We present a theoretical study of the energy levels in a parabolically confined quantum dot in the presence of the Rashba spin-orbit interaction (SOI). The features of some low-lying states in various strengths of the SOI are examined at finite magnetic fields. The presence of a magnetic field enhances the possibility of the spin polarization and the SOI leads to different energy dependence on magnetic fields applied. Furthermore, in high magnetic fields, the spectra of low-lying states show basic features of Fock-Darwin levels as well as Landau levels.

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We report a passively mode-locked erbium-doped fiber laser with pulse widths switchable from 473 fs to 76.8 ns, where the fundamental mode-locking, noise-like pulse, nanosecond mode-locking, and dual-width mode-locking (DML) are obtained by adjusting a polarization controller. Co-existence of femto- and nano-second pulses in DML is attributed to the gain balancing. Analytic modeling of the fiber laser with the cubic-quintic Ginzburg-Landau equation is presented, in which the pulse widths are calculated as functions of dispersion, self-phase modulation (SPM), cubic saturable absorption (SA), and quintic SA. The generation of nanosecond pulses is caused by the weakened intracavity pulse-shortening strength, the reduced effective SPM, and the inclusion of quintic SA in the laser cavity.

We have numerically solved the Hamiltonian of an electron in a semiconductor double ring subjected to the magnetic flux and Rashba spin-orbit interaction. It is found that the Aharonov-Bohm energy spectrum reveals multi-zigzag periodic structures. The investigations of spin-dependent electron dynamics via Rabi oscillations in two-level and three-level systems demonstrate the possibility of manipulating quantum states. Our results show that the optimal control of photon-assisted inter-ring transitions can be achieved by employing cascade-type and Λ-type transition mechanisms. Under chirped pulse impulsions, a robust and complete transfer of an electron to the final state is shown to coincide with the estimation of the Landau-Zener formula.

Both positive- and negative-polarity Gaussian monocycle and doublet pulses, for which the pulse shapes are the first and second derivatives of Gaussian functions plus some continuous-wave backgrounds respectively, are generated in a ring-cavity erbium-doped fiber laser from polarization-locked vector solitons by using passive optical technology. The pulse states are switchable and are found to be the superposition of bright and dark solitons with different widths, amplitudes, time delays, polarizations, and wavelengths. Qualitative analysis of the properties of vector solitons are performed by solving coupled complex Ginzburg–Landau equations, and analytic modeling of the fiber laser is presented. By representing the envelopes of bright soliton by sech- and dark soliton by tanh-based functions, the incoherent superposition of these two soliton components have simulated the experimental observations, and the underlying mechanisms for the formation of monocycle and doublet pulses are attributed to the polarization locking of bright and dark solitons. The theoretical modeling is used to calculate the pulse parameters of the fiber laser, and the intracavity birefringence can be estimated. The results of tunable optical vector solitons are compared with atomic solitons in the system of Bose–Einstein condensation. Since the governing equations for soliton generation in fiber lasers and Bose–Einstein condensation have many properties in common, thus the simulation and propagation of pulsating waves may open a new route to explore the classical solitary dynamics in nonlinear optics and its quantum analogy in ultracold fields.