Supersymmetric and Shape-Invariant Generalization for Nonresonant and Intensity-Dependent Jaynes-Cummings Systems

A class of shape-invariant bound-state problems which represent transition in a two-level system introduced earlier are generalized to include arbitrary energy splittings between the two levels as well as intensity-dependent interactions. We show that the couple-channel Hamiltonians obtained correspond to the generalizations of the nonresonant and intensity-dependent nonresonant Jaynes-Cummings Hamiltonians, widely used in quantized theories of laser. In this general context, we determine the eigenstates, eigenvalues, the time evolution matrix and the population inversion matrix factor.Comment: A combined version of quant-ph/0005045 and quant-ph/0005046. 24 pages, LATE

Exact solution, scaling behaviour and quantum dynamics of a model of an atom-molecule Bose-Einstein condensate

We study the exact solution for a two-mode model describing coherent coupling between atomic and molecular Bose-Einstein condensates (BEC), in the context of the Bethe ansatz. By combining an asymptotic and numerical analysis, we identify the scaling behaviour of the model and determine the zero temperature expectation value for the coherence and average atomic occupation. The threshold coupling for production of the molecular BEC is identified as the point at which the energy gap is minimum. Our numerical results indicate a parity effect for the energy gap between ground and first excited state depending on whether the total atomic number is odd or even. The numerical calculations for the quantum dynamics reveals a smooth transition from the atomic to the molecular BEC.Comment: 5 pages, 4 figure

Quantum integrability and Bethe ansatz solution for interacting matter-radiation systems

A unified integrable system, generating a new series of interacting matter-radiation models with interatomic coupling and different atomic frequencies, is constructed and exactly solved through algebraic Bethe ansatz. Novel features in Rabi oscillation and vacuum Rabi splitting are shown on the example of an integrable two-atom Buck-Sukumar model with resolution of some important controversies in the Bethe ansatz solution including its possible degeneracy for such models.Comment: Latex, 7 pages, 1 figure. Final version to be published in J Phys A (as Letter

Quantum integrable multi atom matter-radiation models with and without rotating wave approximation

New integrable multi-atom matter-radiation models with and without rotating wave approximation (RWA) are constructed and exactly solved through algebraic Bethe ansatz. The models with RWA are generated through ancestor model approach in an unified way. The rational case yields the standard type of matter-radiaton models, while the trigonometric case corresponds to their q-deformations. The models without RWA are obtained from the elliptic case at the Gaudin and high spin limit.Comment: 9 pages, no figure, talk presented in int. conf. NEEDS04 (Gallipoli, Italy, July 2004

Geant4 simulation of production and interaction of muons

A set of models for Monte Carlo simulation of production and interaction of high energy muons is developed in the framework of the Geant4 toolkit. It describes the following physics processes: ionization of high energy muons with radiative corrections, bremsstrahlung, electron-positron pair production, muon induced nuclear reactions, gamma annihilation into muon pair, positron annihilation into muon pair, and into pion pair. These processes are essential for the LHC experiments, for the understanding of the background in underground detectors, for the simulation of effects related with high-energy muons in cosmic ray experiments and for the estimation of backgrounds in future colliders. The applicability area of the models extends to 1 PeV. The major use-cases are discussed

Nonlinear interaction of light with Bose-Einstein condensate: new methods to generate subpoissonian light

We consider $\Lambda$-type model of the Bose-Einstein condensate of sodium atoms interacting with the light. Coefficients of the Kerr-nonlinearity in the condensate can achieve large and negative values providing the possibility for effective control of group velocity and dispersion of the probe pulse. We find a regime when the observation of the "slow" and "fast" light propagating without absorption becomes achievable due to strong nonlinearity. An effective two-level quantum model of the system is derived and studied based on the su(2) polynomial deformation approach. We propose an efficient way for generation of subpoissonian fields in the Bose-Einstein condensate at time-scales much shorter than the characteristic decay time in the system. We show that the quantum properties of the probe pulse can be controlled in BEC by the classical coupling field.Comment: 13 pages, 6 figures, 1 tabl

Fabrication of submicron structures by three-dimensional laser lithography

As a demonstration of unique capabilities of three dimensional laser lithography, an example complex shape microobject and photonic crystals with “woodpile” structure for the infrared spectral range are fabricated by this technique. Photonic dispersion relations for the woodpile structure are calculated for different values of the permittivity contrast and the filling factor.This study was partially supported by the Government of the Russian Federation (project no. 074U01) and the Russian Foundation for Basic Research (project no. 130200186)

Formation of the internal structure of solids under severe action

On the example of a particular problem, the theory of vacancies, a new form of kinetic equations symmetrically incorporation the internal and free energies has been derived. The dynamical nature of irreversible phenomena at formation and motion of defects (dislocations) has been analyzed by a computer experiment. The obtained particular results are extended into a thermodynamic identity involving the law of conservation of energy at interaction with an environment (the 1st law of thermodynamics) and the law of energy transformation into internal degree of freedom (relaxation). The identity is compared with the analogous Jarzynski identity. The approach is illustrated by simulation of processes during severe plastic deformation, the Rybin kinetic equation for this case has been derived.Comment: 9 pages, 5 figure

Leading Order Temporal Asymptotics of the Modified Non-Linear Schrodinger Equation: Solitonless Sector

Using the matrix Riemann-Hilbert factorisation approach for non-linear evolution equations (NLEEs) integrable in the sense of the inverse scattering method, we obtain, in the solitonless sector, the leading-order asymptotics as $t$ tends to plus and minus infinity of the solution to the Cauchy initial-value problem for the modified non-linear Schrodinger equation: also obtained are analogous results for two gauge-equivalent NLEEs; in particular, the derivative non-linear Schrodinger equation.Comment: 29 pages, 5 figures, LaTeX, revised version of the original submission, to be published in Inverse Problem