Suppression of collisional shifts in a strongly interacting lattice clock

Optical lattice clocks have the potential for extremely high frequency stability owing to the simultaneous interrogation of many atoms, but this precision may come at the cost of systematic inaccuracy due to atomic interactions. Density-dependent frequency shifts can occur even in a clock that uses fermionic atoms if they are subject to inhomogeneous optical excitation [1, 2]. Here we present a seemingly paradoxical solution to this problem. By dramatically increasing the strength of atomic interactions, we suppress collisional shifts in lattice sites containing $N$ > 1 atoms; strong interactions introduce an energy splitting into the system, and evolution into a many-particle state in which collisions occur is inhibited. We demonstrate the effectiveness of this approach with the JILA Sr lattice clock by reducing both the collisional frequency shift and its uncertainty by more than a factor of ten [3], to the level of $10^{-17}$. This result eliminates the compromise between precision and accuracy in a many-particle system, since both will continue to improve as the particle number increases.Comment: 13 pages, 6 figure

Topological Quantum Phase Transition in Synthetic Non-Abelian Gauge Potential

The method of synthetic gauge potentials opens up a new avenue for our understanding and discovering novel quantum states of matter. We investigate the topological quantum phase transition of Fermi gases trapped in a honeycomb lattice in the presence of a synthetic non- Abelian gauge potential. We develop a systematic fermionic effective field theory to describe a topological quantum phase transition tuned by the non-Abelian gauge potential and ex- plore its various important experimental consequences. Numerical calculations on lattice scales are performed to compare with the results achieved by the fermionic effective field theory. Several possible experimental detection methods of topological quantum phase tran- sition are proposed. In contrast to condensed matter experiments where only gauge invariant quantities can be measured, both gauge invariant and non-gauge invariant quantities can be measured by experimentally generating various non-Abelian gauges corresponding to the same set of Wilson loops

Analysis of Power-aware Buffering Schemes in Wireless Sensor Networks

We study the power-aware buffering problem in battery-powered sensor networks, focusing on the fixed-size and fixed-interval buffering schemes. The main motivation is to address the yet poorly understood size variation-induced effect on power-aware buffering schemes. Our theoretical analysis elucidates the fundamental differences between the fixed-size and fixed-interval buffering schemes in the presence of data size variation. It shows that data size variation has detrimental effects on the power expenditure of the fixed-size buffering in general, and reveals that the size variation induced effects can be either mitigated by a positive skewness or promoted by a negative skewness in size distribution. By contrast, the fixed-interval buffering scheme has an obvious advantage of being eminently immune to the data-size variation. Hence the fixed-interval buffering scheme is a risk-averse strategy for its robustness in a variety of operational environments. In addition, based on the fixed-interval buffering scheme, we establish the power consumption relationship between child nodes and parent node in a static data collection tree, and give an in-depth analysis of the impact of child bandwidth distribution on parent's power consumption. This study is of practical significance: it sheds new light on the relationship among power consumption of buffering schemes, power parameters of radio module and memory bank, data arrival rate and data size variation, thereby providing well-informed guidance in determining an optimal buffer size (interval) to maximize the operational lifespan of sensor networks

Classification and nondegeneracy of SU(n+1)SU(n+1) Toda system with singular sources

We consider the following Toda system \Delta u_i + \D \sum_{j = 1}^n a_{ij}e^{u_j} = 4\pi\gamma_{i}\delta_{0} \text{in}\mathbb R^2, \int_{\mathbb R^2}e^{u_i} dx -1$,$\delta_0$is Dirac measure at 0, and the coefficients$a_{ij}$form the standard tri-diagonal Cartan matrix. In this paper, (i) we completely classify the solutions and obtain the quantization result:$$\sum_{j=1}^n a_{ij}\int_{\R^2}e^{u_j} dx = 4\pi (2+\gamma_i+\gamma_{n+1-i}), \;\;\forall\; 1\leq i \leq n.$$This generalizes the classification result by Jost and Wang for$\gamma_i=0$,$\forall \;1\leq i\leq n$. (ii) We prove that if$\gamma_i+\gamma_{i+1}+...+\gamma_j \notin \mathbb Z$for all$1\leq i\leq j\leq n$, then any solution$u_i$ is \textit{radially symmetric} w.r.t. 0. (iii) We prove that the linearized equation at any solution is \textit{non-degenerate}. These are fundamental results in order to understand the bubbling behavior of the Toda system.Comment: 28 page

Theoretical analysis of the focusing of acoustic waves by two-dimensional sonic crystals

Motivated by a recent experiment on acoustic lenses, we perform numerical calculations based on a multiple scattering technique to investigate the focusing of acoustic waves with sonic crystals formed by rigid cylinders in air. The focusing effects for crystals of various shapes are examined. The dependance of the focusing length on the filling factor is also studied. It is observed that both the shape and filling factor play a crucial role in controlling the focusing. Furthermore, the robustness of the focusing against disorders is studied. The results show that the sensitivity of the focusing behavior depends on the strength of positional disorders. The theoretical results compare favorably with the experimental observations, reported by Cervera, et al. (Phys. Rev. Lett. 88, 023902 (2002)).Comment: 8 figure

Biharmonic Riemannian submersions from 3-manifolds

An important theorem about biharmonic submanifolds proved independently by Chen-Ishikawa [CI] and Jiang [Ji] states that an isometric immersion of a surface into 3-dimensional Euclidean space is biharmonic if and only if it is harmonic (i.e, minimal). In a later paper [CMO2], Cadeo-Monttaldo-Oniciuc shown that the theorem remains true if the target Euclidean space is replaced by a 3-dimensional hyperbolic space form. In this paper, we prove the dual results for Riemannian submersions, i.e., a Riemannian submersion from a 3-dimensional space form of non-positive curvature into a surface is biharmonic if and only if it is harmonic

Observation of electron-antineutrino disappearance at Daya Bay

The Daya Bay Reactor Neutrino Experiment has measured a non-zero value for the neutrino mixing angle $\theta_{13}$ with a significance of 5.2 standard deviations. Antineutrinos from six 2.9 GW$_{\rm th}$ reactors were detected in six antineutrino detectors deployed in two near (flux-weighted baseline 470 m and 576 m) and one far (1648 m) underground experimental halls. With a 43,000 ton-GW_{\rm th}-day livetime exposure in 55 days, 10416 (80376) electron antineutrino candidates were detected at the far hall (near halls). The ratio of the observed to expected number of antineutrinos at the far hall is $R=0.940\pm 0.011({\rm stat}) \pm 0.004({\rm syst})$. A rate-only analysis finds $\sin^22\theta_{13}=0.092\pm 0.016({\rm stat})\pm0.005({\rm syst})$ in a three-neutrino framework.Comment: 5 figures. Version to appear in Phys. Rev. Let