Phase-matched four wave mixing and quantum beam splitting of matter waves in a periodic potential

We show that the dispersion properties imposed by an external periodic potential ensure both energy and quasi-momentum conservation such that correlated pairs of atoms can be generated by four wave mixing from a Bose-Einstein condensate moving in an optical lattice potential. In our numerical solution of the Gross-Pitaevskii equation, a condensate with initial quasi-momentum k_0 is transferred almost completely (>95%) into a pair of correlated atomic components with quasi-momenta k_1 and k_2, if the system is seeded with a smaller number of atoms with the appropriate quasi-momentum k_1.Comment: 4 pages, 4 figures, version accepted for publication in Phys. Rev. A, Rapid Communication

Dynamics of Bose-Einstein Condensates in One-Dimensional Optical Lattices in the Presence of Transverse Resonances

The dynamics of Bose-Einstein condensates in the lowest energy band of a one-dimensional optical lattice is generally disturbed by the presence of transversally excited resonant states. We propose an effective one-dimensional theory which takes these resonant modes into account and derive variational equations for large-scale dynamics. Several applications of the theory are discussed and a novel type of "triple soliton" is proposed, which consists of a superposition of a wavepacket at the upper band edge and two transversally excited wavepackets which are displaced in quasi-momentum space.Comment: 12 pages, 6 figure

Matter wave soliton collisions in the quasi one dimensional potential

We consider soliton solutions of a two-dimensional nonlinear system with the self-focusing nonlinearity and a quasi-1D confining potential, taking harmonic potential as an example. We investigate a single soliton in detail and find criterion for possible collapse. This information is then used to investigate the dynamics of the two soliton collision. In this dynamics we identify three regimes according to the relation between nonlinear interaction and the excitation energy: elastic collision, excitation and collapse regime. We show that surprisingly accurate predictions can be obtained from variational analysis.Comment: 8 pages 7 figure

Quantum Field Theoretical Analysis on Unstable Behavior of Bose-Einstein Condensates in Optical Lattices

We study the dynamics of Bose-Einstein condensates flowing in optical lattices on the basis of quantum field theory. For such a system, a Bose-Einstein condensate shows a unstable behavior which is called the dynamical instability. The unstable system is characterized by the appearance of modes with complex eigenvalues. Expanding the field operator in terms of excitation modes including complex ones, we attempt to diagonalize the unperturbative Hamiltonian and to find its eigenstates. It turns out that although the unperturbed Hamiltonian is not diagonalizable in the conventional bosonic representation the appropriate choice of physical states leads to a consistent formulation. Then we analyze the dynamics of the system in the regime of the linear response theory. Its numerical results are consitent with as those given by the discrete nonlinear Schrodinger equation.Comment: 16pages, 4figure

Wideband tuning of four-wave mixing in solid-core liquid-filled photonic crystal fibers

We present an experimental study of parametric four-wave mixing generation in photonic crystal fibers that have been infiltrated with ethanol. A silica photonic crystal fiber was designed to have the proper dispersion properties after ethanol infiltration for the generation of widely spaced four-wave mixing (FWM) bands under 1064 nm pumping. We demonstrate that the FWM bands can be tuned in a wide wavelength range through the thermo-optic effect. Band shifts of 175 and over 500 nm for the signal and idler bands, respectively, are reported. The reported results can be of interest in many applications, such as CARS microscopy