In this paper, we studied the evolution of a system of two atoms of different energy levels interacting with a single-mode optical field, with one atom in the ground state and the other in the excited state. Entanglement between atoms was studied using partial transposition of negative eigenvalues and the effects of the dyadic interaction and the photon number on the evolution of the entanglement between the two atoms were discussed separately. The results show that increasing the coupling interactions and decreasing the photon number can lead to increased interatomic entanglement, and that increasing both coupling interactions and photon number can lead to shorter interatomic evolution periods. This study will help to find ways to enhance interatomic entanglement.

High finesse ultra-stable optical Fabry-Perot (F-P) cavity can provide high-precision frequency standard and fine frequency resolution, it plays an important role in optical frequency atomic clock and quantum precision measurement, and controlling its temperature to the zero-expansion temperature can effectively improve the frequency stability. In the experiment, a set of spherical flat concave F-P cavities made of glass ceramics with ultra-low expansion (ULE) coefficient is designed and prepared. It is plated with 1 560.5 nm and 637 nm antireflection film and placed in an ultra-high vacuum system with accurate temperature control. Using the modulated sideband method, the free spectral range of the ultra-stable optical cavity is 3.145 GHz and the cavity linewidth is ～ 100 kHz. The fineness of the ultra-stable optical cavity in the set wavelength laser can be more than 30 000. On this basis, the 1 560.5 nm laser is doubled to 780.25 nm by the frequency-doubling waveguide device. By comparing the resonant frequency of the ultra-stable optical cavity with the saturated absorption spectra of the rubidium atom, the accurate value of the resonant frequency of the ultra-stable optical cavity at different temperatures is obtained. According to the change of the relative cavity length, the thermal expansion characteristics of the ultra-stable optical cavity system are measured, and the zero expansion temperature is 10.688±0.115?°C. The high finesse optical cavity provides a stable frequency reference, and can effectively narrow the laser linewidth and suppress phase noise. It is an important tool for generating high-quality laser sources. We have applied its excellent short-term frequency stability and extremely low-frequency noise to the 318.6 nm narrow linewidth ultraviolet laser with high stability through 637.2 nm laser cavity-enhanced frequency doubling, and further applied it to the study of cesium atom single-step Rydberg direct excitation and Rydberg dressed ground state cesium atom ensemble.

The background magnetic field has an important influence on the long-term closed-loop operation and the uncertainty evaluation for atomic optical clocks. The second-order Zeeman shift introduced by the backgroundmagnetic field is one of the important terms to be considered. In this paper, we firstly measure the spacing difference of the Zeeman splitting corresponding to the two transitions of ytterbium clock transition 1S0→3P0 along with the different background magnetic field. Secondly, the spacing difference of the Zeeman splitting along with the driven current of the shielding magnetic field is obtained. Finally, the driven current of the shielding magnetic field used to generate the minimum the spacing difference of the Zeeman splitting is derived in three dimensions. Based on the measurement, the second-order Zeeman shift can be obtained by tuning the polarizing magnetic field in high and low modes by self-comparison method. The result shows the coefficient of the second-order Zeeman shift is －0.0655(3)?Hz/G2 and the uncertainty due to the second-order Zeeman shift is 5.7×10－17. This work will contribute to the total uncertainty budget of our ytterbium lattice clock in the future.

The atomic polarizability reflects the degree of response of the atomic system to the external field. The Rydberg atom has a very large polarizability, which makes the Rydberg atom have great application prospects in the external field manipulation of quantum states and the measurement of microwave field strength. The measurement accuracy of polarizability will lay a theoretical foundation for the precise measurement of the external field. In this paper, the measurement of atomic polarizability in the Rydberg state of cesium 50D is realized by using the electromagnetically induced transparency technique. In the experiment, based on the stepped electromagnetically induced transparency spectrum, the AC-Stark effectof the 50D state of the cesium atom was first measured, and the relationship between the spectral splitting interval of the atomic energy level and the field strength was studied, and the tensor polarizability and scalar polarizability were calculated. experimental measurements. The experimentally measured values are compared with the calculated values, and the two are basically consistent. The measurement of the Rydberg state polarizability provides a guarantee for the regulation of the energy level by the electric field and the precise measurement of the electric field strength of the radio frequency field.

