Entanglement is an important resource in quantum measurement and quantum information. As a key apparatus of generating entanglement, a non-degenerate optical parametric oscillator (NOPO) can directly output entanglement without any extra operation, unlike the degenerate OPO which needs optical beam coupling of two output squeezings. Most research studies are focusing on the resonant NOPO design, i.e., without detunings, which is the most common cause for generating the best squeezing and entanglement. However, detunings are inevitable and play a crucial role in some experiments such as quantum optomechanics and gravitational wave detection beyond the standard quantum limits with the help of the optical spring effect. NOPO could be used in these experiments to further increase the corresponding sensitivity. Therefore, in this paper, we investigate the effect of detunings on the entanglement degree in the NOPO. Considering the detunings of the pump, signal and idler fields, the quantum Langevin equations are given. Then the stationary solutions for both below and above the threshold of the pump power are obtained and analyzed. The monostable solutions, bistable solutions and unstable solutions are all analyzed. The bipartite entanglement noise spectra of the signal and idler beams are obtained. Analytical solutions below the threshold and numerical solutions above the threshold are both given, and the corresponding results are plotted in 2D/3D. The results show that, the detunings degrade the entanglement degree for most cases, especially at zero frequency or low frequencies. However, the entanglement degree may increase with definite detunings at higher frequencies, i.e., the best entanglement is not at zero frequency, which is the case for NOPO without detunings. Furthermore, the entanglement degree keeps well on a large scale of detunings when the pump detuning and the signal detuning are antisymmetric (one is red detuning, the other blue detuning), much betterthan that of symmetric detuning case, which is an important result from which we can get entanglement of intermediate degree with even large detunings.

Nonlocal correlations between discrete-variable and continuous-variable systems in an entangled state are not only of fundamental interest but also having applications in quantum information processing. These correlations are well manifested by violation of the Bell inequality imposed by theories of local realism. Based on the entanglement state of the hybrid system, which consists of the qubit of the discrete variable and the harmonic oscillator of the continuous variable system. We constructed a special operator, the rotated quantum number parity operator, that distinguishes between the displaced parity operator in previous studies. In this case, we investigated Bell inequality tests with entanglement between aqubit and coherent states of a harmonic oscillator based on joint measurements on the qubit’s spin and the oscillator’s rotated quantum number parity. Results showed that the obtained correlations nearly maximally violated the Bell inequality when the qubit-oscillator entanglement approaches its maximum value. Comparing to the displaced quantum number parity operator, the violate of Bell inequality in rotated quantum number parity operator increased rapidly to the maximal value as the amplitude increased. This result showed that the Bell signal of spin-rotated parity operator is simpler in terms of the varying scales and the experimental conditions in two-partite hybrid entangled state. We further explored the nonlocal correlations for the system with one or more qubits entangled with coherent states of two oscillators, evidenced by violation of the Mermin-Klyshko inequality. The results showed that the nonlocality was quickly strengthened as the amplitudes of the coherent state components increase, and the Mermin-Klyshko inequality can be nearly maximally violated for quite moderate values of the amplitudes of the coherent state components. It showed that the MK signal of spin-rotated parity operator had more obvious effect and and the simpler condition requirements in multi-partite hybrid entangled states. That enhanced the feasibility in experimental.

After studying the classical multi-coin quantum game, aiming at the decoherence phenomenon caused by the coupling between the quantum system and the external environment, using the quantum game theory, the multi-coin quantum game models under the conditions of phase damping channel, amplitude damping channel and depolarization channel are established, and the variation laws of the quantum player’s winning probability under three kinds of noise channels are deduced, The two influencing factors: noise intensity and the number of coins are analyzed, the functional formula is calculated, and it is concluded that there is a significant negative correlation between the quantum player’s winning probability and the noiseintensity and the number of coins. The more coins, the faster the quantum participant’s winning probability changes with the noise intensity. When the noise intensity reaches the maximum, the quantum strategy loses its advantage, It shows that classical participants need to delay time and increase the impact of noise if they want to win when they realize that the other party uses the quantum strategy. And when the system is in a closed state, the number of coins has nothing to do with the game result, the quantum player will always win. In the open environment, the more coins, the faster the winning rate of the quantum player decreases with the increase of noise intensity. In addition, among the three channels mentioned above, the phase damping noise channel has the least impact on the winning rate and the depolarization noise channel has the greatest impact. These laws will not be affected by the number of coins. Therefore, in order to obtain greater advantages in the game, the player using quantum strategy should choose the amplitude damping channel if they can choose, in order to reduce the of quantum player, participants using classical strategies will choose the depolarization channel, which provides a theoretical basis for multi-coin game decision-making under different external environment conditions.

