Hyperpolarizabilities for the one-dimensional infinite single-electron periodic systems: II. Dipole-dipole versus current-current correlations

Based on Takayama-Lin-Liu-Maki model, analytical expressions for the third-harmonic generation, DC Kerr effect, DC-induced second harmonic optical Kerr effect, optical Kerr effect or intensity-dependent index of refraction and DC-electric-field-induced optical rectification are derived under the static current-current($J_0J_0$) correlation for one-dimensional infinite chains. The results of hyperpolarizabilities under $J_0J_0$ correlation are then compared with those obtained using the dipole-dipole ($DD$) correlation. The comparison shows that the conventional $J_0J_0$ correlation, albeit quite successful for the linear case, is incorrect for studying the nonlinear optical properties of periodic systems.Comment: 11 pages, 5 figure

Tailoring optical nonlinearities via the Purcell effect

We predict that the effective nonlinear optical susceptibility can be tailored using the Purcell effect. While this is a general physical principle that applies to a wide variety of nonlinearities, we specifically investigate the Kerr nonlinearity. We show theoretically that using the Purcell effect for frequencies close to an atomic resonance can substantially influence the resultant Kerr nonlinearity for light of all (even highly detuned) frequencies. For example, in realistic physical systems, enhancement of the Kerr coefficient by one to two orders of magnitude could be achieved

Magneto-optical signatures of a cascade of transitions in La2−x_2-xBax_xCuO4_4

Recent experiments in the original cuprate high temperature superconductor, La$_2-x$Ba$_x$CuO$_4$, have revealed a remarkable sequence of transitions [1]. Here we investigate such crystals with Kerr effect which is sensitive to time-reversal-symmetry breaking (TRSB). Concurrent birefringence measurements accurately locate the structural phase transitions from high-temperature tetragonal to low temperature orthorhombic, and then to lower temperature tetragonal, at which temperature a strong Kerr signal onsets. Hysteretic behavior of the Kerr signal suggests that TRSB occurs well above room temperature, an effect that was previously observed in high quality YBa$_2$Cu$_3$O$_{6+x} crystals [2].Comment: 5 pages, 4 figure

Kerr Black Holes and Nonlinear Radiation Memory

The Minkowski background intrinsic to the Kerr-Schild version of the Kerr metric provides a definition of a boosted spinning black hole. There are two Kerr-Schild versions corresponding to ingoing or outgoing principal null directions. The two corresponding Minkowski backgrounds and their associated boosts differ drastically. This has an important implication for the gravitational memory effect. A prior analysis of the transition of a non-spinning Schwarzschild black hole to a boosted state showed that the memory effect in the nonlinear regime agrees with the linearised result based upon the retarded Green function only if the final velocity corresponds to a boost symmetry of the ingoing Minkowski background. A boost with respect to the outgoing Minkowski background is inconsistent with the absence of ingoing radiation from past null infinity. We show that this results extends to the transition of a Kerr black hole to a boosted state and apply it to set upper and lower bounds for the boost memory effect resulting from the collision of two spinning black holes.Comment: 17 pages, revised discussion sectio