Quantum steering is an important quantum resource, which plays an important role in quantum information processing, quantum secure communication, quantum key distribution and other aspects. Compared with other kinds of quantum entanglements, quantum steering has the advantage of natural asymmetry, which can realize one-side device-independent quantum tasks. Quantum steering can be generated by beam splitter network, nonlinear process, optical frequency comb system and optomechanical system. In this paper, we consider incident single pump light into an optomechanical cavity containing a moving cavity mirror under special conditions, which is the frequency of the mechanical oscillator equal to half of the free spectral region of the cavity. Under the action of the radiation pressure of the light field, the mechanical mode can be coupled with the two cavity modes in the cavity, thus producing tripartite entanglement. We study the quantum steering properties of the entanglement region. The results show that the steering of mechanical mode to two optical modes is stronger than that of optical mode to mechanical mode, and the mechanical mode to optical mode steering is more robust to temperature, and the conversion between one-way steering and two-way steering between mechanical and optical modes can be realized by adjusting the detuning and the temperature. Because of the symmetry of the two optical modes, the exchange invariance of the two optical modes is obtained. The steering of mechanical mode and optical mode to single optical modes is stronger than the one-way steering of optical mode to optical mode. The combined steering of two optical modes to mechanical mode is greater than the sum of the steering of the single optical mode to mechanical mode. This research is valuable for realizing more secure quantum communication and constructing quantum networks composed of systems with different frequencies.

Based on the femtosecond pulse synchronously pumped optical parametric oscillator (SPOPO), we can generate the time-domain multi-mode nonclassical light field. and combine it with the space Hermite-Gaussian multi-mode, we can develop the spatio-temporal multi-model nonclassical light field, which is expected to further expand the quantum channel capacity and carry out the quantum measurement. We proposed an experimental scheme for compensation of astigmatism, realizing simultaneous resonance of HG01 and HG10 mode in the SPOPO. However, in the experiment it is found that the non-plane cavity will cause the image rotation of the output beam, thus bringing uncertainty to the experimental system. In this paper, we use the method of constructing the novel coordinate system of Gaussian beam to analyze the cause of coordinate rotation in a nonplane annular cavity. Furthermore, the multi-beam interference method is used to calculate the total rotation Angle of 25.641irc when the beam rotates 3.26, in the resonant cavity. The correctness of the theoretical calculation is verified by experimental simulation, then we analyze the rotation angles of the output mode of the cavity mirror under different coordinate rotationangles and different transmittance lenses. At last, we obtain the relationship between the rotation angles of the output mode and the two obtained. It provides a basis for further optimization of SPOPO system and research of multi-mode entanglement in Non-plane SPOPO.

Quantum repeater is a basic building block for long-distance quantum communications via entanglement distribution. The high retrieval efficiency is an important parameter to realizing ensemble-based quantum repeater in practice. The Duan-Lukin-Cirac-Zoll (DLCZ) protocol based on the cold atomic ensemble and the linear optics can generate and store entanglement, which is regarded as one of the most potential schemes. The DLCZ protocol can probabilistically create a single photon and store an atomic spin-wave simultaneously, then the spin-wave can be transformed into the photon by applying a read beam. Combined with the collective enhancement effect of atomic ensemble and cavity-enhanced mechanism, one can enhance the interaction between photon and atom and improve the retrieval efficiency. Here, we demonstrate the effect of the optical depth (OD) on the retrieval efficiency of cavity-enhanced quantum memory based on the 87Rb cold atomic ensemble. In this work, the ring cavity is placed around the cold atomic ensemble. The cavity length is 3.2 m and the finesse is 13. The optical loss of all ring cavities is 21%, mainly consisting of the loss of optical elements (15%) and the loss of the cell (6%). In order to improve the retrieval efficiency, we need to ensure the triple-mode resonance of the read-out photon, write-out photon and locking beam by selecting the appropriate length of the cavity. We obtain the different OD by changing the detuning of cooling beam relative to the atomic resonant transition. We also measure the retrieval efficiency as a function of the OD and calculate the enhancement factor. The results show that the OD of the ensemble reaches the maximum 14 when the detuning of the coolingbeam relative to the atomic resonant transition is 18.5 MHz, and the retrieval efficiency of transforming the spin-wave to photon is 21%, the cavity-enhanced factor 1.6 folds, the intrinsic retrieval efficiency 43.2%.

