A Quantitative Measure of Interference

We introduce an interference measure which allows to quantify the amount of interference present in any physical process that maps an initial density matrix to a final density matrix. In particular, the interference measure enables one to monitor the amount of interference generated in each step of a quantum algorithm. We show that a Hadamard gate acting on a single qubit is a basic building block for interference generation and realizes one bit of interference, an ``i-bit''. We use the interference measure to quantify interference for various examples, including Grover's search algorithm and Shor's factorization algorithm. We distinguish between ``potentially available'' and ``actually used'' interference, and show that for both algorithms the potentially available interference is exponentially large. However, the amount of interference actually used in Grover's algorithm is only about 3 i-bits and asymptotically independent of the number of qubits, while Shor's algorithm indeed uses an exponential amount of interference.Comment: 13 pages of latex; research done at http://www.quantware.ups-tlse.fr

Macroscopic Quantum Tunneling of Ferromagnetic Domain Walls

Quantum tunneling of domain walls out of an impurity potential in a mesoscopic ferromagnetic sample is investigated. Using improved expressions for the domain wall mass and for the pinning potential, we find that the cross-over temperature between thermal activation and quantum tunneling is of a different functional form than found previously. In materials like Ni or YIG, the crossover temperatures are around 5 mK. We also find that the WKB exponent is typically two orders of magnitude larger than current estimates. The sources for these discrepancies are discussed, and precise estimates for the transition from three-dimensional to one-dimensional magnetic behavior of a wire are given. The cross-over temperatures from thermal to quantum transitions and tunneling rates are calculated for various materials and sample sizes.Comment: 10 pages, 2 postscript figures, REVTe

Master equation for collective spontaneous emission with quantized atomic motion

We derive a markovian master equation for the internal dynamics of an ensemble of two-level atoms including all effects related to the quantization of their motion. Our equation provides a unifying picture of the consequences of recoil and indistinguishability of atoms beyond the Lamb-Dicke regime on both their dissipative and conservative dynamics, and applies equally well to distinguishable and indistinguishable atoms. We give general expressions for the decay rates and the dipole-dipole shifts for any motional states, and we find closed-form formulas for a number of relevant states (Gaussian states, Fock states and thermal states). In particular, we show that dipole-dipole interactions and cooperative photon emission can be modulated through the external state of motion.Comment: 16 pages, 7 figures, minor correction

Recent Star Formation in Sextans A

We investigate the relationship between the spatial distributions of stellar populations and of neutral and ionized gas in the Local Group dwarf irregular galaxy Sextans A. This galaxy is currently experiencing a burst of localized star formation, the trigger of which is unknown. We have resolved various populations of stars via deep UBV(RI)_C imaging over an area with diameter \sim 5.'3. We have compared our photometry with theoretical isochrones appropriate for Sextans A, in order to determine the ages of these populations. We have mapped out the history of star formation, most accurately for times \lesssim 100 Myr. We find that star formation in Sextans A is correlated both in time and space, especially for the most recent (\lesssim 12 Myr) times. The youngest stars in the galaxy are forming primarily along the inner edge of the large H I shell. Somewhat older populations, \lesssim 50 Myr, are found inward of the youngest stars. Progressively older star formation, from \sim 50--100 Myr, appears to have some spatially coherent structure and is more centrally concentrated. The oldest stars we can accurately sample appear to have approximately a uniform spatial distribution, which extends beyond a surface brightness of \mu_B \simeq 25.9 mag arcsec^{-2} (or, a radius r \simeq 2.'3$). Although other processes are also possible, our data provides support for a mechanism of supernova-driven expansion of the neutral gas, resulting in cold gas pileup and compression along the H I shell and sequential star formation in recent times.Comment: 64 pages, 22 figures, to appear in A

