Quantum Spin Dynamics with Pairwise-Tunable, Long-Range Interactions

We present a platform for the simulation of quantum magnetism with full control of interactions between pairs of spins at arbitrary distances in one- and two-dimensional lattices. In our scheme, two internal atomic states represent a pseudo-spin for atoms trapped within a photonic crystal waveguide (PCW). With the atomic transition frequency aligned inside a band gap of the PCW, virtual photons mediate coherent spin-spin interactions between lattice sites. To obtain full control of interaction coefficients at arbitrary atom-atom separations, ground-state energy shifts are introduced as a function of distance across the PCW. In conjunction with auxiliary pump fields, spin-exchange versus atom-atom separation can be engineered with arbitrary magnitude and phase, and arranged to introduce non-trivial Berry phases in the spin lattice, thus opening new avenues for realizing novel topological spin models. We illustrate the broad applicability of our scheme by explicit construction for several well known spin models.Comment: 18 pages, 10 figure

Mining and Incentive Concession Contracts

This paper studies the design of a mining concession contract as a multi-period autoselection problem where production is the depletion of a non renewable resource. As compared to symmetric information, we show that overproduction (resp. underproduction) is optimal in the initial phase (resp. terminal phase ) of the resource extraction program. Also, asymmetric information lengthens the contract duration but reduces the scarcity rent. Finally, when there are several agents competing for contract bid, we show that optimal auctioning could be used to award the concession, assigning the lowest cost agent to carry out the extraction.ADVERSE SELECTION; EXHAUSTIBILITY; OVERPRODUCTION

Computer-aided design of bevel gear tooth surfaces

This paper presents a computer-aided design procedure for generating bevel gears. The development is based on examining a perfectly plastic, cone-shaped gear blank rolling over a cutting tooth on a plane crown rack. The resulting impression on the plastic gear blank is the envelope of the cutting tooth. This impression and envelope thus form a conjugate tooth surface. Equations are presented for the locus of points on the tooth surface. The same procedures are then extended to simulate the generation of a spiral bevel gear. The corresponding governing equations are presented

Quantum many-body models with cold atoms coupled to photonic crystals

Using cold atoms to simulate strongly interacting quantum systems represents an exciting frontier of physics. However, as atoms are nominally neutral point particles, this limits the types of interactions that can be produced. We propose to use the powerful new platform of cold atoms trapped near nanophotonic systems to extend these limits, enabling a novel quantum material in which atomic spin degrees of freedom, motion, and photons strongly couple over long distances. In this system, an atom trapped near a photonic crystal seeds a localized, tunable cavity mode around the atomic position. We find that this effective cavity facilitates interactions with other atoms within the cavity length, in a way that can be made robust against realistic imperfections. Finally, we show that such phenomena should be accessible using one-dimensional photonic crystal waveguides in which coupling to atoms has already been experimentally demonstrated

Superradiance for atoms trapped along a photonic crystal waveguide

We report observations of superradiance for atoms trapped in the near field of a photonic crystal waveguide (PCW). By fabricating the PCW with a band edge near the D$_1$ transition of atomic cesium, strong interaction is achieved between trapped atoms and guided-mode photons. Following short-pulse excitation, we record the decay of guided-mode emission and find a superradiant emission rate scaling as $\bar{\Gamma}_{\rm SR}\propto\bar{N}\cdot\Gamma_{\rm 1D}$ for average atom number $0.19 \lesssim \bar{N} \lesssim 2.6$ atoms, where $\Gamma_{\rm 1D}/\Gamma_0 =1.1\pm0.1$ is the peak single-atom radiative decay rate into the PCW guided mode and $\Gamma_{0}$ is the Einstein-$A$ coefficient for free space. These advances provide new tools for investigations of photon-mediated atom-atom interactions in the many-body regime.Comment: 11 pages, 10 figure

Sloshing dynamics modulated fluid angular momentum and moment fluctuations driven by orbital gravity gradient and jitter accelerations in microgravity

The dynamical behavior of spacecraft propellant affected by the asymmetric combined gravity gradient and jitter accelerations, in particular the effect of surface tension on partially-filled rotating fluids applicable to a full-scale Gravity Probe-B Spacecraft dewar tank has been investigated. Three different cases of orbital accelerations: (1) gravity gradient-dominated, (2) equally weighted between gravity gradient and jitter, and (3) gravity jitter-dominated accelerations are studied. The results of slosh wave excitation along the liquid-vapor interface induced by gravity gradient-dominated accelerations provide a torsional moment with tidal motion of bubble oscillations in the rotating dewar. The results are clearly seen from the twisting shape of the bubble oscillations driven by gravity gradient-dominated acceleration. The results of slosh wave excitation along the liquid-vapor interface induced by gravity jitter-dominated acceleration indicate the results of bubble motion in a manner of down-and-up and leftward-and-rightward movement of oscillation when the bubble is rotating with respect to rotating dewar axis. Fluctuations of angular momentum, fluid moment and bubble mass center caused by slosh wave excitations driven by gravity gradient acceleration or gravity jitter acceleration are also investigated

Interaction induced ferro-electricity in the rotational states of polar molecules

We show that a ferro-electric quantum phase transition can be driven by the dipolar interaction of polar molecules in the presence a micro-wave field. The obtained ferro-electricity crucially depends on the harmonic confinement potential, and the resulting dipole moment persists even when the external field is turned off adiabatically. The transition is shown to be second order for fermions and for bosons of a smaller permanent dipole moment, but is first order for bosons of a larger moment. Our results suggest the possibility of manipulating the microscopic rotational state of polar molecules by tuning the trap's aspect ratio (and other mesoscopic parameters), even though the later's energy scale is smaller than the former's by six orders of magnitude.Comment: 4 pages and 4 figure

Three-dimensional transient flow of spin-up in a filled cylinder with oblique gravity force

Three-dimensional transient flow profiles of spin-up in a fully liquid filled cylinder from rest with gravity acceleration at various direction are numerically simulated and studied. Particular interests are concentrated on the development of temporary reverse flow zones and Ekman layer right after the impulsive start of spin-up from rest, and decay before the flow reaching to the solid rotation. Relationship of these flow developments and differences in the Reynolds numbers of the flow and its size selection of grid points concerning the numerical instabilities of flow computations are also discussed. In addition to the gravitational acceleration along the axial direction of the cylindrical container, a series of complicated flow profiles accompanied by three-dimensional transient flows with oblique gravitational acceleration has been studies