Three-State Feshbach Resonances Mediated By Second-Order Couplings

We present an analytical study of three-state Feshbach resonances induced by second-order couplings. Such resonances arise when the scattering amplitude is modified by the interaction with a bound state that is not directly coupled to the scattering state containing incoming flux. Coupling occurs indirectly through an intermediate state. We consider two problems: (i) the intermediate state is a scattering state in a distinct open channel; (ii) the intermediate state is an off-resonant bound state in a distinct closed channel. The first problem is a model of electric-field-induced resonances in ultracold collisions of alkali metal atoms [Phys. Rev. A 75, 032709 (2007)] and the second problem is relevant for ultracold collisions of complex polyatomic molecules, chemical reaction dynamics, photoassociation of ultracold atoms, and electron - molecule scattering. Our analysis yields general expressions for the energy dependence of the T-matrix elements modified by three-state resonances and the dependence of the resonance positions and widths on coupling amplitudes for the weak-coupling limit. We show that the second problem can be generalized to describe resonances induced by indirect coupling through an arbitrary number of sequentially coupled off-resonant bound states and analyze the dependence of the resonance width on the number of the intermediate states.Comment: 27 pages, 4 figures; added a reference; journal reference/DOI refer to final published version, which is a shortened and modified version of this preprin

A nilpotent IP polynomial multiple recurrence theorem

We generalize the IP-polynomial Szemer\'edi theorem due to Bergelson and McCutcheon and the nilpotent Szemer\'edi theorem due to Leibman. Important tools in our proof include a generalization of Leibman's result that polynomial mappings into a nilpotent group form a group and a multiparameter version of the nilpotent Hales-Jewett theorem due to Bergelson and Leibman.Comment: v4: switch to TeXlive 2016 and biblate

Long-lived memory for electronic spin in a quantum dot: Numerical analysis

Techniques for coherent control of electron spin-nuclear spin interactions in quantum dots can be directly applied in spintronics and in quantum information processing. In this work we study numerically the interaction of electron and nuclear spins in the context of storing the spin-state of an electron in a collective state of nuclear spins. We take into account the errors inherent in a realistic system: the incomplete polarization of the bath of nuclear spins and the different hyperfine interactions between the electron and individual nuclei in the quantum dot. Although these imperfections deteriorate the fidelity of the quantum information retrieval, we find reasonable fidelities are achievable for modest bath polarizations.Comment: RevTex, 10 pages, 9 EPS figure

Deterministic Assembly of Arrays of Lithographically Defined WS2 and MoS2 Monolayer Features Directly from Multilayer Sources into Van der Waals Heterostructures

One of the major challenges in the van der Waals (vdW) integration of two-dimensional (2D) materials is achieving high-yield and high-throughput assembly of predefined sequences of monolayers into heterostructure arrays. Mechanical exfoliation has recently been studied as a promising technique to transfer monolayers from a multilayer source synthesized by other techniques, allowing the deposition of a wide variety of 2D materials without exposing the target substrate to harsh synthesis conditions. Although a variety of processes have been developed to exfoliate the 2D materials mechanically from the source and place them deterministically onto a target substrate, they can typically transfer only either a wafer-scale blanket or one small flake at a time with uncontrolled size and shape. Here, we present a method to assemble arrays of lithographically defined monolayer WS2 and MoS2 features from multilayer sources and directly transfer them in a deterministic manner onto target substrates. This exfoliate-align-release process - without the need of an intermediate carrier substrate - is enabled by combining a patterned, gold-mediated exfoliation technique with a new optically transparent, heat-releasable adhesive. WS2/MoS2 vdW heterostructure arrays produced by this method show the expected interlayer exciton between the monolayers. Light-emitting devices using WS2 monolayers were also demonstrated, proving the functionality of the fabricated materials. Our work demonstrates a significant step toward developing mechanical exfoliation as a scalable dry transfer technique for the manufacturing of functional, atomically thin materials

Near-Field Focusing Sensor for Characterization of Void Content in Thin Dielectric Layers

A sensor concept is developed and analyzed for in situ characterization of a thin dielectric layer. An array of long, planar electrodes is flush-mounted into opposing faces of two substrates on either side of the dielectric layer. The substrates are oriented such that the lengthwise dimensions of the opposing electrodes are orthogonal. Capacitance is measured between single electrode pairs on opposite substrates while all other electrodes are grounded. The electric field between the active electrodes is sharply focused at their crossing point, resulting in high sensitivity to void content in a square detection zone of the dielectric layer. For a fixed interfacial gap size, direct proportionality of the capacitance with void fraction within the detection zone is poor for high electrode-to-electrode spacing on the substrates, but improves dramatically as this spacing is reduced. Three methods of deriving a simulationbased sensitivity response of measured capacitance to any arbitrary two-dimensional void geometry are investigated. The best method requires data from simulations of an empty air gap and a TIM-filled gap, and uses a reduced-order superposition technique to predict the normalized capacitance value obtained for any void geometry to within 10% of that predicted by a high-fidelity direct simulation. The sensing technique is demonstrated using manually introduced voids of 250 μm–2000 μm diameter in a 254 μm thick interface material layer with a dielectric constant of 4.7. The relationship of the capacitance to the void fraction is shown to fall within the predicted bounds

Void Detection in Dielectric Films using a Floating Network of Substrate-Embedded Electrodes

A sensor is developed for simple, in situ characterization of dielectric thermal interface materials (TIMs) at bond line thicknesses less than 100 lm. The working principle is based on the detection of regions of contrasting electric permittivity. An array of long, parallel electrodes is flush-mounted into each opposing substrate face of a narrow gap interface, and exposed to the gap formed between the two surfaces. Electrodes are oriented such that their lengthwise dimension in one substrate runs perpendicular to those in the other. A capacitance measurement taken between opposing electrodes is used to characterize the interface region in the vicinity of their crossing point (junction). The electric field associated with each electrode junction is numerically simulated and analyzed. Criteria are developed for the design of electrode junction geometries that localize the electric fields. The capacitances between floating-ground electrodes in the electrode sensor configuration employed give rise to a nontrivial network of interacting capacitances which strongly influence the measured response at any junction. A generalized solution for analyzing the floating network response is presented. The technique is used to experimentally detect thermal grease spots of 0.2mm to 1.8mm diameter within a 25 lm interface gap. It is necessary to use the generalized solution to the capacitance network developed in this work to properly delineate regions of contrasting permittivity in the interface gap region using capacitance measurements

Capacitive Sensing of Local Bond Layer Thickness and Coverage in Thermal Interface Materials

An instrumentation technique is developed using embedded capacitive sensors to measure the thickness and evenness of coverage of a thin layer of dielectric thermal interface material (TIM) between two substrates. The technique requires an array of sensors embedded into one substrate, with an electrically conductive opposing substrate. Local capacitance measurements are sensitive to both local bond layer thickness and local voiding. We propose a means for using an array of capacitance measurements to interpret both bond layer thickness and local voiding at every sensor location. An algorithm is developed which reveals both characteristics from a single set of capacitance measurements. Experiments are conducted with thermal grease layers of different bond layer thicknesses and void distributions using a prototype system constructed on printed circuit boards. The thickness and void distribution are successfully mapped across the bond layer using the algorithm developed. The technique offers a sensing approach for in situ instrumentation of layers of thermal grease in a thermal test vehicle