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

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 Input-Output Theory for Optical Cavities with Arbitrary Coupling Strength: Application to Two-Photon Wave-Packet Shaping

We develop quantum-optical input-output theory for resonators with arbitrary coupling strength, and for input fields whose spectrum can be wider than the cavity free-spectral range, while ensuring that the field-operator commutator relations in space-time variables are correct. The cavity-field commutator exhibits a series of space-time echoes, representing causal connections of certain space-time points by light propagation. We apply the theory to two-photon wave-packet shaping by cavity reflection, which displays a remarkable illustration of dispersion cancellation. We also show that the theory is amenable to inclusion of intracavity absorbing and emitting atoms, allowing, for example, dissipative losses within the cavity to be incorporated in a quantum mechanically correct way.Comment: v1: Submitted to Phys Rev A (July 14 2013) v2: Accepted Sep. 201

Proposal for a QND which-path measurement using photons

A scheme is proposed for experimentally realizing the famous two-slit gedaenken experiment using photons. As elegantly discussed for electrons by Feynman, a particle's quantum pathways interfere to produce fringes in the probability density for the particle to be found at a particle location. If the path taken by the particle is experimentally determined, the complementarity principle says that the fringes must disappear. To carry out this experiment with photons is difficult because normally the act of determining a photon's location destroys it. We propose to overcome this difficulty by putting a type-2 optical parametric amplifier (OPA) in each arm of a Mach-Zehnder interferometer, and observing fringes at the output. An OPA responds to an input photon by increasing its probability to produce a pair of photons with polarization orthogonal to the input, the detection of which allows partial inference about the path taken by the input photon without destroying it. Thus, the measurement is of the quantum nondemolition (QND) type

White and Non-White Migration between Area Groups in England and Wales

In this paper, we explore internal migration in England and Wales by broad groups of ethnicity, education and employment status from 1991 to 2004. The aim is to identify key differences in the patterns and trends over time so that a better understanding of the processes can take place. Our analyses focus on migration between twelve area groups defined by the Office for National Statistics, which are comprised of Local Authority Districts and include such areas as London Cosmopolitan, London Suburbs, Coastal and Countryside and Industrial Hinterlands. By analysing the migration flows between these area groupings, we can focus our attention on the types of destinations various migrant groups choose given particular origin types. The data come from the 2001 Census and the National Health Service Central Register from 1991 to 2004. Strong stability over time is demonstrated in the aggregate patterns of origin-destination-specific flows. However, when disaggregated by region, ethnicity, education and employment, very different patterns emerge which gives some useful insights into the redistribution of England and Wales' ethnic populations and compositions

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-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