Electromagnetically induced transparency has attracted much attention because of its basic characteristics and its potential applications. With the help of the pump field, the detection field can be transmitted transparently in the medium. When the standing wave field is used as the pump field, the electromagnetically induced transparent medium becomes an electromagnetically induced grating. The electromagnetically induced grating effect is widely used in opticalpath switch, optical storage, quantum Talbot effect, atomic wave interferometry, etc. Its scheme based on electromagnetically induced transparency mainly uses enhanced dispersion to enhance spatial phase modulation, so as to enhance diffraction efficiency. In this paper, spontaneously generated coherence inducing electromagnetically induced phase gratings are studied and compared in different three-level atomic systems: Lamda-type, Ladder-type and V-type. Spontaneously generated coherence refers to the interference between spontaneous emission channels. In Lamda-type and V-type systems, spontaneous emission from a single excited state to two lower near degenerate energy levels or from two near degenerate higher energy levels to the atomic ground state will interfere with each other. Spontaneously generated coherence also probably appears in the Ladder type system in the case of equidistant atomic energy levels. The existence of this coherence depends on whether the two transition dipole moments are orthogonal. The results show that, spontaneously generated coherence can significantly enhance the first-order diffraction efficiency. However the degree of enhancement is different in different systems, and the dependence on the degree of atomic coherence is also different. For Lamda and Ladder type systems, the first-order diffraction efficiency increases with the enhancement of spontaneous emission coherence, especially for the Ladder-type system. In contrast, for the V-type system, the first-order diffraction efficiency increases in the region where the coherence of spontaneous emission is relatively weak. This research has potential applications in the field of quantum optical devices.

Continuous-variable entangled optical fields are important quantum resources for realizing quantum computing, quantum communication and quantum precision measurement. Continuous-variable quantum systems have the advantages of deterministic generation, high-efficiency quantum detection, and excellent compatibility with classical communication systems. Quantum channel capacity is an important figure of merit in quantum communication. Multiplexing is useful in improving the quantum channel capacity, which is realized by combining multiple discrete values of a certain degree of freedom into a single channel, such as wavelength, polarization, and temporal mode. Orbital angular momentum multiplexing is an efficient wayto increase the channel capacity in quantum communication, since in principle the topological charge of orbital angular momentum can be arbitrary integers. Four-wave mixing process based on the double-Λ energy level structure of alkali metal atomic ensemble is an efficient way to prepare a spatially multi-mode entangled state with the advantages of naturally matching the atomic transition. It has been widely used in quantum state engineering, quantum precision measurement, quantum beam splitter, and so on. Recently, our group generates orbital angular momentum multiplexed continuous variable entangled state based on the four-wave mixing process in cesium atomic ensemble, and realized deterministic distribution of orbital angular momentum multiplexed quantum entanglement and quantum steering. In this paper, we experimentally demonstrate that the entanglement of EPR entangled state carrying l=1,?2 order topological charge is the same as that of l=0 order Gaussian mode. Furthermore, we characterize quantum correlation of optical fields carrying l=0,?1,?2 order orbital angular momentum in terms of Gaussian quantum discord and investigate its evolution in a lossy quantum channel. Our results show that Gaussian quantum correlation of orbital angular momentum multiplexed optical fields is robust in a lossy environment. Our results provide references for realizing high channel capacity quantum communication by using orbital angular momentum multiplexed continuous variable entangled state.

