A nonlinear Landau-Zener model was proposed recently to describe, among a number of applications, the nonadiabatic transition of a Bose-Einstein condensate between Bloch bands. Numerical analysis revealed a striking phenomenon that tunneling occurs even in the adiabatic limit as the nonlinear parameter $C$ is above a critical value equal to the gap $V$ of avoided crossing of the two levels. In this paper, we present analytical results that give quantitative account of the breakdown of adiabaticity by mapping this quantum nonlinear model into a classical Josephson Hamiltonian. In the critical region, we find a power-law scaling of the nonadiabatic transition probability as a function of $C/V-1$ and $\alpha $, the crossing rate of the energy levels. In the subcritical regime, the transition probability still follows an exponential law but with the exponent changed by the nonlinear effect. For $C/V>>1$, we find a near unit probability for the transition between the adiabatic levels for all values of the crossing rate.Comment: 9 figure

Focus Serial: Frontiers of Nonlinear Optics

We consider a harmonic charging field as an energy charger for the quantum battery, which consists of an ensemble of two-level atoms. The charging of noninteracting atoms is completely fulfilled, which exhibits a substantial improvement over previous static charging fields. Involving the repulsive interactions of atoms, the fully charging is achieved with shorter charged period over the noninteracting case, yielding an advantage for the charing. Excluding the charging field, a quantum phase transition is induced by the attractive atom-atom interactions, and the interacting atoms become to be degenerate in the ground state. We find that the degenerate states play a negative role in the charging due to the gapless energies. The atoms with strong attractive interactions can not be charged completely, which is accompanied by a drop of the maximum stored energy.

We demonstrate low-threshold supercontinuum generated in a highly nonlinear arsenic selenide chalcogenide nanowire with tailored dispersion. The tapered submicrometer chalcogenide fiber exhibits an ultrahigh nonlinearity, n(2) approximately 1.1x10(-17) m(2)/W and an effective mode area of 0.48 mum(2), yielding an effective nonlinearity of gamma approximately 93.4 W/m, which is over 80,000 times larger than standard silica single-mode fiber at a wavelength of approximately 1550 nm. This high nonlinearity, in conjunction with the engineered anomalous dispersion, enables low-threshold soliton fission leading to large spectral broadening at a dramatically reduced peak power of several watts, corresponding to picojoule energy.