Quantum optical properties of polariton waves

We develop a quantum-mechanical Hamiltonian formulation to treat the polariton in the frame- work of quantum optics. We exploit two specific Hamiltonians: the conventional Hopfield model, and a more general Hamiltonian. For both of these, exciton-polariton quantum states are found to be squeezed (intrinsic polariton squeezing) with respect to states of an intrinsic, nonpolaritonic, mixed photon-exciton boson. The amount and duration of intrinsic squeezing during the polariton period are calculated for exciton polaritons in typical I-VII and III-V semiconductors. Among the noteworthy features is the possibility of tuning the amount of intrinsic squeezing by varying the frequency —wave-vector dispersion of the polariton mode. We further analyze the photon statistics of the electromagnetic component of the polariton. Tunable non-Poissonian photon statistics and squeezing (optical polariton squeezing) are found in the radiative component of the exciton polari- ton. This entails the reduction of the Auctuations of the polariton electromagnetic field component below the limit set by the vacuum Iluctuations. The Mandel Q factor for the number distribution of photons in a polariton coherent state has been evaluated. Although small, for I-VII and III-V ma- terials in the range of modes analyzed, the Q factor could be enhanced for phonon polaritons as well as for other materials. Interpretations of the origin of squeezing in polariton states are presented

Electronic structure of a quasiperiodic system

The general solution of a Schrödinger equation with a quasiperiodic potential in n dimensions is obtained. A boost technique is presented, which will transform the problem to the solution of a periodic pseudo-Schrödinger equation in n+m dimensions, to which Floquet-Bloch theory is applicable. We show that the eigenfunctions of the original problem and the boosted problem are related to each other by a simple radon transform, and the eigenvalues are exactly equal. We identify the hierarchical gap structure in the energy spectrum observed in numerical simulations and we show that the location of gaps can be indexed by the reciprocal wave vector given by the diffraction pattern of the quasicrystal. The position and the magnitude of the gaps so predicted are in qualitative agreement with numerical simulations

Competing order parameters for increased Tc in "polytype" multilayer Cu-O systems

Using a simple phenomenological model with coupled order parameters for polytype multilayer copper oxide systems, it is demonstrated that polytypism can increase Tc. Explicit expressions and results are given for Tc(N) where N is the polytype number (N=2, 3, , . Classes of structures investigated are monolayer polytypes such as [-(CuO2)N-]; bilayer TlO polytypes such as [-(TlOTlO(CuO2)N-]; and monolayer TlO polytypes; and 1:2:3 polytypes such as [-(CuO2)-(CuO-CuO2)n-]. Two types of nearest-layer bilinear coupling were studied: weak link (Josephson) and spin-spin. Polytypism is predicted to increase Tc in all classes; except in one case. For the same N, monolayer TlO polytypes have lower Tc than the bilayer TlO analog. Using reasonable values of parameters we predict a maximum Tc of 140 K in the monolayer and bilayer TlO series

Mistakes in quasilattices

We studied a class of mistakes or faults in quasilattices. The effect of a random distribution of mistakes on the diffraction of 1D, and a special class of 3D, quasilattices is calculated exactly. Mistakes change the diffraction pattern qualitatively: Some Bragg peaks decrease in intensity as expected, but some are enhanced. As a result some spots disappear and some new ones appear. The diffuse scattering is also calculated. Results are given comparing calculated diffraction patterns in fivefold, threefold, and twofold symmetry directions for a 3D quasicrystal with and without mistakes

Acoustic-wave propagation in quasiperiodic, incommensurate, and random systems

We have studied acoustic-wave propagation in one-dimensional systems with quasiperiodic, incommensurate, and random modulation. In the short-wavelength limit we found that if the initial pulse is narrow (with spatial extension of the order of a few lattice spacings), the pulse is localized in a quasiperiodic system as in the case of a random system. This result shows that at short length scales a quasiperiodic system is similar to a random system. Therefore, those transport properties that do not depend on long-range order should behave similarly in quasicrystals and in an amorphous metallic glass, in agreement with experimental findings. On the other hand, if the injected wave has a wavelength much larger than the lattice spacing, we found that there are resonances for quasiperiodic and incommensurate systems when the wave vector satisfies the Bragg conditions. In this case propagation appears to be diffusive rather than propagative; namely, the total energy of the initial wave does not propagate along the chain as it does otherwise, but is homogeneously distributed over the region of space where the wave front passed. We solved the problem analytically in the long-wavelength limit in terms of two-mode-coupling theory and the Fourier spectrum of the quasiperiodic system. Analytical results are in full agreement with numerical simulations. These indicate that on a long-range scale quasiperiodic order is important not only for the crystal structure but also for those physical properties which depend on long-range order, such as acoustic-wave and microwave propagation

