Rabi model has been a hot topic in recent years. In this paper, quantum phase transitions and multistable states in Rabi model are presented under multiple-photon transition. By means of spin-coherent-state variational method, the equivalent pseudospin Hamiltonian is diagonalized and the energy functional is obtained. Then according to the results of the variational method, the photon number solutions and the critical values are given. Finally, phase diagrams areplotted based on the photon number solutions and the stabilities. The main results are what effects do the numbers of transitions photons have on quantum states, multistability and quantum phase transitions in Rabi model. The results are helpful to induce interesting quantum phase transition by modulating the frequency of the optical cavity.

Rabi model has been a hot topic in recent years. In this paper, quantum phase transitions and multistable states in Rabi model are presented under multiple-photon transition. By means of spin-coherent-state variational method, the equivalent pseudospin Hamiltonian is diagonalized and the energy functional is obtained. Then according to the results of the variational method, the photon number solutions and the critical values are given. Finally, phase diagrams areplotted based on the photon number solutions and the stabilities. The main results are what effects do the numbers of transitions photons have on quantum states, multistability and quantum phase transitions in Rabi model. The results are helpful to induce interesting quantum phase transition by modulating the frequency of the optical cavity.

Continuous-variable quantum remote state teleportation plays an important role in constructing continuous-variable quantum computing and quantum information networks. In practical communication processes, quantumentanglement typically interacts with the surrounding environment due to environmental interference, resulting in a reduction of entanglement and consequently affecting the correct transmission of quantum information, leading to a decrease in the fidelity of teleportation. A practical communication system is a more complex network than a simple point-to-point connection. Therefore, it is necessary to use multipartite entangled light fields to establish complex quantum networks. In this paper, a quantum teleportation network based on four-mode GHZ entangled light fields is constructed. The fidelity formula for transmitting quantum states in this network system is derived, and simulation results show the relationship between the fidelity and the gain factor under different compression parameters. The simulations indicate that for a given compression parameter, there exists an optimal gain factor that maximizes the fidelity. The fidelity initially increases and then decreases as the gain factor increases. A larger compression parameter results in better fidelity recovery of the quantum state. However, even with a large compression parameter, the fidelity cannot reach high values if the gain factor is not properly chosen. By increasing the compression parameter r and selecting the appropriate gain factor, the fidelity can be improved. However, in the actual system, factors such as optical device loss, noise and detector performance need considering comprehensively to achieve the best transmission and detection efficiency to achieve higher fidelity. In the design and experiment, it is necessary to comprehensively consider the transmission efficiency and detection efficiency to optimize the system parameters to achieve higher fidelity. Ideally, when the squeezing parameter r approaches infinity and the gain factor achieves the optimal value, the quantum correlation between the four sub-modes satisfies that the input state is equal to the output state, that is, the input state and the output state are completely consistent.The multi-component entangled state provides more resources, which help achieve more complex communication tasks. It can expand the communication channels and transmission capabilities of quantum teleportation and achieve higher-level secure communication. The results emphasize the importance of transmission efficiency and detection efficiency in quantum teleportation, which provide key factors and strategies for optimizing fidelity. It is of guiding significance for realizing high-fidelity quantum teleportation.

Gravitational waves (GWs) are ripples in space-time generated by massive accelerating objects. Although Einstein predicted the gravitational waves in 1916, the first direct demonstration of their existence didn’tarrive until 2016, 100 years after his prediction. Since then, over 90 gravitational wave events have been detected, including binary black hole mergers, binary neutron star mergers, neutron star and black hole coalescences. The direct detection of gravitational wave has revolutionized humanity’s view of the universe, and opened a new era of gravitational wave astronomy. The operational second-generation (2G) ground-based gravitational wave detectors include two LIGOs in Hanford and Livingston in the United States, Virgo in Italy and KAGRA in Japan. However, the strain sensitivity of the second-generation gravitational wave detectors is not enough to detect the majority of stellar-mass black hole and neutron star coalescences in the universe. This problem can be addressed by the third generation (3G) gravitational wave observatory whose strain sensitivity (10-24Hz-1/2) is ten times that of the 2G gravitational wave detectors. Based on the low-noise laser source from Shanxi University and abandoned coal mines in Shanxi, the provincial government has approved to build a third-generation ground-based gravitational wave detector, naming “Diting”. To date, all the operational ground-based gravitational wave detectors are based on large scale Michelson interferometer with arm length of several kilometers. In this paper, we calculated the frequency responses of the Michelson interferometer, the Fabry-Perot Michelson interferometer and the power-recycled Fabry-Perot interferometer respectively. To meet the strain sensitivity of 10-24Hz-1/2, we determine the amplitude reflectivity of Fabry-Perot cavity and the power-recycled mirror. Thispaper paves the way to build a third-generation ground-based gravitational wave detector in China.

