Dynamics of a two-species Bose-Einstein condensate in a double well

We study the dynamics of a two-species Bose-Einstein condensate in a double well. Such a system is characterized by the intraspecies and interspecies s-wave scattering as well as the Josephson tunneling between the two wells and the population transfer between the two species. We investigate the dynamics for some interesting regimes and present numerical results to support our conclusions. In the case of vanishing intraspecies scattering lengths and a weak interspecies scattering length, we find collapses and revivals in the population dynamics. A possible experimental implementation of our proposal is briefly discussed.Comment: 7 pages, 5 figure

Detection of a single-charge defect in a metal-oxide-semiconductor structure using vertically coupled Al and Si single-electron transistors

An Al-AlO_x-Al single-electron transistor (SET) acting as the gate of a narrow (~ 100 nm) metal-oxide-semiconductor field-effect transistor (MOSFET) can induce a vertically aligned Si SET at the Si/SiO_2 interface near the MOSFET channel conductance threshold. By using such a vertically coupled Al and Si SET system, we have detected a single-charge defect which is tunnel-coupled to the Si SET. By solving a simple electrostatic model, the fractions of each coupling capacitance associated with the defect are extracted. The results reveal that the defect is not a large puddle or metal island, but its size is rather small, corresponding to a sphere with a radius less than 1 nm. The small size of the defect suggests it is most likely a single-charge trap at the Si/SiO_2 interface. Based on the ratios of the coupling capacitances, the interface trap is estimated to be about 20 nm away from the Si SET.Comment: 5 pages and 5 figure

From random walks to distances on unweighted graphs

Large unweighted directed graphs are commonly used to capture relations between entities. A fundamental problem in the analysis of such networks is to properly define the similarity or dissimilarity between any two vertices. Despite the significance of this problem, statistical characterization of the proposed metrics has been limited. We introduce and develop a class of techniques for analyzing random walks on graphs using stochastic calculus. Using these techniques we generalize results on the degeneracy of hitting times and analyze a metric based on the Laplace transformed hitting time (LTHT). The metric serves as a natural, provably well-behaved alternative to the expected hitting time. We establish a general correspondence between hitting times of the Brownian motion and analogous hitting times on the graph. We show that the LTHT is consistent with respect to the underlying metric of a geometric graph, preserves clustering tendency, and remains robust against random addition of non-geometric edges. Tests on simulated and real-world data show that the LTHT matches theoretical predictions and outperforms alternatives.Comment: To appear in NIPS 201

Shintani functions, real spherical manifolds, and symmetry breaking operators

For a pair of reductive groups $G \supset G'$, we prove a geometric criterion for the space $Sh(\lambda, \nu)$ of Shintani functions to be finite-dimensional in the Archimedean case. This criterion leads us to a complete classification of the symmetric pairs $(G,G')$ having finite-dimensional Shintani spaces. A geometric criterion for uniform boundedness of $dim Sh(\lambda, \nu)$ is also obtained. Furthermore, we prove that symmetry breaking operators of the restriction of smooth admissible representations yield Shintani functions of moderate growth, of which the dimension is determined for $(G, G') = (O(n+1,1), O(n,1))$.Comment: to appear in Progress in Mathematics, Birkhause

Creation of collective many-body states and single photons from two-dimensional Rydberg lattice gases

The creation of collective many-body quantum states from a two-dimensional lattice gas of atoms is studied. Our approach relies on the van-der-Waals interaction that is present between alkali metal atoms when laser excited to high-lying Rydberg s-states. We focus on a regime in which the laser driving is strong compared to the interaction between Rydberg atoms. Here energetically low-lying many-particle states can be calculated approximately from a quadratic Hamiltonian. The potential usefulness of these states as a resource for the creation of deterministic single-photon sources is illustrated. The properties of these photon states are determined from the interplay between the particular geometry of the lattice and the interatomic spacing.Comment: 12 pages, 8 figure

Site-dependent charge transfer at the Pt(111)-ZnPc interface and the effect of iodine

The electronic structure of ZnPc, from sub-monolayers to thick films, on bare and iodated Pt(111) is studied by means of X-ray photoelectron spectroscopy (XPS), X-ray absorption spectroscopy (XAS) and scanning tunneling microscopy (STM). Our results suggest that at low coverage ZnPc lies almost parallel to the Pt(111) substrate, in a non-planar configuration induced by Zn-Pt attraction, leading to an inhomogeneous charge distribution within the molecule and charge transfer to the molecule. ZnPc does not form a complete monolayer on the Pt surface, due to a surface-mediated intermolecular repulsion. At higher coverage ZnPc adopts a tilted geometry, due to a reduced molecule-substrate interaction. Our photoemission results illustrate that ZnPc is practically decoupled from Pt, already from the second layer. Pre-deposition of iodine on Pt hinders the Zn-Pt attraction, leading to a non-distorted first layer ZnPc in contact with Pt(111)-I $\left(\sqrt{3}\times\sqrt{3}\right)$ or Pt(111)-I $\left(\sqrt{7}\times\sqrt{7}\right)$, and a more homogeneous charge distribution and charge transfer at the interface. On increased ZnPc thickness iodine is dissolved in the organic film where it acts as an electron acceptor dopant.Comment: 12 pages, 9 figure

Freeform Bioprinting of Liver Encapsulated in Alginate Hydrogels Tissue Constructs for Pharmacokinetic Study

An in vitro model that can be realistically and inexpensively used to predict human response to various drug administration and toxic chemical exposure is needed. By fabricating a microscale 3D physiological tissue construct consisting of an array of channels and tissue-embedded chambers, one can selectively develop various biomimicking mammalian tissues for a number of pharmaceutical applications, for example, experimental pharmaceutical screening for drug efficacy and toxicity along with apprehending the disposition and metabolic profile of a candidate drug. This paper addresses issues relating to the development and implementation of a bioprinting process for freeform fabrication of a 3D cell-encapsulated hydrogel-based tissue construct, the direct integration onto a microfluidic device for pharmacokinetic study, and the underlying engineering science for the fabrication of a 3D microscale tissue chamber as well as its application in pharmacokinetic study. To this end, a prototype 3D microfluidic tissue chamber embedded with liver cells encapsulated within a hydrogel matrix construct is bioprinted as a physiological in vitro model for pharmacokinetic study. The developed fabrication processes are further validated and parameters optimized by assessing cell viability and liver cell phenotype, in which metabolic and synthetic liver functions are quantitated.Mechanical Engineerin