Perturbative Aspects of Heterotically Deformed CP(N-1) Sigma Model. I

In this paper we begin the study of renormalizations in the heterotically deformed N=(0,2) CP(N-1) sigma models. In addition to the coupling constant g^2 of the undeformed N=(2,2) model, there is the second coupling constant \gamma describing the strength of the heterotic deformation. We calculate both \beta functions, \beta_g and \beta_\gamma at one loop, determining the flow of g^2 and \gamma. Under a certain choice of the initial conditions, the theory is asymptotically free. The \beta function for the ratio \rho =\gamma^2/g^2 exhibits an infrared fixed point at \rho={1}{2}. Formally this fixed point lies outside the validity of the one-loop approximation. We argue, however, that the fixed point at \rho ={1}{2} may survive to all orders. The reason is the enhancement of symmetry - emergence of a chiral fermion flavor symmetry in the heterotically deformed Lagrangian - at \rho ={1}{2}. Next we argue that \beta_\rho formally obtained at one loop, is exact to all orders in the large-N (planar) approximation. Thus, the fixed point at \rho = {1}{2} is definitely the feature of the model in the large-N limit.Comment: 27 pages, 8 figure

Carrier-envelope phase dependence in single-cycle laser pulse propagation with the inclusion of counter-rotating terms

We focus on the propagation properties of a single-cycle laser pulse through a two-level medium by numerically solving the full-wave Maxwell-Bloch equations. The counter-rotating terms in the spontaneous emission damping are included such that the equations of motion are slightly different from the conventional Bloch equations. The counter-rotating terms can considerably suppress the broadening of the pulse envelope and the decrease of the group velocity rooted from dispersion. Furthermore, for incident single-cycle pulses with envelope area 4$\pi$, the time-delay of the generated soliton pulse from the main pulse depends crucially on the carrier-envelope phase of the incident pulse. This can be utilized to determine the carrier-envelope phase of the single-cycle laser pulse.Comment: 6 pages, 5 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

Digital optical phase conjugation of fluorescence in turbid tissue

We demonstrate a method for phase conjugating fluorescence. Our method, called reference free digital optical phase conjugation, can conjugate extremely weak, incoherent optical signals. It was used to phase conjugate fluorescent light originating from a bead covered with 0.5 mm of light-scattering tissue. The phase conjugated beam refocuses onto the bead and causes a local increase of over two orders of magnitude in the light intensity. Potential applications are in imaging, optical trapping, and targeted photochemical activation inside turbid tissue

Semivariogram methods for modeling Whittle-Mat\'ern priors in Bayesian inverse problems

We present a new technique, based on semivariogram methodology, for obtaining point estimates for use in prior modeling for solving Bayesian inverse problems. This method requires a connection between Gaussian processes with covariance operators defined by the Mat\'ern covariance function and Gaussian processes with precision (inverse-covariance) operators defined by the Green's functions of a class of elliptic stochastic partial differential equations (SPDEs). We present a detailed mathematical description of this connection. We will show that there is an equivalence between these two Gaussian processes when the domain is infinite -- for us, $\mathbb{R}^2$ -- which breaks down when the domain is finite due to the effect of boundary conditions on Green's functions of PDEs. We show how this connection can be re-established using extended domains. We then introduce the semivariogram method for estimating the Mat\'ern covariance parameters, which specify the Gaussian prior needed for stabilizing the inverse problem. Results are extended from the isotropic case to the anisotropic case where the correlation length in one direction is larger than another. Finally, we consider the situation where the correlation length is spatially dependent rather than constant. We implement each method in two-dimensional image inpainting test cases to show that it works on practical examples

Coulomb drag in double quantum wells with a perpendicular magnetic field

Momentum transfer due to electron-electron interaction (Coulomb drag) between two quantum wells, separated by a distance $d$, in the presence of a perpendicular magnetic field, is studied at low temperatures. We find besides the well known Shubnikov-de Haas oscillations, which also appear in the drag effect, the momentum transfer is markedly enhanced by the magnetic field.Comment: 8 pages, Revtex, 4 Postscript figures are available upon request, Accepted by Mod. Phys. Lett.