A high-performance transportable ultra-stable cavity is the key to achieve the high-stability transportable optical clock. Vibration noise and temperature fluctuation noise are the main factors that affect the stability of the ultra-stable cavity. In this paper, we used the Pound-Drever-Hall (PDH) technique to achieve the locking of the 171Yb optical clock laser to a 30 cm transportable ultra-stable cavity, and studied the evaluation method of the vibration noise, temperature fluctuation noise and stability of the ultra-stable cavity. By applying active vibration excitation to the cavity, we obtained the vibration sensitivities of the cavity in three orthogonal directions as 5.6×10-10/g, rm4.8×10-10/g and 1.5×10-10/g, respectively. By measuring the change of the cavity resonance frequency with the cavity temperature, we fit its zero-crossing temperature to be 34.0(0.4)°C. Finally, by comparing with two independent 30 cm ultra-stable cavities with three-cornered hat method, we evaluated the independent stability of this ultra-stable cavity, and obtained a stability of 4.1×10-16 at an averaging time of 2 s by using correlation removed algorithm.Noise spectrum analysis shows that stability of cavity is mainly limited by vibration noise. These studies provide us with directions for further optimizing the stability of the transportable ultra-stable clock laser.

The normal-mode splitting in the optomechanical systems has attracted widely attention. This behavior of mode splitting arises due to the strong interaction between the oscillator and optical light circulating inside the cavity, when the system is in the resolved side band regime. Recently, many methods are proposed to produce the larger splitting by increasing the optomechanical coupling. It is proved that the observation of the normal-mode splitting is more accessible by placing the optical parametric amplifier inside the cavity, which is due mainly to the increase of the coupling between the oscillator and the cavity field. On the other hand, quadratic coupling can also increase the effective optomechanical coupling. Our paper is based on the above general background, and we study the important influence of quadratic optomechanical coupling and the parametric amplifier on normal-mode splitting in the optomechanical system with both linear and quadratic dispersion coupling. To investigate the normal-mode splitting effect, we calculate the output spectrum of the cavity and the spectrum of the mechanical oscillator displacement. Then, the calculated spectrum is plotted as a function of normalized frequency. The output spectrum of the cavity and the mechanical oscillator’s position spectrum all exhibit the double-peak structure. Thus, we can obtain the conclusions that both the cavity field and the mechanical field have normal-mode splitting behaviors. Further analysis of width of the normal-mode splitting peaks is analysed by discussing the spectra with different quadratic couplings and the parametric gain values. We find that the width of double-peak structure of the spectrum is increasing with the quadratic coupling, as well as the parametric gain. The physical explanation leading to such a phenomenon is that the increasing of quadratic coupling and the parametric gain aids in producing more number of cavity photons. As a result, this also leads to the increasing in effective optomechanical coupling. Quadratic coupling and the parametric gain have similar effects on the normal-mode splitting. In other words, the the normal-mode splitting behavior can be controlled by quadratic coupling or the parametric gain. Thus, It also proves the conclusion of the reference [Journal of Modern Optics 66(5): 494-501 (2019)]that the optomechanical systems with linear coupling and quadratic coupling can be seen as a alternative platforms to hybrid-optomechanical systems with the parametric amplifier.

