Pairwise entanglement and readout of atomic-ensemble and optical wave-packet modes in traveling-wave Raman interactions

We analyze quantum entanglement of Stokes light and atomic electronic polarization excited during single-pass, linear-regime, stimulated Raman scattering in terms of optical wave-packet modes and atomic-ensemble spatial modes. The output of this process is confirmed to be decomposable into multiple discrete, bosonic mode pairs, each pair undergoing independent evolution into a two-mode squeezed state. For this we extend the Bloch-Messiah reduction theorem, previously known for discrete linear systems (S. L. Braunstein, Phys. Rev. A, vol. 71, 055801 (2005)). We present typical mode functions in the case of one-dimensional scattering in an atomic vapor. We find that in the absence of dispersion, one mode pair dominates the process, leading to a simple interpretation of entanglement in this continuous-variable system. However, many mode pairs are excited in the presence of dispersion-induced temporal walkoff of the Stokes, as witnessed by the photon-count statistics. We also consider the readout of the stored atomic polarization using the anti-Stokes scattering process. We prove that the readout process can also be decomposed into multiple mode pairs, each pair undergoing independent evolution analogous to a beam-splitter transformation. We show that this process can have unit efficiency under realistic experimental conditions. The shape of the output light wave packet can be predicted. In case of unit readout efficiency it contains only excitations originating from a specified atomic excitation mode

The Estimation of Place-to-Place Migration Flows Using an Alternative Log-Linear Parameter Coding Scheme

The log-linear model, with an alternative parameter coding scheme, is used in this paper to obtain estimates of place-to-place migration flows in situations where the data are inadequate or missing. The alternative parameter coding scheme is particularly useful in constructing the origin-destination interaction structure. To illustrate the method, two empirical examples are presented. The first demonstrates the effectiveness of the methodology by estimating known migration flows between states in the Western region of the United States during the 1985-1990 period. The second example focuses on estimating international migration flows in the Northern region of Europe during the 1999-2000 period where the data are incomplete. Both examples demonstrate the usefulness and generality of this particular method for estimating migration flows

The mixing time of the fifteen puzzle

We show that there are universal positive constants c and C such that the mixing time T_{mix} for the fifteen puzzle in an n by n torus satisfies cn^4 log n < T_{mix} < Cn^4 log^2 n.Comment: 30 pages, 9 figure

Quantum efficiency of single-photon sources in the cavity-QED strong-coupling regime

We calculate the integrated-pulse quantum efficiency of single-photon sources in the cavity quantum electrodynamics (QED) strong-coupling regime. An analytical expression for the quantum efficiency is obtained in the Weisskopf-Wigner approximation. Optimal conditions for a high quantum efficiency and a temporally localized photon emission rate are examined. We show the condition under which the earlier result of Law and Kimble [J. Mod. Opt. 44, 2067 (1997)] can be used as the first approximation to our result.Comment: 8 pages, 3 figures, final version, tex file uploade

Quantum-Fluctuation-Initiated Coherence in Multi-Octave Raman Optical Frequency Combs

We show experimentally and theoretically that the spectral components of a multi-octave frequency comb spontaneously created by stimulated Raman scattering in a hydrogen-filled hollow-core photonic crystal fiber exhibit strong self coherence and mutual coherence within each 12 ns driving laser pulse. This coherence arises in spite of the field's initiation being from quantum zero-point fluctuations, which causes each spectral component to show large phase and energy fluctuations. This points to the possibility of an optical frequency comb with nonclassical correlations between all comb lines.Comment: Accepted for publication, Physical Review Letters, 201

Hoyle-Lyttleton Accretion in Three Dimensions

We investigate the stability of gravitational accretion of an ideal gas onto a compact object moving through a uniform medium at Mach 3. Previous three-dimensional simulations have shown that such accretion is not stable, and that strong rotational 'disk-like' flows are generated and accreted on short time scales. We re-address this problem using overset spherical grids that provide a factor of seven improvement in spatial resolution over previous simulations. With our higher spatial resolution we found these 3D accretion flows remained remarkably axisymmetric. We examined two cases of accretion with different sized accretors. The larger accretor produced very steady flow, with the mass accretion rate varying by less than 0.02% over 30 flow times. The smaller accretor exhibited an axisymmetric breathing mode that modulated the mass accretion rate by a constant 20%. Nonetheless, the flow remained highly axisymmetric with only negligible accretion of angular momentum in both cases.Comment: 6 pages, 6 figures. Submitted to Ap

Testing the Alchian-Allen Theorem: A Study of Consumer Behavior in the Gasoline Market

This paper uses a data set of daily sales at a single gasoline station over a seven year period to determine if consumers respond to relative price changes among the three grades of gasoline. Based on the reasoning of Alchian and Allen (1964) and Barzel (1976), market shares of higher quality gasoline should increase at the expense of regular grade gasoline when overall gasoline prices increase. The empirical results do not conform to this expectation. We find instead that the consumers in this sample responded to higher gasoline prices by switching to mid grade gasoline from premium grade gasoline leaving the market share of regular gasoline unchanged.Alchian-Allen Theorem