We dedicate ourselves to investigating light-matter interactions via both theoretical and experimental perspectives. We expect to understand the nature of light and then find a way to explore the nonlinear and quantum phenomena of many-body systems with light.

•  We theoretically investigate the ground state properties and dynamics of 2D rapidly rotating quantum droplets (QD) confined in a symmetric anharmonic trap. In the presence of a rotation field, radial confinement is reduced by the centrifugal potential, and the Coriolis force experienced by the droplets in the rotating frame is equivalent to the Lorentz force on a charged particle. As the analogy between quantum Hall effects and rapidly rotating BECs in dilute gases has been precisely recognized, it will be interesting to see whether artificial Lorentz forces can also be engineered for a new type of quantum liquid such that the generation of exotic phases carrying nonzero topological charges can be observed, the route for the quantum phase transition can be depicted, and the singularity and stability of the quantum states can be managed in this system. These explorations would make it possible to simulate quantum Hall-type effects in a controlled manner with low-dimensional non-uniform quantum liquids. Because the combined impact of interactions and quantum statistics eventually determines the features of the many-body ground state, such rotating systems allow for the study of artificial orbital magnetism in quantum liquids.

• We theoretically investigate the Bloch oscillations (BO) and the formation of discrete solitons in a dilute Bose-Einstein QD of liquids governed by the Lee-Huang-Yang (LHY)-amended time-dependent Gross-Pitaevskii equation (GPE). We will derive Hamilton’s equation for the quantum droplets by applying the Bloch theorem. Implementing the super-Gaussian associated envelope function will help establish the Euler-Lagrange equations for tracing the characteristic parameters. Determining the group velocity and the effective mass from the effective Hamiltonian will allow us to specify the droplet’s configuration. In the coordinate space, an effective external force-driven damped spring-mass second-order differential equation will also be derived to position the droplet’s center of mass. We expect to establish a parametric hyperspace for the particle number, the lattice depth, and the externally applied force, and depict the domain walls for BO, Landau-Zener tunneling, and Mott-insulator to superfluid phase transition that can separately be observed therein. 

• Using the variational method with the trial wavefunction consisting of a super-Gaussian envelope and the von Neumann lattice function, this work theoretically investigates the formation of triangular, square, and honeycomb vortex lattices and their ground state properties in two-dimensional rotating QDs subjected to s-wave contact interaction, LHY nonlinear interaction, and the dipolar interaction. Within the semiclassical approximation, the vibration dynamics and phonon modes of the honeycomb lattices are also investigated in terms of an effective simple harmonic oscillation model.

• Experiment: we make ultra-broadband long-period fiber gratings (LPGs) in a few-mode fiber (FMF) with periodic mechanical stress. The induced LPGs can provide LP01-to-LP11 mode conversion in a spectral range more extensive than 150 nm by adjusting the stress gradient along the FMF. The few-mode LPGs are then utilized to generate optical doughnut beams with a tunable ytterbium-doped fiber laser. 

• Theory: we define the general form of the Jones vector and establish the Jones matrix for polarizers, wave plates, Faraday rotators, Q-plates, and spiral phase plates. Then we derive the generalized Jones calculus for vortex, vector, and vortex-vector beam transformations. Systematic formalism presents theoretical arrangements for manipulating the phase and polarization of structured light.

• Theory: we study the interaction of electromagnetic (EM) waves with asymmetric triangular apertures and lattices. We find that the center of the 0th-order diffraction spot for an asymmetric triangular aperture is off-axial and frequency-dependent, contrary to conventional symmetric apertures. For asymmetric triangular lattices, an incident wave of a given polarization state can be diffracted into several reflection and transmission modes determined by the EM frequency and lattice structures, and it is available to manipulate the number of diffraction orders and the EM-wave polarization and handedness. The theoretical simulations suggest that the asymmetric triangle apertures and lattices have potential applications in angle-resolved wave scattering detectors, economic spectrum analyzers, tunable frequency filters, polarization beam splitters, and polarization controllers.

• Experiment: we design an Arduino-based network analyzer (NA) via the AD9850 direct digital synthesizer. Our NA may serve as the resonant frequency calibrator of the device under test. The data acquisition is employed under the visualized LabVIEW-for-Arduino instrumentation platform. With the wideband radio-frequency amplifier, we use the enhanced and robust EM wave of 13.56MHz for ultrasonic vibration sensing and demonstrate the relativistic effect on engineering inspection.

