter quantum interface that can create quantum-correlations or entanglement between a photon and one atomic collective excitation is a fundamental building block for a quantum repeater. The intrinsic limit is that the probability of preparing such non-classical atom-photon correlations has to be kept low in order to suppress multi-excitation. To enhance this probability without introducing multi-excitation errors, a promising scheme is to apply multimode memories into the interface. Significant progresses have been made in temporal, spectral, and spatial multiplexing memories, but the enhanced probability for generating the entangled atom-photon pair has not been experimentally realized. Here, by using 6 spin-wave-photon entanglement sources, a switching network and feed-forward control, we build a multiplexed light-matter interface and then demonstrate a ~6-fold (~4-fold) probability increase in generating entangled atom-photon (photon-photon) pairs. The measured compositive Bell parameter for the multiplexed interface is 2.49+-0.03 combined with a memory lifetime of up to ~60 microseconds.

quant-ph↗

arXiv2017

Measure Upper Bounds for Nodal Sets of Eigenfunctions of the bi-Harmonic Operator

In this article, we consider eigenfunctions $u$ of the bi-harmonic operator, i.e., $\triangle^2u=λ^2u$ on $Ω$ with some homogeneous linear boundary conditions. We assume that $Ω\subseteq\mathbb{R}^n$ ($n\geq2$) is a $C^{\infty}$ bounded domain, $\partialΩ$ is piecewise analytic and $\partialΩ$ is analytic except a set $Γ\subseteq\partialΩ$ which is a finite union of some compact $(n-2)$ dimensional submanifolds of $\partialΩ$. The main result of this paper is that the measure upper bounds of the nodal sets of the eigenfunctions is controlled by $\sqrtλ$. We first define a frequency function and a doubling index related to these eigenfunctions. With the help of establishing the monotonicity formula, doubling conditions and various a priori estimates, we obtain that the $(n-1)$ dimensional Hausdorff measures of nodal sets of these eigenfunctions in a ball are controlled by the frequency function and $\sqrtλ$. In order to further control the frequency function with $\sqrtλ$, we first establish the relationship between the frequency function and the doubling index, and then separate the domain $Ω$ into two parts: a domain away from $Γ$ and a domain near $Γ$, and develop iteration arguments to deal with the two cases respectively.

math.AP↗

arXiv2017

Phase diagram and neutron spin resonance of superconducting NaFe$_{1-x}$Cu$_x$As

We use transport and neutron scattering to study the electronic phase diagram and spin excitations of NaFe$_{1-x}$Cu$_x$As single crystals. Similar to Co- and Ni-doped NaFeAs, a bulk superconducting phase appears near $x\approx2\%$ with the suppression of stripe-type magnetic order in NaFeAs. Upon further increasing Cu concentration the system becomes insulating, culminating in an antiferromagnetically ordered insulating phase near $x\approx 50\%$. Using transport measurements, we demonstrate that the resistivity in NaFe$_{1-x}$Cu$_x$As exhibits non-Fermi-liquid behavior near $x\approx1.8\%$. Our inelastic neutron scattering experiments reveal a single neutron spin resonance mode exhibiting weak dispersion along $c$-axis in NaFe$_{0.98}$Cu$_{0.02}$As. The resonance is high in energy relative to the superconducting transition temperature $T_{\rm c}$ but weak in intensity, likely resulting from impurity effects. These results are similar to other iron pnictides superconductors despite the superconducting phase in NaFe$_{1-x}$Cu$_x$As is continuously connected to an antiferromagnetically ordered insulating phase near $x\approx 50\%$ with significant electronic correlations. Therefore, electron correlations is an important ingredient of superconductivity in NaFe$_{1-x}$Cu$_x$As and other iron pnictides.

cond-mat.supr-con↗

arXiv2016

Generation of narrow-band polarization-entangled photon pairs at a rubidium D1 line

Using the process of cavity-enhanced spontaneous parametric down-conversion (SPDC), we generate a narrow-band polarization-entangled photon pair resonant on the rubidium (Rb) D1 line (795 nm). The degenerate single-mode photon pair is selected by multiple temperature controlled etalons. The linewidth of generated polarization-entangled photon pairs is 15 MHz which matches the typical atomic memory bandwidth. The measured Bell parameter for the polarization-entangled photons S=2.73+-0.04 which violates the Bell-CHSH inequality by ~18 standard deviations. The presented entangled photon pair source could be utilized in quantum communication and quantum computing based on quantum memories in atomic ensemble.

quant-ph↗

arXiv2015

Simultaneous generation of two spin-wave-photon entangled states in an atomic ensemble

The generation and storage of entangled photons play important roles in quantum information technique. Spontaneous Raman scattering (SRS) in atomic ensembles provides a promising method to generate entangled photons capable of storage. In the past experiments, a spin-wave-photon entangled state is produced via SRS in an atomic ensemble, with which a pair of entangled photons is obtained. Here, we report a scheme of simultaneously generating two spin-wave-photon entangled states in an atomic ensemble by collecting Stokes photons at two different directions. Based on the obtained two atom-photon entangled sources, we generate a three-photon GHZ polarization-entangled state and conditionally prepare a polarization-entangled photon pair, respectively.

quant-ph↗

arXiv2013

Long lifetime and high-fidelity quantum memory of photonic polarization qubit by lifting Zeeman degeneracy

Long-lived and high-fidelity memory for photonic polarization qubit (PPQ) is crucial for constructing quantum networks. Here we present an EIT-based millisecond storage system in which a moderate magnetic field is applied on a cold-atom cloud to lift Zeeman degeneracy. PPQ states are stored as two magnetic-field-insensitive spin waves. Especially, the influence of magnetic-field-sensitive spin waves on the storage performances is almost totally avoided. The measured average fidelities of polarization states are 98.6% at 200 us and 78.4% at 4.5 ms, respectively.

physics.atom-ph↗