More recently, Bose-Einstein condensates of atoms with long-range and anisotropic dipolar atomic interaction are studied experimentally and theoretically. The dipole-dipole interaction can be either attractive orrepulsive. Therefore, it can induce various interesting phenomena, making dipolar Bose-Einstein condensates an ideal candidate for exploring a variety of novel experimental phenomena. In this paper, the interference of the dipolar Bose-Einstein condensates released from a double-well potential is investigated, and the influence of the polarization direction of dipolar atoms on the interference between dipolar Bose-Einstein condensates is studied via virtual time evolution method and time-splitting Fourier spectrum method. According to comparing the interference patterns of the different polarization direction of dipolar atoms, it’s found that, when the projection direction of the polarization vector of the dipolar atoms on the plane where the condensatesis located is symmetrical about the initial parting line of the two dipolar condensates, the interference patterns are also symmetrical about the parting line, and the chirality of vortices generated in the interference process is just opposite. When thedipolar atom interaction shows obvious anisotropy, the interference patterns have the following characteristics: when the projection direction of the polarization vector is parallel to the initial parting line of the two dipolar condensates, no vortex will be generated during the interference process, the interference fringes are straight and the fringe width is the same; when the angle between the projection direction of the polarization vector and the initial parting line of the two dipolar condensatesis close to /4 (or 3/4), visible vortices (or antivortices) distributed along a straight line will be formed in the central area of the interference pattern; when the angle between the projection direction of the polarization vector and theinitial parting line of the two dipolar condensates is close to /2, vortex-antivortex pairs will be formed in the central region of the interference pattern.

Based on the fractional derivative Schrdinger equation with variable coefficients, the propagation and interaction of cosine-Gaussian beams are studied by means of the split-step Fourier algorithm. In the linear case, a single non-chirped cosine-Gaussian beam splits into two identical Gaussian beams during transmission and forms a Y-shaped beam structure, while a chirped cosine-Gaussian beam generates two asymmetric beams during transmission. The value of chirped parameter affects the bifurcation of the cosine-Gaussian beams. The two branches of the cosine-Gaussian beams are asymmetrically distributed as the chirp parameter increases. One branch of the cosine-Gaussian beams disappears completely when the value of the chirp parameter is up to 1.5. When the Lévy index is 1, the shape remains unchanged after the interaction of the two chirped cosine-Gaussian beams. In addition, the cosine-Gaussian beam under the action of fractional diffraction modulated by periodic function, linear function, and power function, the transmission results show periodic structure, parabolic trajectory transmission, and shape-invariant transmission, respectively. In the nonlinear case, the saturating nonlinear effect destroys the periodic structure of the cosine-Gaussian beam while suppressing the propagation broadening of the cosine-Gaussian beam. Especially, the cosine-Gaussian beam can be trapped to form localized modes similar to an optical soliton, which retains its profile during propagations under the action of the saturating nonlinear effect. These results of the research may be used to control the cosine-Gaussian beam trajectory.

Electromagnetically induced transparency (EIT) is an intriguing phenomenon in quantum optics, and has a wide range of applications in the fields of quantum information processing, quantum precision metrology, etc. Recently, with the rapid development of the generation and detection of vortex beams, the combination of EIT and vortex beams offers new and novel functionalities and applications, such as EIT-based atomic compass, spatially dependent EIT, and storage, transfer, and arithmetic of orbit angular momentum of light. For these investigations and applications, the propagation and evolution of vortex beams in EIT media are of crucial importance. In this article, the propagation evolution properties of a Laguerre-Gaussian (LG) vortex beam in an EIT medium with Λ-type three-level atoms are studied. Based on the generalized Huygens-Fresnel principle and the ABCD transfer matrix of the EIT medium, the analytical expression of the LG vortex beam propagatingin the EIT medium is derived. The propagation evolution of the intensity and phase of the beam and their dependences on the parameters such as the topological charge, the radial index, and the coherence length are studied. It is shown that the LG vortex beam propagating in the EIT medium experiences focusing and diverging periodically. For a partially coherent LG vortex beam, a smaller topological charge or larger radial index leads to the hiding of the phase singularity. Besides, the phase singularity splits and the phase singularities with opposite topological charges are generated during propagation. As the increasing of the coherence length of the beam, the hiding, splitting and generating of the phase singularities vanish. The results could find applications in developing new EIT-based techniques.

