We study the stationary and propagating solutions for a Bose-Einstein condensate (BEC) in a periodic optical potential with an additional confining optical or magnetic potential. Using an effective mass approximation we express the condensate wave function in terms of slowly-varying envelopes modulating the Bloch modes of the optical lattice. In the limit of a weak nonlinearity, we derive a nonlinear Schrdinger equation for propagation of the envelope function which does not contain the rapid oscillation of the lattice. We then consider the ground state solutions in detail in the regime of weak, moderate and strong nonlinear interactions. We describe the form of solution which is appropriate in each regime, and place careful limits on the validity of each type of solution. Finally we extend the study to the propagating dynamics of a spinor atomic BEC in an optical lattice and some interesting phenomena are revealed.
We review our recent experimental progress in quantum technology employing amplification effect of four-wave mixing in a rubidium vapor. We have produced an intensity difference squeezed light source at frequencies as low as 1.5 kHz which is so far the lowest frequency at which squeezing has been observed in an atomic system. Moreover, we find that the bandwidth of our squeezed light source can be controlled with light intensity pumping. Using our non-classical light source, we have further developed a nonlinear Mach-Zehnder (MZ) interferometer, for which the maximum fringe intensity depends quadratically on the intensity of the phase-sensing field at the high-gain regime, leading to much better sensitivity than a linear MZ interferometer in which the beam splitters have the same phase-sensing intensity. The quantum technologies developed by our group could have great potential in areas such as precision measurement and quantum information.