Quantum scrambling is a common dynamic phenomenon in quantum information processing, which refers to initially localized information spreads over the global degrees of freedom in the system due to global entanglement resulting in local measurements failing to obtain complete information. Recent studies have found that the damaged scrambling information can be recovered through time inversion protocol. For example, by using a 4-qubits quantum circuit, Bin Yan and Nikolai Sinitsyn [Phys Rev Lett, 125, 0406054 (2020)]simulated the damaged information recovery process of a central qubit in an environment bath of two qubits and calculated the measurement probability of the central qubit use out-of-time-ordered correlators (OTOC), and proved the possibility of damaged information recovery under time inversion with a high fidelity of 0.983 on the IBM platform. The damaged information recovery processes are crucial for protecting quantum information against environmental damage and testing the quantumness of quantum computers.The quantum scrambling and damaged information recovery process is simulated by a quantum circuit composed of perfect single-qubit gates operation and two-qubit gates operation in the above verification. However in the actual quantum evolution process, the form of real noise is more complex, and the induced decoherence process is unavoidable. There are several popular models for noise simulation such as unitary noise models and pure attenuation models, and for quantum gates operation collision models have a good approximation of the noise in reality. We import the noise of collision models to quantum gates operation in Bin Yan and Nikolai A. Sinitsyn’s protocol to investigate the effect of noise-induced decoherence on the dynamical processes of information scrambling and recovery of damaged information. The introduction of decoherence noise interferes with the quantum scrambling process, decaying the out-of-time-ordered correlators and generating "false" quantum scrambling signals. So we calculate and analyze the changes of trance distance, quantum mutual information and fidelity in information-theoretic field after each step of operation to explore the dynamics of quantum information scrambling and damaged information recovery. Specifically, the trace distance is used to measure the outflow and inflow of quantum information from the central qubit system into the environmental bath system, the quantum mutual information is used to study the distribution of quantum information flow into environmental bath system and the fidelity is used to research the dynamical change in specific initial states of central qubit.The results indicate that decoherence induced by noise can not only suppress information scrambling and recovery, but also advance the time node of information recovery. When the central qubit initial state is |0?Q1 two-qubit noise intensity is gt=/4 or gt=/8 advance the time node of information recovery and this advancement is an effect of the asymmetric distribution of information induced by the noise. The choice of initial state on central qubit and the measurements in step 8 both determine whether this phenomenon occurs. In general, imperfect CNOT gates operation and imperfect H gates operation under the influence of noise will inhibit information recovery. However, under special parameters when noise intensity is gt=/8, WT=3/8 combination of the two imperfect gates operation produces a lower mutual information values and higher fidelity values than only applying imperfect CNOT gates operation. It reusults in the fact that the imperfect H gates operation act as a modulation on the imperfect CNOT gates operation under this noise parameter, and more information can be extracted from the environmental bath system. This strange phenomenon can be used for information preservation in quantum computation in the noisy background, providing a new approach for realizing high-quality quantum computation processes.

In order to improve the security and economy of information transmission, this paper proposes a controllable dense coding scheme using 4-particle cluster states as quantum channels, and a 5×2×2×2-dimensional asymmetric coding channel. In this scheme, the control party is changed from one to two, and the safety is higher. The asymmetric encoding method can transmit more information. The operation of the control side is one-dimensional orthogonal base measurement and projection measurement, which is easier to realize. The selected quantum channel is a 4-particle cluster state, which has continuous entanglement and maximum connectivity compared with the GHZ state and W state, and is more suitable for quantum channel.

Bragg gratings are used in various applications including optical communication systems and sensors. The influencing parameters of the reflectivity of Bragg gratings hold significant importance in the research ofoptical sensors. Both domestically and internationally, there exist various external parameters including vibration sensing characteris temperature sensing characteristics and lateral force characteristics of fiber gratings. However, the comprehensive exploration on how these external parameters impact the fiber grating is insufficient. Thus, it is crucial to delve into the internal characteristics of waveguide gratings. This paper investigates the transmission characteristics of electromagnetic waves inwaveguide gratings by changing internal parameters.The Bragg grating is taken as an example in this paper to derive the coupling mode equation of the grating from the wave equation of the light field, and then the 2×2 matrix characterizing the grating characteristics is reproduced by solving the coupling mode equation and applied to a matrix derivation that can characterize the characteristics of the sampling grating. The formula of the equations is deduced, and a simplified formulation linking the reflection coefficient to the grating length, effective refractive index, and coupling intensity is obtained. For uniform Bragg grating and sampling grating, the influence of parameters on their reflectance spectrum and transmission spectrum was studied by MATLAB numerical simulation method. As the influential factors, the grating length, effective refractive index, coupling intensity, grating segment length, blank segment length and grating period are included. The numerical simulation spectrum and experimental results are also givenThe results demonstrate that, for the uniform Bragg grating, as the length of the grating segment increases, both the reflectance peaks in the reflection spectrum and transmission spectrum exhibit an upward; a decrease in effective refractive index leadsto a blue shift in the position of both reflection and transmission spectra; an increase in coupling intensity results in higher reflectance peak heights and wider spectral widths. For the sampling grating, the increase in the length of the grating segment leads to an increase in the coupling intensity of the sampling grating, resulting in a wider interval between the reflection peaks; the length of the blank segment increased, while the reflection peaks at all levels remained unchanged and there is a decrease in the spacing between the reflection peaks; the increase in the number of grating periods leads to a longer transmission distance of the light field within the grating, resulting in an increased number of backward transmissions and enhanced intensity of reflection peaks at all levels in the reflection spectrum.The simulation analysis presented in our work offers theoretical support for the preparation and design of target gratings in various applications, such as FBG sensing, distributed Bragg feedback (DBR) lasers and grating filters.

