Classical and quantum dynamics of a model for atomic-molecular Bose--Einstein condensates

We study a model for a two-mode atomic-molecular Bose--Einstein condensate. Starting with a classical analysis we determine the phase space fixed points of the system. It is found that bifurcations of the fixed points naturally separate the coupling parameter space into four regions. The different regions give rise to qualitatively different dynamics. We then show that this classification holds true for the quantum dynamics.Comment: 13 pages, 7 eps figure

Instability Heating of Sympathetically-Cooled Ions in a Linear Paul Trap

Sympathetic laser cooling of ions stored within a linear-geometry, radio frequency, electric-quadrupole trap has been investigated using computational and theoretical techniques. The simulation, which allows 5 sample ions to interact with 35 laser-cooled atomic ions, revealed an instability heating mechanism, which can prevent ions below a certain critical mass from being sympathetically cooled. This critical mass can however be varied by changing the trapping field parameters thus allowing ions with a very large range of masses to be sympathetically cooled using a single ion species. A theoretical explanation of this instability heating mechanism is presented which predicts that the cooling-heating boundary in trapping parameter space is a line of constant $q_u$ (ion trap stability coefficient), a result supported by the computational results. The threshold value of $q_u$ depends on the masses of the interacting ions. A functional form of this dependence is given

Time-dependent unitary perturbation theory for intense laser driven molecular orientation

We apply a time-dependent perturbation theory based on unitary transformations combined with averaging techniques, on molecular orientation dynamics by ultrashort pulses. We test the validity and the accuracy of this approach on LiCl described within a rigid-rotor model and find that it is more accurate than other approximations. Furthermore, it is shown that a noticeable orientation can be achieved for experimentally standard short laser pulses of zero time average. In this case, we determine the dynamically relevant parameters by using the perturbative propagator, that is derived from this scheme, and we investigate the temperature effects on the molecular orientation dynamics.Comment: 16 pages, 6 figure

A continuous source of translationally cold dipolar molecules

The Stark interaction of polar molecules with an inhomogeneous electric field is exploited to select slow molecules from a room-temperature reservoir and guide them into an ultrahigh vacuum chamber. A linear electrostatic quadrupole with a curved section selects molecules with small transverse and longitudinal velocities. The source is tested with formaldehyde (H2CO) and deuterated ammonia (ND3). With H2CO a continuous flux is measured of approximately 10^9/s and a longitudinal temperature of a few K. The data are compared with the result of a Monte Carlo simulation.Comment: 4 pages, 4 figures v2: small changes in the abstract, text and references. Figures 1 & 2 regenerated to prevent errors in the pd

Dirac field on Moyal-Minkowski spacetime and non-commutative potential scattering

The quantized free Dirac field is considered on Minkowski spacetime (of general dimension). The Dirac field is coupled to an external scalar potential whose support is finite in time and which acts by a Moyal-deformed multiplication with respect to the spatial variables. The Moyal-deformed multiplication corresponds to the product of the algebra of a Moyal plane described in the setting of spectral geometry. It will be explained how this leads to an interpretation of the Dirac field as a quantum field theory on Moyal-deformed Minkowski spacetime (with commutative time) in a setting of Lorentzian spectral geometries of which some basic aspects will be sketched. The scattering transformation will be shown to be unitarily implementable in the canonical vacuum representation of the Dirac field. Furthermore, it will be indicated how the functional derivatives of the ensuing unitary scattering operators with respect to the strength of the non-commutative potential induce, in the spirit of Bogoliubov's formula, quantum field operators (corresponding to observables) depending on the elements of the non-commutative algebra of Moyal-Minkowski spacetime.Comment: 60 pages, 1 figur

