Entangling two atoms in spatially separated cavities through both photon emission and absorption processes

We consider a system consisting of a $\Lambda$-type atom and a V-type atom, which are individually trapped in two spatially separated cavities that are connected by an optical fibre. We show that an extremely entangled state of the two atoms can be deterministically generated through both photon emission of the $\Lambda$-type atom and photon absorption of the V-type atom in an ideal situation. The influence of various decoherence processes such as spontaneous emission and photon loss on the fidelity of the entangled state is also investigated. We find that the effect of photon leakage out of the fibre on the fidelity can be greatly diminished in some special cases. As regards the effect of spontaneous emission and photon loss from the cavities, we find that the present scheme with a fidelity higher than 0.98 may be realized under current experiment conditions.Comment: 12 pages, 4 figure

Green's Function of 3-D Helmholtz Equation for Turbulent Medium: Application to Optics

The fundamental problem of optical wave propagation is the determination of the field at an observation point, given a disturbance specified over some finite aperture. In both vacuum and inhomogeneous media, the solution of this problem is given approximately by the superposition integral, which is a mathematical expression of the extended Huygens-Fresnel principle. In doing so, it is important to find the atmospheric impulse response (Green's function). Within a limited but useful region of validity, a satisfactory optical propagation theory for the earth's clear turbulent atmosphere could be developed by using Rytov's method to approximate the Helmholtz equation. In particular, we deal with two optical problems which are the time reversal and apodization problems. The background and consequences of these results for optical communication through the atmosphere are briefly discussed

Characterization of Alaskan HMA Mixtures with the Simple Performance Tester

INE/AUTC 12.2

Testing Small Set Expansion in General Graphs

We consider the problem of testing small set expansion for general graphs. A graph $G$ is a $(k,\phi)$-expander if every subset of volume at most $k$ has conductance at least $\phi$. Small set expansion has recently received significant attention due to its close connection to the unique games conjecture, the local graph partitioning algorithms and locally testable codes. We give testers with two-sided error and one-sided error in the adjacency list model that allows degree and neighbor queries to the oracle of the input graph. The testers take as input an $n$-vertex graph $G$, a volume bound $k$, an expansion bound $\phi$ and a distance parameter $\varepsilon>0$. For the two-sided error tester, with probability at least $2/3$, it accepts the graph if it is a $(k,\phi)$-expander and rejects the graph if it is $\varepsilon$-far from any $(k^*,\phi^*)$-expander, where $k^*=\Theta(k\varepsilon)$ and $\phi^*=\Theta(\frac{\phi^4}{\min\{\log(4m/k),\log n\}\cdot(\ln k)})$. The query complexity and running time of the tester are $\widetilde{O}(\sqrt{m}\phi^{-4}\varepsilon^{-2})$, where $m$ is the number of edges of the graph. For the one-sided error tester, it accepts every $(k,\phi)$-expander, and with probability at least $2/3$, rejects every graph that is $\varepsilon$-far from $(k^*,\phi^*)$-expander, where $k^*=O(k^{1-\xi})$ and $\phi^*=O(\xi\phi^2)$ for any $0<\xi<1$. The query complexity and running time of this tester are $\widetilde{O}(\sqrt{\frac{n}{\varepsilon^3}}+\frac{k}{\varepsilon \phi^4})$. We also give a two-sided error tester with smaller gap between $\phi^*$ and $\phi$ in the rotation map model that allows (neighbor, index) queries and degree queries.Comment: 23 pages; STACS 201