Affine configurations and pure braids

We show that the fundamental group of the space of ordered affine-equivalent configurations of at least five points in the real plane is isomorphic to the pure braid group modulo its centre. In the case of four points this fundamental group is free with eleven generators.Comment: 5 pages, 1 figure, final version; to appear in Discrete & Computational Geometry, available from the publishers at http://www.springerlink.com/content/384516n7q24811ph

Microscopic model for high-Tc oxide superconductors

We report results of a BCS-pairing theory of high-Tc superconductors based on a model using interlayer charge-transfer excitation as the intermediate boson. We apply the model specifically to YBa2Cu3O7. The relevant electronic band structure is calculated analytically using the tight-binding approximation, which is in agreement with numerical results. A specific interlayer charge-transfer excitation is identified. The Eliashberg equations are solved in the Kirzhnits-Maksimov-Khomskii approximation to obtain Tc and the gap . We find 2/KTc1014, and Tc increasing exponentially with a decrease in the Cu(2)-O(4) bond length. These results are in general agreement with some recent experiments

Properties of one-dimensional quasilattices

We study the properties of one-dimensional quasilattices numerically and analytically. The geometrical properties of general one-dimensional quasilattices are discussed. The Ising model on these lattices is studied by a decimation transformation: The critical temperature and critical exponents do not differ from those for a regular periodic chain. The vibrational spectrum in the harmonic approximation is analyzed numerically. The system exhibits characteristics of both a regular periodic system and a disordered system. In the low-frequency region, the system behaves as a regular periodic system; wave functions appear extended. In the high-frequency region, the spectrum is self-similar and there is no unique behavior for the wave functions. The spectrum shows many gaps and Van Hove singularities. The gaps in the spectrum are also obtained analytically by examining the convergence of a continued-fraction expansion plus decimation transformation. The energy spectrum of a tight-binding electron Hamiltonian on the Fibonacci chain is also analyzed; it shows similar characteristics to those of the lattice vibration spectrum

Optical Resonances in Reflectivity near Crystal Modes with Spatial Dispersion

We study the effect of spatial dispersion of crystal modes on optical properties such as the reflectivity $R$. As an example for isotropic media, we investigate the simplest model for phonons in ionic crystals and compare with previous results for highly anisotropic plasmons, which are now understood from a more general point of view. As a consequence of the wave vector dependence of the dielectric function small changes in the lineshape are predicted. Beyond that, if the frequency of minimal $R$ is near a pole of the dispersionless dielectric function, the relative amplitude of dips in $R$ with normal and anomalous dispersion differ significantly, if dissipation and disorder are low.Comment: 4 pages, 7 eps figures, minor change

Theory of Coexistence of Superconductivity and Ferroelectricity : A Dynamical Symmetry Model

We propose and investigate a model for the coexistence of Superconductivity (SC) and Ferroelectricity (FE) based on the dynamical symmetries $su(2)$ for the pseudo-spin SC sector, $h(4)$ for the displaced oscillator FE sector, and $su(2) \otimes h(4)$ for the composite system. We assume a minimal symmetry-allowed coupling, and simplify the hamiltonian using a double mean field approximation (DMFA). A variational coherent state (VCS) trial wave-function is used for the ground state: the energy, and the relevant order parameters for SC and FE are obtained. For positive sign of the SC-FE coupling coefficient, a non-zero value of either order parameter can suppress the other (FE polarization suppresses SC and vice versa). This gives some support to "Matthias' Conjecture" [1964], that SC and FE tend to be mutually exclusive. For such a Ferroelectric Superconductor we predict: a) the SC gap $\Delta$ (and $T_c$) will increase with increasing applied pressure when pressure quenches FE as in many ferroelectrics, and b) the FE polarization will increase with increaesing magnetic field up to $H_c$. The last result is equivalent to the prediction of a new type of Magneto-Electric Effect in a coexistent SC-FE material. Some discussion will be given of the relation of these results to the cuprate superconductors.Comment: 46 page