Bloch oscillations of magnetic solitons in anisotropic spin-1/2 chains

We study the quantum dynamics of soliton-like domain walls in anisotropic spin-1/2 chains in the presence of magnetic fields. In the absence of fields, domain walls form a Bloch band of delocalized quantum states while a static field applied along the easy axis localizes them into Wannier wave packets and causes them to execute Bloch oscillations, i.e. the domain walls oscillate along the chain with a finite Bloch frequency and amplitude. In the presence of the field, the Bloch band, with a continuum of extended states, breaks up into the Wannier-Zeeman ladder -- a discrete set of equally spaced energy levels. We calculate the dynamical structure factor in the one-soliton sector at finite frequency, wave vector, and temperature, and find sharp peaks at frequencies which are integer multiples of the Bloch frequency. We further calculate the uniform magnetic susceptibility and find that it too exhibits peaks at the Bloch frequency. We identify several candidate materials where these Bloch oscillations should be observable, for example, via neutron scattering measurements. For the particular compound CoCl_2.2H_2O we estimate the Bloch amplitude to be on the order of a few lattice constants, and the Bloch frequency on the order of 100 GHz for magnetic fields in the Tesla range and at temperatures of about 18 Kelvin.Comment: 31 single-spaced REVTeX pages, including 7 figures embedded with eps

The CHARA Array Angular Diameter of HR 8799 Favors Planetary Masses for Its Imaged Companions

HR 8799 is an hF0 mA5 gamma Doradus, lambda Bootis, Vega-type star best known for hosting four directly imaged candidate planetary companions. Using the CHARA Array interferometer, we measure HR 8799's limb-darkened angular diameter to be 0.342 +/- 0.008 mas; this is the smallest interferometrically measured stellar diameter to date, with an error of only 2%. By combining our measurement with the star's parallax and photometry from the literature, we greatly improve upon previous estimates of its fundamental parameters, including stellar radius (1.44 +/- 0.06 R_Sun), effective temperature (7193 +/- 87 K, consistent with F0), luminosity (5.05 +/- 0.29 L_Sun), and the extent of the habitable zone (1.62 AU to 3.32 AU). These improved stellar properties permit much more precise comparisons with stellar evolutionary models, from which a mass and age can be determined, once the metallicity of the star is known. Considering the observational properties of other lambda Bootis stars and the indirect evidence for youth of HR 8799, we argue that the internal abundance, and what we refer to as the effective abundance, is most likely near-solar. Finally, using the Yonsei-Yale evolutionary models with uniformly scaled solar-like abundances, we estimate HR 8799's mass and age considering two possibilities: 1.516 +0.038/-0.024 M_Sun and 33 +7/-13 Myr if the star is contracting toward the zero age main-sequence or 1.513 +0.023/-0.024 M_Sun and 90 +381/-50 Myr if it is expanding from it. This improved estimate of HR 8799's age with realistic uncertainties provides the best constraints to date on the masses of its orbiting companions, and strongly suggests they are indeed planets. They nevertheless all appear to orbit well outside the habitable zone of this young star.Comment: Accepted for publication in ApJ; 37 pages, 6 tables, 13 figure

Boundary conditions, the critical conductance distribution, and one-parameter scaling

Published versio

Motor coordination: when two have to act as one

Trying to pass someone walking toward you in a narrow corridor is a familiar example of a two-person motor game that requires coordination. In this study, we investigate coordination in sensorimotor tasks that correspond to classic coordination games with multiple Nash equilibria, such as “choosing sides,” “stag hunt,” “chicken,” and “battle of sexes”. In these tasks, subjects made reaching movements reflecting their continuously evolving “decisions” while they received a continuous payoff in the form of a resistive force counteracting their movements. Successful coordination required two subjects to “choose” the same Nash equilibrium in this force-payoff landscape within a single reach. We found that on the majority of trials coordination was achieved. Compared to the proportion of trials in which miscoordination occurred, successful coordination was characterized by several distinct features: an increased mutual information between the players’ movement endpoints, an increased joint entropy during the movements, and by differences in the timing of the players’ responses. Moreover, we found that the probability of successful coordination depends on the players’ initial distance from the Nash equilibria. Our results suggest that two-person coordination arises naturally in motor interactions and is facilitated by favorable initial positions, stereotypical motor pattern, and differences in response times