Quantum entanglement is of great importance for quantum information, quantum computing, and quantum metrology. In this paper, a scheme for generating quadripartite entanglement is proposed by combining three four-wave mixing (FWM) processes. The effect of intensity gain of three FWM processes on quadripartite entanglement is studied by applying the positivity under partial transposition (PPT) criterion. We find that the quadripartite entanglement exists in this system, and the quadripartite entanglement is enhanced by increasing the gain of three FWM processes. Furthermore, the eigenvalues and eigenmodes of this system is investigated, and the results show that this system is composed of four independent squeezedmodes. Our theoretical results will provide a feasible scheme and theoretical support for the experimental generation of quadripartite entanglement.

In this paper, the propagation characteristics of third-order and fourth-order vortex beams in Bessel lattices in 0-order, 1-order and 2-order self-focusing photorefractive media are studied. The effects of different Bessel lattice orders and different lattice transverse scales on the propagation characteristics of third-order and fourth-order vortex beams are mainly discussed. The results show that when the third and fourth-order vortex beams propagate in the Bessel lattice in the self-focusing photorefractive medium, by controlling the amplitude of the input vortex beam and selecting the appropriate Bessel lattice depth, applied bias and lattice transverse scale, the third and fourth-order vortex beams can formstable vortex solitons in the 0-order, 1-order and 2-order Bessel lattice and can transmit stably. When the amplitude of the input vortex beam is fixed, by adjusting the depth of Bessel lattice, the transverse scale of lattice and the externally applied bias, we can obtain the vortex soliton and the vortex soliton can propagate stably, whereas the energy of the input vortex beam is all within the first ring of lattice. And the lattice depth of the fourth-order vortex beam is larger than that of the third-order vortex beam. When propagating in the same order Bessel lattice, the lattice depth required for stable transmission of the fourth-order vortex beam is larger than that of the third-order vortex beam.

Based on the nonlinear fractional Schrdinger equation, the effects of nonlinear gain and linear loss on the propagation characteristics of Gaussian beams are numerically studied. The results show that: the gaussian beam quickly evolved into the breathing soliton and we can control breathing soliton transmission behavior by changing system parameters. The changes in Lévy index have a good control effect on the pulse width, amplitude and period of the breathing solion. A larger Lévy index makes the pulse width larger, the amplitude smaller, and the soliton period larger. When there is no linear loss, the nonlinear gain weakened the beam diffraction, the pulse width is smaller in the transmission process, the soliton period decreases and the amplitude increases faster. Constant linear loss enhanced the diffraction of breathing soliton, the soliton period increases faster along the transmission direction, and the amplitude decreases faster at the same time. Therefore, the peak intensity of breathing soliton at the maximum compression can be kept unchanged by selecting the constant linear loss and the nonlinear gain reasonably. Cosine linear loss coefficient τ0 makes the soliton period increase faster along the transmission distance, but the frequency parameter β of the cosine function makes the soliton period increase slower along the transmission distance. So we can obtain the breathing soliton stability transmission by adjusting two parameters of the cosine function. When the nonlinear gain is not zero, comprehensively adjust various parameters, and the breathing soliton can be transmitted more stably. Exponential linear loss make the breathing soliton skew to left and the peak intensity attenuates exponentially along the transmission direction. The coefficient τ0 is larger, the attenuation rate is larger and the soliton period increases faster. The index β make the soliton skew to left further and the soliton period change slower. However, the nonlinear gain cannot balance the effect of exponential linear loss on the breathing solitons to obtain stable transmission. The results not only prove the controllability of gaussian beam propagation in nonuniform nonlinear fractional Schrdinger equation, but also provide a theoretical reference for optical signal processing in nonlinear optics.

