Fast atomic transport without vibrational heating

We use the dynamical invariants associated with the Hamiltonian of an atom in a one dimensional moving trap to inverse engineer the trap motion and perform fast atomic transport without final vibrational heating. The atom is driven non-adiabatically through a shortcut to the result of adiabatic, slow trap motion. For harmonic potentials this only requires designing appropriate trap trajectories, whereas perfect transport in anharmonic traps may be achieved by applying an extra field to compensate the forces in the rest frame of the trap. The results can be extended to atom stopping or launching. The limitations due to geometrical constraints, energies and accelerations involved are analyzed, as well as the relation to previous approaches (based on classical trajectories or "fast-forward" and "bang-bang" methods) which can be integrated in the invariant-based framework.Comment: 10 pages, 5 figure

Nonlinearity Management in Higher Dimensions

In the present short communication, we revisit nonlinearity management of the time-periodic nonlinear Schrodinger equation and the related averaging procedure. We prove that the averaged nonlinear Schrodinger equation does not support the blow-up of solutions in higher dimensions, independently of the strength in the nonlinearity coefficient variance. This conclusion agrees with earlier works in the case of strong nonlinearity management but contradicts those in the case of weak nonlinearity management. The apparent discrepancy is explained by the divergence of the averaging procedure in the limit of weak nonlinearity management.Comment: 9 pages, 1 figure

Bi-stable tunneling current through a molecular quantum dot

An exact solution is presented for tunneling through a negative-U d-fold degenerate molecular quantum dot weakly coupled to electrical leads. The tunnel current exhibits hysteresis if the level degeneracy of the negative-U dot is larger than two (d>2). Switching occurs in the voltage range V1 < V < V2 as a result of attractive electron correlations in the molecule, which open up a new conducting channel when the voltage is above the threshold bias voltage V2. Once this current has been established, the extra channel remains open as the voltage is reduced down to the lower threshold voltage V1. Possible realizations of the bi-stable molecular quantum dots are fullerenes, especially C60, and mixed-valence compounds.Comment: 5 pages, 1 figure. (v2) Figure updated to compare the current hysteresis for degeneracies d=4 and d>>1 of the level in the dot, minor corrections in the text. To appear in Phys. Rev.

Observation of narrow baryon resonance decaying into pKs0pK^0_s in pA-interactions at 70GeV/c70 GeV/c with SVD-2 setup

SVD-2 experiment data have been analyzed to search for an exotic baryon state, the $\Theta^+$-baryon, in a $pK^0_s$ decay mode at $70 GeV/c$ on IHEP accelerator. The reaction $pA \to pK^0_s+X$ with a limited multiplicity was used in the analysis. The $pK^0_s$ invariant mass spectrum shows a resonant structure with $M=1526\pm3(stat.)\pm 3(syst.) MeV/c^2$ and $\Gamma < 24 MeV/c^2$. The statistical significance of this peak was estimated to be of $5.6 \sigma$. The mass and width of the resonance is compatible with the recently reported $\Theta^+$- baryon with positive strangeness which was predicted as an exotic pentaquark ($uudd\bar{s}$) baryon state. The total cross section for $\Theta^+$ production in pN-interactions for $X_F\ge 0$ was estimated to be $(30\div120) \mu b$ and no essential deviation from A-dependence for inelastic events $(\sim A^{0.7})$ was found.Comment: 8 pages, 7 figures, To be submitted to Yadernaya Fizika. v3-v5 - Some references added, minor typos correcte

The Minimum-Uncertainty Squeezed States for for Atoms and Photons in a Cavity

We describe a six-parameter family of the minimum-uncertainty squeezed states for the harmonic oscillator in nonrelativistic quantum mechanics. They are derived by the action of corresponding maximal kinematical invariance group on the standard ground state solution. We show that the product of the variances attains the required minimum value 1/4 only at the instances that one variance is a minimum and the other is a maximum, when the squeezing of one of the variances occurs. The generalized coherent states are explicitly constructed and their Wigner function is studied. The overlap coefficients between the squeezed, or generalized harmonic, and the Fock states are explicitly evaluated in terms of hypergeometric functions. The corresponding photons statistics are discussed and some applications to quantum optics, cavity quantum electrodynamics, and superfocusing in channeling scattering are mentioned. Explicit solutions of the Heisenberg equations for radiation field operators with squeezing are found.Comment: 27 pages, no figures, 174 references J. Phys. B: At. Mol. Opt. Phys., Special Issue celebrating the 20th anniversary of quantum state engineering (R. Blatt, A. Lvovsky, and G. Milburn, Guest Editors), May 201

Stability and collapse of localized solutions of the controlled three-dimensional Gross-Pitaevskii equation

On the basis of recent investigations, a newly developed analytical procedure is used for constructing a wide class of localized solutions of the controlled three-dimensional (3D) Gross-Pitaevskii equation (GPE) that governs the dynamics of Bose-Einstein condensates (BECs). The controlled 3D GPE is decomposed into a two-dimensional (2D) linear Schr\"{o}dinger equation and a one-dimensional (1D) nonlinear Schr\"{o}dinger equation, constrained by a variational condition for the controlling potential. Then, the above class of localized solutions are constructed as the product of the solutions of the transverse and longitudinal equations. On the basis of these exact 3D analytical solutions, a stability analysis is carried out, focusing our attention on the physical conditions for having collapsing or non-collapsing solutions.Comment: 21 pages, 14 figure

Adiabatic invariants and Mixmaster catastrophes

We present a rigorous analysis of the role and uses of the adiabatic invariant in the Mixmaster dynamical system. We propose a new invariant for the global dynamics which in some respects has an improved behaviour over the commonly used one. We illustrate its behaviour in a number of numerical results. We also present a new formulation of the dynamics via Catastrophe Theory. We find that the change from one era to the next corresponds to a fold catastrophe, during the Kasner shifts the potential is an Implicit Function Form whereas, as the anisotropy dissipates, the Mixmaster potential must become a Morse 0--saddle. We compare and contrast our results to many known works on the Mixmaster problem and indicate how extensions could be achieved. Further exploitation of this formulation may lead to a clearer understanding of the global Mixmaster dynamics.Comment: 24 pages, LaTeX, 5 figures (which can be obtained by sending a message to the first author), submitted to Phys.Rev.

Properties of Neutral Charmed Mesons in Proton--Nucleus Interactions at 70 GeV

The results of treatment of data obtained in the SERP-E-184experiment "Investigation of mechanisms of the production of charmed particles in proton-nucleus interactions at 70 GeV and their decays" by irradiating the active target of the SVD-2 facility consisting of carbon, silicon, and lead plates, are presented. After separating a signal from the two-particle decay of neutral charmed mesons and estimating the cross section for charm production at a threshold energy {\sigma}(c\v{c})=7.1 \pm 2.4(stat.) \pm 1.4(syst.) \mub/nucleon, some properties of D mesons are investigated. These include the dependence of the cross section on the target mass number (its A dependence); the behavior of the differential cross sections d{\sigma}/dpt2 and d{\sigma}/dxF; and the dependence of the parameter {\alpha} on the kinematical variables xF, pt2, and plab. The experimental results in question are compared with predictions obtained on the basis of the FRITIOF7.02 code.Comment: 9 pages, 9 figures,3 table