Based on the complex cubic-quintic Ginzburg-Landau equation with high-order effects, we numerically investigated the propagation characteristics of bound state solitons and pulsating-like solitons which are generated by Airy pulses by using the split-step Fourier method. The results show that the transmission directions of the two solitons are deflected to the right under the influence of self-frequency shift effect and self-steepening effect, and the deflect speed can be controlled by adjusting the parameters. In addition, the peak power of the bound state solitons decreases with the increase of the self-frequency shift effect. However, the change of self-steepening effect has little effect on the peak power of the bound state solitons. The third-order dispersion effect will also cause the bound state solitons to deflect to the right or left, but the direction of the deflection is determined by the sign of the third-order dispersion effect. For the pulsating-like solitons, the addition of the self-frequency shift effect will deflect them to the right, and the deflect speed increases with the increase of the self-frequency shift effect, and the peak power decreases with the increase of the self-frequency shift effect. However, when the higher-order effect exceeds a certain critical value, the propagation characteristics of the pulsating-like solitons will change abnormally. The pulsating-like solitons will be transformed into fixed-shape solitons under the influence of the self-frequency shift effect; the self-steepening effect will affect the stability of the solitons and deflect the propagation of pulsating-like solitons to the left, while the third-order dispersion effect makes pulsating-like solitons evolve into rectangular-like pulses, and the peak power of pulsating-like solitons decreases with the increase of higher-order effects. The relevant results not only enrich the propagation dynamics of Airy beams, but also have certain potential applications in the manipulation of Airy pulses. At the same time, it will also provide a certain theoretical reference for research in the fields of light guides and optical switches.

Metal-dielectric-metal metasurface narrowband absorbers are widely used, but the inherent ohmic loss of metal leads to large full width at half maxima of the absorption peak, which affects the application of the absorber in the sensing field. In this paper, a hybrid metasurface narrowband absorber with dielectric-dielectric-metal structure is proposed, which has three layers: Al2O3 inverted frustum top array, SiO2 intermediate dielectric layer and silver film substrate. The absorber combines the perfect absorption characteristics of the metal metasurface narrowband absorber and the narrow bandwidth characteristics of the dielectric metasurface narrowband absorber, and has better sensing performance. The absorption spectrum of the absorber was simulated by finite element method. The simulation results showed that the absorber had an absorption curve with a maximum absorption of 99.88% and a full width at half maxima of 2.26 nm in the visible band (676.3 nm). By comparing the absorption spectrum and the electric field distribution at the absorption peak of the metasurface narrowband absorber with the metal-dielectric-metal structure with the same parameters, the different absorption principles of the two structures are analyzed and compared. Finally, we simulated and analyzed the effect of size parameters on the absorption peak of a hybrid metasurface narrowband absorber and the sensor performance of the absorber to the external refractive index. These works provide a reference for the adjustability and stability of the absorber and its application in refractive index sensing. Simulation experiments for seawater refractive index detection of the metasurface narrowband absorber were conducted to compare the comprehensive performance of the absorbers by calculating the sensitivity and quality factor of refractive index sensing, and to verify that the absorber has a higher stability of refractive index sensing and is more advantageous for the application of seawater refractive index detection. The above work can provide a reference for the structural optimization design of metasurface narrowband absorber and the application of metasurface to marine refractive index sensing.

Due to the rapid development of quantum computing and quantum information, the physical study of solid-state quantum systems has revived significant interest. Among the possible schemes for the experimental realization of quantum computing, mesoscopic circuits containing small solid-state devices have attracted much attention, because of their advantages of easy integration and large-scale characteristics. Since the actual mesoscopic circuit is always in a certain environment, it is inevitably affected by the environment. For example, a mesoscopic circuit is radiated by an external electromagnetic field. The transitions will occur between different energy levels of the system. It is valuable to find the rules of energy level transition. In this paper, a more general mesoscopic LC circuit with complex coupling is chosen as the research object. By virtue of the canonical quantization method, the mesoscopic circuit is quantized and the Hamiltonian operator of the system is obtained. With the help of unitary transformation and analogy with a one-dimensional quantum harmonic oscillator, it is found that the mesoscopic LC circuits with complex couplings can be considered as two independent quantum mechanical harmonic oscillators. Then, the energy level formula and state vector expression of the system are deduced easily. In addition, the mean square quantum fluctuations, in the ground state, of the charges on one plate of the capacitor in the two branches of the mesoscopic circuit, and the equivalent magnetic flux passing through the two loops, are discussed. Considering that, once the mesoscopic circuit is irradiated by the external electromagnetic field, its state will change and a transition between the corresponding energy levels will occur. By using the “invariant Eigen-operator” method, the selection rules of energy-level transition for the mesoscopic LC circuit with complex couplings are obtained conveniently. It is believed that the application of this methodwill enrich the theoretical research on mesoscopic circuit from a fresh point of view.