An ultra-bright atom laser

We present a novel, ultra-bright atom-laser and ultra-cold thermal atom beam. Using rf-radiation we strongly couple the magnetic hyperfine levels of 87Rb atoms in a magnetically trapped Bose-Einstein condensate. At low rf-frequencies gravity opens a small hole in the trapping potenital and a well collimated, extremely bright atom laser emerges from just below the condensate. As opposed to traditional atom lasers based on weak coupling, this technique allows us to outcouple atoms at an arbitrarily large rate. We demonstrate an increase in flux per atom in the BEC by a factor of sixteen compared to the brightest quasi-continuous atom laser. Furthermore, we produce by two orders of magnitude the coldest thermal atom beam to date (200 nK).Comment: 20 pages, 9 figures, supplementary material online at http://www.bec.g

Angular Pseudomomentum Theory for the Generalized Nonlinear Schr\"{o}dinger Equation in Discrete Rotational Symmetry Media

We develop a complete mathematical theory for the symmetrical solutions of the generalized nonlinear Schr\"odinger equation based on the new concept of angular pseudomomentum. We consider the symmetric solitons of a generalized nonlinear Schr\"odinger equation with a nonlinearity depending on the modulus of the field. We provide a rigorous proof of a set of mathematical results justifying that these solitons can be classified according to the irreducible representations of a discrete group. Then we extend this theory to non-stationary solutions and study the relationship between angular momentum and pseudomomentum. We illustrate these theoretical results with numerical examples. Finally, we explore the possibilities of the generalization of the previous framework to the quantum limit.Comment: 18 pages; submitted to Physica

Sine-Gordon Soliton on a Cnoidal Wave Background

The method of Darboux transformation, which is applied on cnoidal wave solutions of the sine-Gordon equation, gives solitons moving on a cnoidal wave background. Interesting characteristics of the solution, i.e., the velocity of solitons and the shift of crests of cnoidal waves along a soliton, are calculated. Solutions are classified into three types (Type-1A, Type-1B, Type-2) according to their apparent distinct properties.Comment: 11 pages, 5 figures, Contents change

Hysteresis and metastability of Bose-Einstein condensed clouds of atoms confined in ring potentials

We consider a Bose-Einstein condensed cloud of atoms which rotate in a toroidal/annular potential. Assuming one-dimensional motion, we evaluate the critical frequencies associated with the effect of hysteresis and the critical coupling for stability of the persistent currents. We perform these calculations using both the mean-field approximation and the method of numerical diagonalization of the many-body Hamiltonian which includes corrections due to the finiteness of the atom number.Comment: 7 pages, 5 figures, section on experimental relevance added, final versio

Interaction of matter-wave gap solitons in optical lattices

We study mobility and interaction of gap solitons in a Bose-Einstein condensate (BEC) confined by an optical lattice potential. Such localized wavepackets can exist only in the gaps of the matter-wave band-gap spectrum and their interaction properties are shown to serve as a measure of discreteness imposed onto a BEC by the lattice potential. We show that inelastic collisions of two weakly localized near-the-band-edge gap solitons provide simple and effective means for generating strongly localized in-gap solitons through soliton fusion.Comment: 12 pages, 7 figure

Random-Phase Solitons in Nonlinear Periodic Lattices

We predict the existence of random phase solitons in nonlinear periodic lattices. These solitons exist when the nonlinear response time is much longer than the characteristic time of random phase fluctuations. The intensity profiles, power spectra, and statistical (coherence) properties of these stationary waves conform to the periodicity of the lattice. The general phenomenon of such solitons is analyzed in the context of nonlinear photonic lattices

Stability of vortex solitons in a photorefractive optical lattice

Stability of off-site vortex solitons in a photorefractive optical lattice is analyzed. It is shown that such solitons are linearly unstable in both the high and low intensity limits. In the high-intensity limit, the vortex looks like a familiar ring vortex, and it suffers oscillatory instabilities. In the low-intensity limit, the vortex suffers both oscillatory and Vakhitov-Kolokolov instabilities. However, in the moderate-intensity regime, the vortex becomes stable if the lattice intensity or the applied voltage is above a certain threshold value. Stability regions of vortices are also determined at typical experimental parameters.Comment: 3 pages, 5 figure

Surface Gap Soliton Ground States for the Nonlinear Schr\"{o}dinger Equation

We consider the nonlinear Schr\"{o}dinger equation $(-\Delta +V(x))u = \Gamma(x) |u|^{p-1}u$, $x\in \R^n$ with $V(x) = V_1(x) \chi_{\{x_1>0\}}(x)+V_2(x) \chi_{\{x_1<0\}}(x)$ and $\Gamma(x) = \Gamma_1(x) \chi_{\{x_1>0\}}(x)+\Gamma_2(x) \chi_{\{x_1<0\}}(x)$ and with $V_1, V_2, \Gamma_1, \Gamma_2$ periodic in each coordinate direction. This problem describes the interface of two periodic media, e.g. photonic crystals. We study the existence of ground state $H^1$ solutions (surface gap soliton ground states) for $0<\min \sigma(-\Delta +V)$. Using a concentration compactness argument, we provide an abstract criterion for the existence based on ground state energies of each periodic problem (with $V\equiv V_1, \Gamma\equiv \Gamma_1$ and $V\equiv V_2, \Gamma\equiv \Gamma_2$) as well as a more practical criterion based on ground states themselves. Examples of interfaces satisfying these criteria are provided. In 1D it is shown that, surprisingly, the criteria can be reduced to conditions on the linear Bloch waves of the operators $-\tfrac{d^2}{dx^2} +V_1(x)$ and $-\tfrac{d^2}{dx^2} +V_2(x)$.Comment: definition of ground and bound states added, assumption (H2) weakened (sign changing nonlinearity is now allowed); 33 pages, 4 figure