More on the Isomorphism SU(2)⊗SU(2)≅SO(4)SU(2)\otimes SU(2)\cong SO(4)

In this paper we revisit the isomorphism $SU(2)\otimes SU(2)\cong SO(4)$ to apply to some subjects in Quantum Computation and Mathematical Physics. The unitary matrix $Q$ by Makhlin giving the isomorphism as an adjoint action is studied and generalized from a different point of view. Some problems are also presented. In particular, the homogeneous manifold $SU(2n)/SO(2n)$ which characterizes entanglements in the case of $n=2$ is studied, and a clear-cut calculation of the universal Yang-Mills action in (hep-th/0602204) is given for the abelian case.Comment: Latex ; 19 pages ; 5 figures ; minor changes. To appear in International Journal of Geometric Methods in Modern Physics (vol.4, no.3

Optical nonlinearity enhancement of graded metallic films

The effective linear and third-order nonlinear susceptibility of graded metallic films with weak nonlinearity have been investigated. Due to the simple geometry, we were able to derive exactly the local field inside the graded structures having a Drude dielectric gradation profile. We calculated the effective linear dielectric constant and third-order nonlinear susceptibility. We investigated the surface plasmon resonant effect on the optical absorption, optical nonlinearity enhancement, and figure of merit of graded metallic films. It is found that the presence of gradation in metallic films yields a broad resonant plasmon band in the optical region, resulting in a large enhancement of the optical nonlinearity and hence a large figure of merit. We suggest experiments be done to check our theoretical predictions, because graded metallic films can be fabricated more easily than graded particles.Comment: 11 pages, 2 eps figures, submitted to Applied Physics Letter

Strong fields induce ultrafast rearrangement of H-atoms in H2_2O

H-atoms in H$_2$O are rearranged by strong optical fields generated by intense, 10 fs laser pulses to form H$_2^+$, against prevailing wisdom that strong fields inevitably lead to multiple molecular ionization and the subsequent Coulomb explosion into fragments. This atomic rearrangement is shown to occur within a single 10 fs pulse. Comparison with results obtained with $\sim$300-attosecond long strong fields generated using fast Si$^{8+}$ ions helps establish thresholds for field strength and time required for such rearrangements. Quantum-chemical calculations reveal that H$_2^+$ originates in the $^1$A state of H$_2$O$^{2+}$ when the O-H bond elongates to 1.15 a.u. and the H-O-H angle becomes 120$^o$. Bond formation on the ultrafast timescale of molecular vibrations (10 fs for H$_2^+$) has hitherto not been reported.Comment: Submitted to Physical Review Lotter

Quantum dynamics of proton migration in H2O dications: formation of H2+ on ultrafast timescales

Irradiation of isolated water molecules by few-cycle pulses of intense infrared laser light can give rise to ultrafast rearrangement resulting in formation of the H2+ ion. Such unimolecular reactions occur on the potential energy surface of the H2O2+ dication that is accessed when peak laser intensities in the 1015 W cm-2 range and pulse durations as short as 9-10 fs are used; ion yields of ~1.5% are measured. We also study such reactions by means of time-dependent wavepacket dynamics on an ab initio potential energy surface of the dication and show that a proton, generated from O-H bond rupture, migrates towards the H-atom, and forms vibrationally-excited H2+ in a well-defined spatial zone.Comment: To appear in J. Chem. Phys. (tentatively the 22 January 2012 issue

Optical nonlinearity enhancement of graded metal-dielectric composite films

We have derived the local electric field inside graded metal-dielectric composite films with weak nonlinearity analytically, which further yields the effective linear dielectric constant and third-order nonlinear susceptibility of the graded structures. As a result, the composition-dependent gradation can produce a broad resonant plasmon band in the optical region, resulting in a large enhancement of the optical nonlinearity and hence a large figure of merit.Comment: 11 pages, 2 figures. To be published in Europhysics Letter

Spectral representation of the effective dielectric constant of graded composites

We generalize the Bergman-Milton spectral representation, originally derived for a two-component composite, to extract the spectral density function for the effective dielectric constant of a graded composite. This work has been motivated by a recent study of the optical absorption spectrum of a graded metallic film [Applied Physics Letters, 85, 94 (2004)] in which a broad surface-plasmon absorption band has been shown to be responsible for enhanced nonlinear optical response as well as an attractive figure of merit. It turns out that, unlike in the case of homogeneous constituent components, the characteristic function of a graded composite is a continuous function because of the continuous variation of the dielectric function within the constituent components. Analytic generalization to three dimensional graded composites is discussed, and numerical calculations of multilayered composites are given as a simple application.Comment: Physical Review E, submitted for publication

Quantum Magnetic Deflagration in Mn12 Acetate

We report controlled ignition of magnetization reversal avalanches by surface acoustic waves in a single crystal of Mn12 acetate. Our data show that the speed of the avalanche exhibits maxima on the magnetic field at the tunneling resonances of Mn12. Combined with the evidence of magnetic deflagration in Mn12 acetate (Suzuki et al., cond-mat/0506569) this suggests a novel physical phenomenon: deflagration assisted by quantum tunneling.Comment: 4 figure