Resolvable Mendelsohn designs and finite Frobenius groups

We prove the existence and give constructions of a $(p(k)-1)$-fold perfect resolvable $(v, k, 1)$-Mendelsohn design for any integers $v > k \ge 2$ with $v \equiv 1 \mod k$ such that there exists a finite Frobenius group whose kernel $K$ has order $v$ and whose complement contains an element $\phi$ of order $k$, where $p(k)$ is the least prime factor of $k$. Such a design admits $K \rtimes \langle \phi \rangle$ as a group of automorphisms and is perfect when $k$ is a prime. As an application we prove that for any integer $v = p_{1}^{e_1} \ldots p_{t}^{e_t} \ge 3$ in prime factorization, and any prime $k$ dividing $p_{i}^{e_i} - 1$ for $1 \le i \le t$, there exists a resolvable perfect $(v, k, 1)$-Mendelsohn design that admits a Frobenius group as a group of automorphisms. We also prove that, if $k$ is even and divides $p_{i} - 1$ for $1 \le i \le t$, then there are at least $\varphi(k)^t$ resolvable $(v, k, 1)$-Mendelsohn designs that admit a Frobenius group as a group of automorphisms, where $\varphi$ is Euler's totient function.Comment: Final versio

Elastic Wave Scattering and Dynamic Stress Concentrations in Stretching Thick Plates with Two Cutouts by Using the Refined Dynamic Theory

Based on the refined dynamic equation of stretching plates, the elastic tension–compression wave scattering and dynamic stress concentrations in the thick plate with two cutouts are studied. In view of the problem that the shear stress is automatically satisfied under the free boundary condition, the generalized stress of the first-order vanishing moment of shear stress is considered. The numerical results indicate that, as the cutout is thick, the maximum value of the dynamic stress factor obtained using the refined dynamic theory is 19% higher than that from the solution of plane stress problems of elastic dynamics

Primary-Filling e/3 Quasiparticle Interferometer

We report experimental realization of a quasiparticle interferometer where the entire system is in 1/3 primary fractional quantum Hall state. The interferometer consists of chiral edge channels coupled by quantum-coherent tunneling in two constrictions, thus enclosing an Aharonov-Bohm area. We observe magnetic flux and charge periods h/e and e/3, equivalent to creation of one quasielectron in the island. Quantum theory predicts a 3h/e flux period for charge e/3, integer statistics particles. Accordingly, the observed periods demonstrate the anyonic statistics of Laughlin quasiparticles

Nonlinear dynamics of a cigar-shaped Bose-Einstein condensate coupled with a single cavity mode

We investigate the nonlinear dynamics of a combined system which is composed of a cigar-shaped Bose-Einstein condensate and an optical cavity. The two sides couple dispersively. This system is characterized by its nonlinearity: after integrating out the freedom of the cavity mode, the potential felt by the condensate depends on the condensate itself. We develop a discrete-mode approximation for the condensate. Based on this approximation, we map out the steady configurations of the system. It is found that due to the nonlinearity of the system, the nonlinear levels of the system can fold up in some parameter regimes. That will lead to the breakdown of adiabaticity. Analysis of the dynamical stability of the steady states indicates that the same level structure also results in optical bistability.Comment: 8 pages, 5 figure

Nuclear spin qubits in a trapped-ion quantum computer

Physical systems must fulfill a number of conditions to qualify as useful quantum bits (qubits) for quantum information processing, including ease of manipulation, long decoherence times, and high fidelity readout operations. Since these conditions are hard to satisfy with a single system, it may be necessary to combine different degrees of freedom. Here we discuss a possible system, based on electronic and nuclear spin degrees of freedom in trapped ions. The nuclear spin yields long decoherence times, while the electronic spin, in a magnetic field gradient, provides efficient manipulation, and the optical transitions of the ions assure a selective and efficient initialization and readout.Comment: 7 page

Tunable quantum spin liquidity in the 1/6th-filled breathing kagome lattice

We present measurements on a series of materials, Li$_2$In$_{1-x}$Sc$_x$Mo$_3$O$_8$, that can be described as a 1/6th-filled breathing kagome lattice. Substituting Sc for In generates chemical pressure which alters the breathing parameter non-monotonically. $\mu$SR experiments show that this chemical pressure tunes the system from antiferromagnetic long range order to a quantum spin liquid phase. A strong correlation with the breathing parameter implies that it is the dominant parameter controlling the level of magnetic frustration, with increased kagome symmetry generating the quantum spin liquid phase. Magnetic susceptibility measurements suggest that this is related to distinct types of charge order induced by changes in lattice symmetry, in line with the theory of Chen et al. [Phys. Rev. B 93, 245134 (2016)]. The specific heat for samples at intermediate Sc concentration and with minimal breathing parameter, show consistency with the predicted $U(1)$ quantum spin liquid.Comment: Accepted for publication in Physical Review Letter