We study the non-Markovianity and quantum speedup of a two-level atom (quantum system of interest) in a dissipative Jaynes-Cumming model, where the atom is embedded in a single-mode cavity, which is leaky being coupled to an external reservoir with Ohmic spectral density. We obtain the non-Markovianity characterized by using the probability of the atomic excited state and the negative decoherence rate in the time-local master equation. We also calculate the quantum speed limit time (QSLT) of the evolution process of the atom. The results show that, the atom-cavity coupling is the main physical reasons of the transition from Markovian to non-Markovian dynamics and the transition from no speedup to speedup process, and the critical value of this sudden transition only depends on the Ohmicity parameter. The atom-cavity coupling and the appropriate reservoir parameters can effectively improve the non-Markovianity in the dynamics process and speed up the evolution of the atom. Moreover, the initial non-Markovian dynamics first turns into Markovian and then back to non-Markovian with increasing the atom-cavity coupling under certain condition. Finally, the physical interpretation is provided.

The generation of vector beams with complex spatial distributions is significant in the field of optical manipulation, optical metrology, optical microscopy, and so on. In this work, we propose a method to generate arbitrary vector beams, which is based on the complex amplitude beam shaping technology and the interferometric optical path configuration. With the method, we can achieve pixel-level control of amplitude, phase, and polarization of an arbitrary vector beam. Furthermore, different polarization states and orientations can be designed to coexist in one beam. The method has been verified with theoretical analysis and experimental results. The proposed method expands the application range of vector beams and provides a conducive way to explore the optical properties of the vector beams.

In this work, we investigate the non-Markovianity, quantum Fisher information (QFI) and quantum coherence of a qubit in a nonequilibrium environment and have obtained the expressions of QFI and quantum coherence as well as their relationship. We have also discussed in detail the influences of the different environment parameters on these quantum effects. The results show that the suitable parameters of the nonequilibrium environment can retard the QFI and quantum coherence in both Markovian and non-Markovian regions. In addition, the smaller memory effects and the larger the jumping rate, the greater the QFI and quantum coherence. And a larger QFI naturally corresponds to a larger quantum coherence, which indicates that the quantum coherence can enlarge the QFI and can effectively enhance the quantum metrology.

The auto-focusing beam based on the circular Airy beam and segmented vortex phase, termed circular Airy segmented vortex beam (CASVB), was generated. During propagation, the focusing properties of the CASVB can be flexibly tunable for multiple degrees of freedom. The results show that the segmentation type of the vortex phase are determined by the number and position of phase jumps, which results in the beam split. Moreover, the number and position of the CASVB gaps coincide with the number and position of the phase jumps. In addition, the edge images can be enhanced by combining the phase of the beam with the phase of the lens. Due to its adjustable number and position of gaps, the CASVB will likely give rise to potential applications in manipulating particles along different segmented intensity trajectories.

Beams with auto-focusing property and a controllable number of wave lobes are of special significance. In this work, based on the helical phase-tuning and the Airy beam, we generate a chiral optical light, which focuses with both radial and angular self-accelerations. The light using the three-dimensional (3D) velocity to control the propagation dimension and the auto-rotating property of intensity peak for the two transverse dimensions is termed as 3D auto-focusing-type chiral optical light (ACOL), which can be controlled by multi-parameters theoretically and experimentally for possessing the characteristics of chiral, focusing, acceleration, rotation, etc. Owing to these characteristics, the ACOL has promising applications in optical micro-manipulation and super-resolution imaging.

In this work, we obtain an analytical representation of the density operator of an atom in a dissipative cavity when the reservoir is at zero temperature and the total number of excitations is N = 1. We also investigated the quantum speed limit time (QSLT) of the atom and the non-Markovianity in the dynamics process. The results show that the QSLT and the non-Markovianity can be effectively manipulated by the atom–cavity coupling and the reservoir parameters. Both of the atom–cavity coupling and the detuning can induce a sudden transition from Markovian to non-Markovian dynamics, and this transition is the main physical reason of the quantum speed-up process. The critical value of the sudden transition from no speed-up to speed-up the atom–cavity coupling and the reservoir parameters. The corresponding physical explanation is also provided for our results.