Quantum limited measurements of atomic scattering properties

We propose a method to perform precision measurements of the interaction parameters in systems of N ultra-cold spin 1/2 atoms. The spectroscopy is realized by first creating a coherent spin superposition of the two relevant internal states of each atom and then letting the atoms evolve under a squeezing Hamiltonian. The non-linear nature of the Hamiltonian decreases the fundamental limit imposed by the Heisenberg uncertainty principle to N^(-2), a factor of N smaller than the fundamental limit achievable with non-interacting atoms. We study the effect of decoherence and show that even with decoherence, entangled states can outperform the signal to noise limit of non-entangled states. We present two possible experimental implementations of the method using Bose-Einstein spinor condensates and fermionic atoms loaded in optical lattices and discuss their advantages and disadvantages.Comment: 7 pages, 5 figures. References adde

Expanded mixed multiscale finite element methods and their applications for flows in porous media

We develop a family of expanded mixed Multiscale Finite Element Methods (MsFEMs) and their hybridizations for second-order elliptic equations. This formulation expands the standard mixed Multiscale Finite Element formulation in the sense that four unknowns (hybrid formulation) are solved simultaneously: pressure, gradient of pressure, velocity and Lagrange multipliers. We use multiscale basis functions for the both velocity and gradient of pressure. In the expanded mixed MsFEM framework, we consider both cases of separable-scale and non-separable spatial scales. We specifically analyze the methods in three categories: periodic separable scales, $G$- convergence separable scales, and continuum scales. When there is no scale separation, using some global information can improve accuracy for the expanded mixed MsFEMs. We present rigorous convergence analysis for expanded mixed MsFEMs. The analysis includes both conforming and nonconforming expanded mixed MsFEM. Numerical results are presented for various multiscale models and flows in porous media with shales to illustrate the efficiency of the expanded mixed MsFEMs.Comment: 33 page

A fast and robust approach to long-distance quantum communication with atomic ensembles

Quantum repeaters create long-distance entanglement between quantum systems while overcoming difficulties such as the attenuation of single photons in a fiber. Recently, an implementation of a repeater protocol based on single qubits in atomic ensembles and linear optics has been proposed [Nature 414, 413 (2001)]. Motivated by rapid experimental progress towards implementing that protocol, here we develop a more efficient scheme compatible with active purification of arbitrary errors. Using similar resources as the earlier protocol, our approach intrinsically purifies leakage out of the logical subspace and all errors within the logical subspace, leading to greatly improved performance in the presence of experimental inefficiencies. Our analysis indicates that our scheme could generate approximately one pair per 3 minutes over 1280 km distance with fidelity (F>78%) sufficient to violate Bell's inequality.Comment: 10 pages, 4 figures, 5 tables (Two appendixes are added to justify two claims used in the maintext.

Phase-reference VLBI Observations of the Compact Steep-Spectrum Source 3C 138

We investigate a phase-reference VLBI observation that was conducted at 15.4 GHz by fast switching VLBA antennas between the compact steep-spectrum radio source 3C 138 and the quasar PKS 0528+134 which are about 4$^\circ$ away on the sky. By comparing the phase-reference mapping with the conventional hybrid mapping, we demonstrate the feasibility of high precision astrometric measurements for sources separated by 4$^\circ$. VLBI phase-reference mapping preserves the relative phase information, and thus provides an accurate relative position between 3C 138 and PKS 0528+134 of $\Delta\alpha=-9^m46^s.531000\pm0^s.000003$ and $\Delta\delta=3^\circ6^\prime26^{\prime\prime}.90311\pm0^{\prime\prime}.00007$ (J2000.0) in right ascension and declination, respectively. This gives an improved position of the nucleus (component A) of 3C 138 in J2000.0 to be RA=$05^h 21^m 9^s.885748$ and Dec=$16^\circ 38' 22''.05261$ under the assumption that the position of calibrator PKS 0528+134 is correct. We further made a hybrid map by performing several iterations of CLEAN and self-calibration on the phase-referenced data with the phase-reference map as an input model for the first phase self-calibration. Compared with the hybrid map from the limited visibility data directly obtained from fringe fitting 3C 138 data, this map has a similar dynamic range, but a higher angular resolution. Therefore, phase-reference technique is not only a means of phase connection, but also a means of increasing phase coherence time allowing self-calibration technique to be applied to much weaker sources.Comment: 9 pages plus 2 figures, accepted by PASJ (Vol.58 No.6

Cavity QED with atomic mirrors

A promising approach to merge atomic systems with scalable photonics has emerged recently, which consists of trapping cold atoms near tapered nanofibers. Here, we describe a novel technique to achieve strong, coherent coupling between a single atom and photon in such a system. Our approach makes use of collective enhancement effects, which allow a lattice of atoms to form a high-finesse cavity within the fiber. We show that a specially designated "impurity" atom within the cavity can experience strongly enhanced interactions with single photons in the fiber. Under realistic conditions, a "strong coupling" regime can be reached, wherein it becomes feasible to observe vacuum Rabi oscillations between the excited impurity atom and a single cavity quantum. This technique can form the basis for a scalable quantum information network using atom-nanofiber systems.Comment: 20 pages, 4 figure