A Sensitive Faraday Rotation Setup Using Triple Modulation

The utilization of polarized targets in scattering experiments has become a common practice in many major accelerator laboratories. Noble gases are especially suitable for such applications, since they can be easily hyper-polarized using spin exchange or metastable pumping techniques. Polarized helium-3 is a very popular target because it often serves as an effective polarized neutron due to its simple nuclear structure. A favorite cell material to generate and store polarized helium-3 is GE-180, a relatively dense aluminosilicate glass. In this paper, we present a Faraday rotation method, using a new triple modulation technique, where the measurement of the Verdet constants of SF57 flint glass, pyrex glass, and air were tested. The sensitivity obtained shows that this technique may be implemented in future cell wall characterization and thickness measurements. We also discuss the first ever extraction of the Verdet constant of GE-180 glass for four wavelength values of 632 nm, 773 nm, 1500 nm, and 1547 nm, whereupon the expected 1/{\lambda}^{2} dependence was observed.Comment: 4 pages, 2 figures Updated version for RSI submissio

Resonance solutions of the nonlinear Schr\"odinger equation in an open double-well potential

The resonance states and the decay dynamics of the nonlinear Schr\"odinger (or Gross-Pitaevskii) equation are studied for a simple, however flexible model system, the double delta-shell potential. This model allows analytical solutions and provides insight into the influence of the nonlinearity on the decay dynamics. The bifurcation scenario of the resonance states is discussed, as well as their dynamical stability properties. A discrete approximation using a biorthogonal basis is suggested which allows an accurate description even for only two basis states in terms of a nonlinear, nonhermitian matrix problem.Comment: 21 pages, 14 figure

Exact number conserving phase-space dynamics of the M-site Bose-Hubbard model

The dynamics of M-site, N-particle Bose-Hubbard systems is described in quantum phase space constructed in terms of generalized SU(M) coherent states. These states have a special significance for these systems as they describe fully condensed states. Based on the differential algebra developed by Gilmore, we derive an explicit evolution equation for the (generalized) Husimi-(Q)- and Glauber-Sudarshan-(P)-distributions. Most remarkably, these evolution equations turn out to be second order differential equations where the second order terms scale as 1/N with the particle number. For large N the evolution reduces to a (classical) Liouvillian dynamics. The phase space approach thus provides a distinguished instrument to explore the mean-field many-particle crossover. In addition, the thermodynamic Bloch equation is analyzed using similar techniques.Comment: 11 pages, Revtex

Hamiltonian chaos in a coupled BEC -- optomechanical cavity system

We study a hybrid optomechanical system consisting of a Bose-Einstein condensate (BEC) trapped inside a single-mode optical cavity with a moving end-mirror. The intracavity light field has a dual role: it excites a momentum side-mode of the condensate, and acts as a nonlinear spring that couples the vibrating mirror to that collective density excitation. We present the dynamics in a regime where the intracavity optical field, the mirror, and the side-mode excitation all display bistable behavior. In this regime we find that the dynamics of the system exhibits Hamiltonian chaos for appropriate initial conditions.Comment: 5 figure

Bloch oscillations of Bose-Einstein condensates: Quantum counterpart of dynamical instability

We study the Bloch dynamics of a quasi one-dimensional Bose-Einstein condensate of cold atoms in a tilted optical lattice modeled by a Hamiltonian of Bose-Hubbard type: The corresponding mean-field system described by a discrete nonlinear Schr\"odinger equation can show a dynamical (or modulation) instability due to chaotic dynamics and equipartition over the quasimomentum modes. It is shown, that these phenomena are related to a depletion of the Floquet-Bogoliubov states and a decoherence of the condensate in the many-particle description. Three different types of dynamics are distinguished: (i) decaying oscillations in the region of dynamical instability, and (ii) persisting Bloch oscillations or (iii) periodic decay and revivals in the region of stability.Comment: 12 pages, 14 figure

Evidence for a Single-Spin Azimuthal Asymmetry in Semi-inclusive Pion Electroproduction

Single-spin asymmetries for semi-inclusive pion production in deep-inelastic scattering have been measured for the first time. A significant target-spin asymmetry of the distribution in the azimuthal angle φ of the pion relative to the lepton scattering plane was formed for π^+ electroproduction on a longitudinally polarized hydrogen target. The corresponding analyzing power in the sinφ moment of the cross section is 0.022±0.005±0.003. This result can be interpreted as the effect of terms in the cross section involving chiral-odd spin distribution functions in combination with a chiral-odd fragmentation function that is sensitive to the transverse polarization of the fragmenting quark

Chirality of wave functions for three coalescing levels

The coalescence of three levels has particular attractive features. Even though it may be difficult to realise such event in the laboratory (three additional real parameters must be adjusted), to take up the challenge seems worthwhile. In the same way as the chiral behaviour of a usual EP can give a direction on a line, the state vectors in the vicinity of an EP3 provide an orientation in the plane. The distinction between left and right handedness depends on the distribution of the widths of the three levels in the vicinity of the point of coalescence.Comment: Manuscript has been discussed in June 2007 with the experimental group under Professor Achim Richter at the TU Darmstadt. It has been presented at the 6th International Workshop on Pseudo Hermitian Hamiltonians, London, 16-18 July 2007. An expanded version is being prepared for publication. 3 Figures, 11 page

Kicked Bose-Hubbard systems and kicked tops -- destruction and stimulation of tunneling

In a two-mode approximation, Bose-Einstein condensates (BEC) in a double-well potential can be described by a many particle Hamiltonian of Bose-Hubbard type. We focus on such a BEC whose interatomic interaction strength is modulated periodically by $\delta$-kicks which represents a realization of a kicked top. In the (classical) mean-field approximation it provides a rich mixed phase space dynamics with regular and chaotic regions. By increasing the kick-strength a bifurcation leads to the appearance of self-trapping states localized on regular islands. This self-trapping is also found for the many particle system, however in general suppressed by coherent many particle tunneling oscillations. The tunneling time can be calculated from the quasi-energy splitting of the corresponding Floquet states. By varying the kick-strength these quasi-energy levels undergo both avoided and even actual crossings. Therefore stimulation or complete destruction of tunneling can be observed for this many particle system