Photoassociative Production and Trapping of Ultracold KRb Molecules

We have produced ultracold heteronuclear KRb molecules by the process of photoassociation in a two-species magneto-optical trap. Following decay of the photoassociated KRb*, the molecules are detected using two-photon ionization and time-of-flight mass spectroscopy of KRb$^+$. A portion of the metastable triplet molecules thus formed are magnetically trapped. Photoassociative spectra down to 91 cm$^{-1}$ below the K(4$s$) + Rb (5$p_{1/2}$) asymptote have been obtained. We have made assignments to all eight of the attractive Hund's case (c) KRb* potential curves in this spectral region.Comment: 4 pages, 4 figure

The LQG -- String: Loop Quantum Gravity Quantization of String Theory I. Flat Target Space

We combine I. background independent Loop Quantum Gravity (LQG) quantization techniques, II. the mathematically rigorous framework of Algebraic Quantum Field Theory (AQFT) and III. the theory of integrable systems resulting in the invariant Pohlmeyer Charges in order to set up the general representation theory (superselection theory) for the closed bosonic quantum string on flat target space. While we do not solve the, expectedly, rich representation theory completely, we present a, to the best of our knowledge new, non -- trivial solution to the representation problem. This solution exists 1. for any target space dimension, 2. for Minkowski signature of the target space, 3. without tachyons, 4. manifestly ghost -- free (no negative norm states), 5. without fixing a worldsheet or target space gauge, 6. without (Virasoro) anomalies (zero central charge), 7. while preserving manifest target space Poincar\'e invariance and 8. without picking up UV divergences. The existence of this stable solution is exciting because it raises the hope that among all the solutions to the representation problem (including fermionic degrees of freedom) we find stable, phenomenologically acceptable ones in lower dimensional target spaces, possibly without supersymmetry, that are much simpler than the solutions that arise via compactification of the standard Fock representation of the string. Moreover, these new representations could solve some of the major puzzles of string theory such as the cosmological constant problem. The solution presented in this paper exploits the flatness of the target space in several important ways. In a companion paper we treat the more complicated case of curved target spaces.Comment: 46 p., LaTex2e, no figure

Constraints, gauge symmetries, and noncommutative gravity in two dimensions

After an introduction into the subject we show how one constructs a canonical formalism in space-time noncommutative theories which allows to define the notion of first-class constraints and to analyse gauge symmetries. We use this formalism to perform a noncommutative deformation of two-dimensional string gravity (also known as Witten black hole).Comment: Based on lectures given at IFSAP-2004 (St.Petersburg), to be submitted to Theor. Math. Phys., dedicated to Yu.V.Novozhilov on the occasion of his 80th birthda

Causality and dispersion relations and the role of the S-matrix in the ongoing research

The adaptation of the Kramers-Kronig dispersion relations to the causal localization structure of QFT led to an important project in particle physics, the only one with a successful closure. The same cannot be said about the subsequent attempts to formulate particle physics as a pure S-matrix project. The feasibility of a pure S-matrix approach are critically analyzed and their serious shortcomings are highlighted. Whereas the conceptual/mathematical demands of renormalized perturbation theory are modest and misunderstandings could easily be corrected, the correct understanding about the origin of the crossing property requires the use of the mathematical theory of modular localization and its relation to the thermal KMS condition. These new concepts, which combine localization, vacuum polarization and thermal properties under the roof of modular theory, will be explained and their potential use in a new constructive (nonperturbative) approach to QFT will be indicated. The S-matrix still plays a predominant role but, different from Heisenberg's and Mandelstam's proposals, the new project is not a pure S-matrix approach. The S-matrix plays a new role as a "relative modular invariant"..Comment: 47 pages expansion of arguments and addition of references, corrections of misprints and bad formulation

t→bWt \to b W in NonCommutative Standard Model

We study the top quark decay to b quark and W boson in the NonCommutative Standard Model (NCSM). The lowest contribution to the decay comes from the terms quadratic in the matrix describing the noncommutative (NC) effects while the linear term is seen to identically vanish because of symmetry. The NC effects are found to be significant only for low values of the NC characteristic scale.Comment: 11 page Latex file containing 2 eps figures (redrawn). More discussion included. To appear in PR