Tailoring and enhancing spontaneous two-photon emission processes using resonant plasmonic nanostructures

The rate of spontaneous emission is known to depend on the environment of a light source, and the enhancement of one-photon emission in a resonant cavity is known as the Purcell effect. Here we develop a theory of spontaneous two-photon emission for a general electromagnetic environment including inhomogeneous dispersive and absorptive media. This theory is used to evaluate the two-photon Purcell enhancement in the vicinity of metallic nanoparticles and it is demonstrated that the surface plasmon resonances supported by these particles can enhance the emission rate by more than two orders of magnitude. The control over two-photon Purcell enhancement given by tailored nanostructured environments could provide an emitter with any desired spectral response and may serve as an ultimate route for designing light sources with novel properties

Berry phases for the nonlocal Gross-Pitaevskii equation with a quadratic potential

A countable set of asymptotic space -- localized solutions is constructed by the complex germ method in the adiabatic approximation for the nonstationary Gross -- Pitaevskii equation with nonlocal nonlinearity and a quadratic potential. The asymptotic parameter is 1/T, where $T\gg1$ is the adiabatic evolution time. A generalization of the Berry phase of the linear Schr\"odinger equation is formulated for the Gross-Pitaevskii equation. For the solutions constructed, the Berry phases are found in explicit form.Comment: 13 pages, no figure

Isotropic Conductivity of Two-Dimensional Three-Component Symmetric Composites

The effective dc-conductivity problem of isotropic, two-dimensional (2D), three-component, symmetric, regular composites is considered. A simple cubic equation with one free parameter for $\sigma_{e}(\sigma_1,\sigma_2,\sigma_3)$ is suggested whose solutions automatically have all the exactly known properties of that function. Numerical calculations on four different symmetric, isotropic, 2D, three-component, regular structures show a non-universal behavior of $\sigma_{e}(\sigma_1,\sigma_2,\sigma_3)$ with an essential dependence on micro-structural details, in contrast with the analogous two-component problem. The applicability of the cubic equation to these structures is discussed. An extension of that equation to the description of other types of 2D three-component structures is suggested, including the case of random structures. Pacs: 72.15.Eb, 72.80.Tm, 61.50.AhComment: 8 pages (two columns), 8 figures. J. Phys. A - submitte

Quantum analogue of the spin-flop transition for a spin pair

Quantum (step-like) magnetization curves are studies for a spin pair with antiferromagnetic coupling in the presence of a magnetic field parallel to the easy axis of the magnetic anisotropy. The consideration is done both analytically and numerically for a wide range of the anisotropy constants and spins up to $S \gtrsim 100$. Depending on the origin of the anisotropy (exchange or single-ion), the magnetization curve can demonstrate the jumps more than unity and the concentration of the unit jumps in a narrow range of the field. We also point the region of the problem parameters, where the behavior is quasiclassical for $S = 5$, and where system is substantially quantum in the limit $S \to \infty$.Comment: 5 pages, 5 figure

Microscopic model of Purcell enhancement in hyperbolic metamaterials

We study theoretically a dramatic enhancement of spontaneous emission in metamaterials with the hyperbolic dispersion modeled as a cubic lattice of anisotropic resonant dipoles. We analyze the dependence of the Purcell factor on the source position in the lattice unit cell and demonstrate that the optimal emitter position to achieve large Purcell factors and Lamb shifts are in the local field maxima. We show that the calculated Green function has a characteristic cross-like shape, spatially modulated due to structure discreteness. Our basic microscopic theory provides fundamental insights into the rapidly developing field of hyperbolic metamaterials.Comment: 9 pages, 11 figure

Towards the theory of ferrimagnetism

Two-sublattice ferrimagnet, with spin-$s_1$ operators $\bf{S_{1i}}$ at the sublattice $A$ site and spin-$s_2$ operators $\bf{S_{2i}}$ at the sublattice $B$ site, is considered. The magnon of the system, the transversal fluctuation of the total magnetization, is a complicate mixture of the transversal fluctuations of the sublattice $A$ and $B$ spins. As a result, the magnons' fluctuations suppress in a different way the magnetic orders of the $A$ and $B$ sublattices and one obtains two phases. At low temperature $(0,T^*)$ the magnetic orders of the $A$ and $B$ spins contribute to the magnetization of the system, while at the high temperature $(T^*,T_N)$, the magnetic order of the spins with a weaker intra-sublattice exchange is suppressed by magnon fluctuations, and only the spins with stronger intra-sublattice exchange has non-zero spontaneous magnetization. The $T^*$ transition is a transition between two spin-ordered phases in contrast to the transition from spin-ordered state to disordered state ($T_N$-transition). There is no additional symmetry breaking, and the Goldstone boson has a ferromagnetic dispersion in both phases. A modified spin-wave theory is developed to describe the two phases. All known Neel's anomalous $M(T)$ curves are reproduced, in particular that with "compensation point". The theoretical curves are compared with experimental ones for sulpho-spinel $MnCr2S_{4-x}Se_{x}$ and rare earth iron garnets.Comment: 9 pages, 8 figure