• Theory: we study the Rashba and Dresselhaus spin-orbit interactions (RSOI, DSOI) on the magneto-optical dynamics of electrons and excitons in the two-dimensional semiconductor quantum dots and quantum rings. We find that there are open channels for spontaneous recombination for scalar excitons resulting in bright photoluminescence (PL) spectrum, whereas the forbidden recombination of dipolar excitons results in a dark PL spectrum. Moreover, a coherently moving dipolar exciton acquires a nontrivial dual Aharonov-Casher phase, creating the possibility to generate persistent dipole currents and spin dipole currents. A spinor exciton moving coherently or incoherently in the quantum rings would carry a spin angular momentum orienting in the definite directions and rotating spatial-synchronously with the exciton. When both the DSOI and the RSOI provide off-diagonal torques that drive anti-circulating flows, the torsion provided by the RSOI is homogeneous, whereas it is sinusoidally varying when caused by the DSOI. By tuning the strength of the SOIs, we observed the evolution of spin density waves of these spin textures and the tunneling of Bloch walls formed by the SOIs. By controlling the spin degeneracy, we also successfully established sequential light-dark pair ground states. Our study reveals that in the presence of certain spin-orbit generated fields, the manipulation of the magnetic field provides a potential application for quantum-ring spinor excitons to be utilized in nano-scaled magneto-optical switches.

• To further understand many-body effects for the 2D quantum-ring excitons, we also investigate the Raman scattering of spinor excitons with longitudinal optical (LO) phonons. The resonant Raman transition is completed via the exciton-radiation interactions intermediated by the exciton-phonon interaction. We apply the Loudon model for uniaxial crystals with anisotropic dielectric tensor to describe LO phonons' backscattering from an [001]-oriented surface of a stressed zincblende structure. Based on the classical electromagnetic theory, we have constructed the microscopic model for lattice vibrations and the generation of LO phonons under the influences of Coulomb interactions, charge polarization, SOIs, and optical fields. With proper boundary conditions, the Fröhlich potential and the Hamiltonian for the exciton-phonon interaction in a single heterostructure can be derived. Up to the present, the two-photon transition processes have been preliminarily investigated via the calculations of transition amplitude and the differential cross-section. The calculation of the Raman scattering intensity associated with the diagonal of the Raman polarizability reveals the relations for the coupling constant of the exciton-phonon with Raman shift and electromagnetic parameters.

• Experiment: we construct a ring-cavity passively mode-locked EDFL whose pulsewidth can be switched from 473 fs to 1.89 ps and then to 76.8 ns. The mode-locking mechanism of this fiber laser is nonlinear polarization evolution. Various laser operation states, including continuous wave, fundamental mode-locking (FML), noise-like pulse, harmonic mode-locking, nanosecond mode-locking (NML), and dual-width mode-locking, can be obtained by simply adjusting an intracavity polarization controller.

• Theory: we are the first group to perform analytic modeling of the femto/pico/nanosecond mode-locked fiber laser based on the cubic-quintic Ginzburg-Landau equation (CQGLE). Based on a modified and square-root-inversed cosh-based trail function, the pulsewidths of the fiber laser can be calculated as functions of intracavity dispersion, self-phase modulation, cubic saturable absorption, and quintic saturable absorption. Our calculation shows that a broad NML pulse solution is available in the CQGLE modeling with positive quintic SA and positive shaping parameters. For FML pulses, the system with positive SPM and shaping parameters has the potential to form broader pulses at anomalous dispersions, but the broadening effect is limited by the negative shaping parameter at normal dispersions.

• Experiment: By using passive optical technology, we are able to generate both positive- and negative-polarity Gaussian monocycle and doublet pulses in a ring-cavity erbium-doped fiber laser from polarization-locked vector solitons.   

• Theory: Qualitative analysis of vector solitons' properties is performed by analytically solving coupled complex Ginzburg-Landau equations. We also apply the numerical simulation to calculate the fiber laser's pulse parameters and estimate the intracavity birefringence. 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 common properties, 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.