A graphene surface plasmon-based nano-parallel wire waveguide composed of two elliptical cylindrical and one cylindrical dielectric nanowires coated with graphene is designed. Using the finite element method, thetransmission characteristics of the five lowest-order modes supported by the waveguide are analyzed. The results show that these modes supported by the waveguide can be synthesized from the fundamental mode and the first-order mode of the graphene-coatedelliptical cylindrical and cylindrical dielectric nanowires. When the working wavelength or the Fermi energy of graphene changes, the changing trend of the transmission characteristics of these modes remains the same. The transmission characteristics of mode 1 and mode 2 are relatively greatly affected by the semi-major axis of the elliptical cylindrical nanowire, the center distance, and the height of the cylindrical nanowire. The transmission characteristics of Mode 3 are relatively less affected by structural parameters. The transmission characteristics of mode 4 and mode 5 are relatively greatly affected by the semi-major axis of the elliptical cylindrical nanowire, the center distance, and the radius of the cylindrical nanowire. The waveguide designed in this paper adopts an elliptical cylindrical structure and increases adjustable parameters. Its transmission performance is better than that of a waveguide composed of three cylindrical dielectric nanowires coated with graphene. The waveguide designed in this paper has certain application prospects in the field of micro-nano optical device integration and sensors.

A type of dual tunable broadband metamaterial absorber based on graphene and vanadium dioxide pattern is designed, of which the dynamically tunable characteristics can be achieved based on the properties of vanadium dioxide (VO2) and graphene. It is well known that VO2 has the characteristic of phase transition at a temperature of 68°C, while the conductivity of graphene can be changed by adjusting its chemical potential. When the conductivity of VO2 and the chemical potential of graphene are 200 000 S/m and 0.5 eV, respectively, the bandwidth of the proposed absorber with an absorption rate exceeding 90% can reach 4.2 THz. Study results will show that by keeping the conductivity of VO2 unchanged, the location and the smoothness of the broad absorption band can be adjusted by the chemical potential of graphene to a certain degree. If the chemical potential of the graphene is fixed at 0.5 eV, the maximum absorptionrate of the broad absorption band can be significantly adjusted by the conductivity of VO2, and the maximum modulation depth can be as high as 75%. Therefore, the proposed metamaterial absorber not only has the characteristic of dynamically tunable absorption bandwidth but also has the function of modulating or switching in the electromagnetic waves. The absorption mechanism is analyzed according to the distribution of the electric fields along the VO2 and graphene. Next, the effect of different geometric parameters of the absorber on the absorption properties has also been studied, from which optimal geometrical parameter ranges can be selected for further laboratory fabricating and testing. Meanwhile, through the research of the absorption properties under different polarization angles and incident angles, it is found that the proposed metamaterial absorber possesses the characteristics of polarization-insensitive and wide incident angles. In terms of the dual tunable properties originating from the conductivity of VO2 and the chemical potential of graphene, it makes the proposed metamaterial absorber have potential applications in the area of THz absorbing, switching and modulating.

Continuous-wave (CW) single-frequency coherent laser sources in the blue spectral region are useful for applications in biomedicine, metrology, display technology, atomic-trapping, quantum optics, and so on owingto their intrinsic merits of low-intensity noise, narrow linewidth as well as the good beam quality. The single-frequency 455 nm laser is in the band of blue-green (400～500 nm) optically transparent window of seawater, and seawater has very little photon absorption and low transmission loss. Moreover, the wavelength of 455 nm is just corresponding to the higher state excitation transition 6S127P32 of Cs atoms, which can be used for the development of long-distance underwater quantum communication based on quantum storage nodes of the cesium atom system. It also corresponds to the transition 6S126P32 of 138Ba2+, which can be used in the field of quantum computing to reduce systematic errors. In this paper, the continuous wave single-frequency 455 nm laser generation from intracavity frequency-doubled Ti:S laser is presented. By optimizing the curvature radii of the resonator mirrors, the beam waist of the fundamental wave at the Ti:S crystal is focused, and the threshold pump power is effectively decreased. When a quasi-phase matched MgO: PPSLT crystal is used as the intracavity frequency doubler, the highest output power of 427 mW at 455 nm is attained under the pump power of 11.5 W with an optical conversion efficiency of 3.7%. The measured blue laser beam quality is better than 1.18.