Mixed Weyl Symbol Calculus and Spectral Line Shape Theory

A new and computationally viable full quantum version of line shape theory is obtained in terms of a mixed Weyl symbol calculus. The basic ingredient in the collision--broadened line shape theory is the time dependent dipole autocorrelation function of the radiator-perturber system. The observed spectral intensity is the Fourier transform of this correlation function. A modified form of the Wigner--Weyl isomorphism between quantum operators and phase space functions (Weyl symbols) is introduced in order to describe the quantum structure of this system. This modification uses a partial Wigner transform in which the radiator-perturber relative motion degrees of freedom are transformed into a phase space dependence, while operators associated with the internal molecular degrees of freedom are kept in their original Hilbert space form. The result of this partial Wigner transform is called a mixed Weyl symbol. The star product, Moyal bracket and asymptotic expansions native to the mixed Weyl symbol calculus are determined. The correlation function is represented as the phase space integral of the product of two mixed symbols: one corresponding to the initial configuration of the system, the other being its time evolving dynamical value. There are, in this approach, two semiclassical expansions -- one associated with the perturber scattering process, the other with the mixed symbol star product. These approximations are used in combination to obtain representations of the autocorrelation that are sufficiently simple to allow numerical calculation. The leading O(\hbar^0) approximation recovers the standard classical path approximation for line shapes. The higher order O(\hbar^1) corrections arise from the noncommutative nature of the star product.Comment: 26 pages, LaTeX 2.09, 1 eps figure, submitted to 'J. Phys. B.

WIMP-nucleon cross-section results from the second science run of ZEPLIN-III

We report experimental upper limits on WIMP-nucleon elastic scattering cross sections from the second science run of ZEPLIN-III at the Boulby Underground Laboratory. A raw fiducial exposure of 1,344 kg.days was accrued over 319 days of continuous operation between June 2010 and May 2011. A total of eight events was observed in the signal acceptance region in the nuclear recoil energy range 7-29 keV, which is compatible with background expectations. This allows the exclusion of the scalar cross-section above 4.8E-8 pb near 50 GeV/c^2 WIMP mass with 90% confidence. Combined with data from the first run, this result improves to 3.9E-8 pb. The corresponding WIMP-neutron spin-dependent cross-section limit is 8.0E-3 pb. The ZEPLIN programme reaches thus its conclusion at Boulby, having deployed and exploited successfully three liquid xenon experiments of increasing reach

Population of isomers in decay of the giant dipole resonance

The value of an isomeric ratio (IR) in N=81 isotones ($^{137}$Ba, $^{139}$Ce, $^{141}$Nd and $^{143}$Sm) is studied by means of the ($\gamma, n)$ reaction. This quantity measures a probability to populate the isomeric state in respect to the ground state population. In ($\gamma, n)$ reactions, the giant dipole resonance (GDR) is excited and after its decay by a neutron emission, the nucleus has an excitation energy of a few MeV. The forthcoming $\gamma$ decay by direct or cascade transitions deexcites the nucleus into an isomeric or ground state. It has been observed experimentally that the IR for $^{137}$Ba and $^{139}$Ce equals about 0.13 while in two heavier isotones it is even less than half the size. To explain this effect, the structure of the excited states in the energy region up to 6.5 MeV has been calculated within the Quasiparticle Phonon Model. Many states are found connected to the ground and isomeric states by $E1$, $E2$ and $M1$ transitions. The single-particle component of the wave function is responsible for the large values of the transitions. The calculated value of the isomeric ratio is in very good agreement with the experimental data for all isotones. A slightly different value of maximum energy with which the nuclei rest after neutron decay of the GDR is responsible for the reported effect of the A-dependence of the IR.Comment: 16 pages, 4 Fig