We investigate a special class of nonlinear periodic waves and their stabilities for a Bose–Einstein condensate in a pure cosine nonlinear lattice. It is shown that for a specific range of the ...lattice parameters, we can obtain two different types of exact periodic waves, one-period and double-period solutions. Landau and dynamical instabilities of these extended states are analyzed. The stability phase diagrams for these exact solutions are identified numerically. Our results indicate that as the modulation amplitude of the nonlinear lattice is increased, the double-period solutions are more stable than the one-period solutions.
•For certain specific lattice parameters, we obtain new exact one-period and double-period solutions for a Bose–Einstein condensate in a pure cosine nonlinear lattice.•The stability phase diagrams for Landau and dynamical instabilities of these exact periodic waves are identified numercially.•For a large modulation amplitude of the nonlinear lattice, the double-period solutions are more dynamically stable than the one-period solutions.
We present exact analytical results for bright and dark solitons in a type of one-dimensional spatially inhomogeneous nonlinearity. We show that the competition between a homogeneous self-defocusing ...(SDF) nonlinearity and a localized self-focusing (SF) nonlinearity supports stable fundamental bright solitons. For a specific choice of the nonlinear parameters, exact analytical solutions for fundamental bright solitons have been obtained. By applying both variational approximation and Vakhitov-Kolokolov stability criterion, it is found that exact fundamental bright solitons are stable. Our analytical results are also confirmed numerically. Additionally, we show that a homogeneous SF nonlinearity modulated by a localized SF nonlinearity allows the existence of exact dark solitons, for certain special cases of nonlinear parameters. By making use of linear stability analysis and direct numerical simulation, it is found that these exact dark solitons are linearly unstable.
In this study we have investigated the quantum tunneling of two repulsive bosons in a triple-well potential, subject to a high-frequency driving field. By means of the multiple-time-scale asymptotic ...analysis, we evidence a far-off-resonant strongly interacting regime in which the dominant tunneling of doublons (paired states) is a second-order process and the selected coherent destruction of tunneling occurs either between doublons or between unpaired states. Two Floquet quasienergy bands of both kinds of states are given analytically, where a fine structure up to the second-order corrections is displayed. The analytical results are confirmed numerically, based on the exact model, and may be particularly relevant to controlling correlated tunneling in experiments.
We introduce three different types of periodically-driven multiparametric two-level models whose analytical solutions are given in terms of Heun functions. These results are applied to obtain exact ...analytical results for certain types of periodic potentials and asymmetric double-well potentials. In particular, it is shown that under special parameter conditions, an experimentally realised periodic potential supports the exact in-gap solutions. In the asymmetric double-well potentials, some exact results of the bound-state wave functions and associated energies are found in explicit form.
All-solid-state 228.5 nm Deep Ultraviolet (DUV) laser has been studied with two-step second harmonious generation (SHG) of Nd:YVO 4 914 nm fundamental laser, by optimizing its resonator design and ...SHG configurations. Adopting three-mirror folded V cavity and acousto-optical Q-switching, high peak power 457 nm laser output has been achieved by intracavity frequency-doubling of LD pumped Nd:YVO 4 914 nm fundamental laser. At pump power of 41 W, the average output power for 457 nm laser has reached 600 mW at repetition frequency 10 kHz, 50 ns pulse width. With Type-I phase matching BBO crystal, external frequency doubling of 457 nm blue output was realized and optimized. Under LD pump power of 41 W, DUV laser at 228.5 nm with average output power of 35 mW has been achieved, at repetition frequency 10 kHz and pulse width of 46 ns. Under these conditions, the frequency doubling conversion efficiency is 5.8%, and the DUV laser output power instability is less than 2% in 2-hour test.
We show that the frequently encountered physical model of a monochromatically driven two-level system is exactly solvable. We present an analytical exact solution to this driven system in terms of ...two known special functions. Our analytical solution is valid for all parameter regimes and may find applications in current solid-state experiments.
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