In order to meet the needs of modern stealth technology and achieve the dual purpose of near-mid-infrared and laser compatible stealth, a Distributed Bragg reflector (DBR) with defects constructed by Ag and ZnS is designed.Using the COMSOL 5.6 ray optical module, it aims to seek a kind of membrane layer upon layer number is less, coating film thickness thinner compatibility in the near infrared and laser stealth coating structure. Using the doping principle, defects are introduced into metal-containing DBR, and defect modes appear at 1 060 nm in the band gap range of 650～5?000nm.The reflection performance of the DBR with defect layer and laser is calculated, and the influence of the cycle number and the thickness of the defect layer on the near mid-infrared and defect mode is studied. The influence law of period number Nc and defect layer film thickness on near-middle infrared reflection and defect layer was explored, and the influence law of period numberon defect modulus and location was further explored.The results show that the defect modes shift to blue light with the decrease of defect film thickness. With the increase in the periodic structure Nc with defect, the width of the defect modes becomes narrower, and the defect modes appear in pairs with the central wavelength as the center, showing the characteristics of a good reflective comb filter. With the increase of the period number Nc of the structure containing defects, the defect modes are centered on the central wavelength and appear in pairs, showing the characteristics of a well-reflected comb filter. The relationship between the number of defect modes L and the number of periods Nc is as follows: L=2 (Nc-1), that is, by controlling Nc, the number of teeth and tooth spacingof the comb filter can be effectively controlled. When Nc=1, the total reflection in 650～5?000nm band can be realized, and the defect mode appears at 1 060 nm, and its reflectivity is only 4%. This kind of metal-containing DBR with the characteristic of pectral hollowing" can be used for stealth in near-mid-infrared band compatible with laser at 1 060 nm. Compared with heterojunction dielectric photonic crystals, the structure designed in this paper has the advantages in symmetrical structure, simple structure, and small number of membrane layers.

In the application of vacuum optical tweezers, a dipole trap formed by laser light with a spatial gradient is usually used to trap neutral atoms or micro/nano particles. In the experiment of optical trapping neutral atoms, dipole trap with laser frequency far detuned from the atomic transition is usually adopted in order to suppress the photon scattering rate from the trapped atom. The storage time of the optically trapped atoms is mainly affected by the intensity noise and the pointing noise associated with the dipole field. The storage time is far less than the value determined by the background vapor pressure. In order to prolong the storage time as well as the decoherence time of the trapped particles, we invent a method to use a single-stage feedback loop based on an electro-optical amplitude modulator (EOAM) to suppress the low-frequency intensity noise associated with a 1 064 nm laser beam. The intensity noise from 0 Hz to 1 MHz can be effectively suppressed with a reduction up to 20 dB below 100 kHz and 10 dB below 500 kHz. The standard deviation of optical power fluctuation has decreased to 0.5%, which is an order of magnitude improvement. The noise-suppressing range covers the typical parametric heating frequencies of the optical dipole trap. Therefore, it can be used to improve the trapping performance of these particles, such as the storage time of particles and the coherence time of quantum states. By applying the setup to our single cesium atom experiment, the atomic heating rate is reduced by two orders of magnitude. Thus, we can extend the storage time of a single atom by two orders of magnitude. The measured decoherence time is also enhanced five times. The setup is simple and flexible, so it can be easily applied to the optical trapping of a neutral atom or nano/micron particles with a laser with all kinds of wavelengths.

The interaction of laser beams carrying phase singularities, namely vortex beams, with turbulent media has been of interest due to its relevance in many areas such as free space optical communications, quantum communications, optical tweezers and so on. In the past several years, the evolution properties of different laser beams have been studied related to the propagation factor and effective radius of curvature. The propagation factor is an important factor forvaluing the propagation beam quality in practical application, and the radius of curvature of laser beams is an important parameter for describing beam wavefront properties. On the other hand, the turbulent ocean is also a distinct turbulent medium, while the propagation of the ocean depends on the salinity fluctuation and temperature of the ocean turbulence. In present paper, the partially coherent Lommel-Gaussian Beam (PCLGB) is chosen as an example, which is a typical non-diffracting beam, and the transverse intensity shape can be conveniently regulated by a symmetry parameter. By the use of Wigner distribution function, analytical formulas of the propagation parametric of the PCLGB and partially coherent Bessel-Gaussian beam (PCBGB) through turbulent ocean are derived. Propagation properties of the effective radius of curvature and the propagation factor of PCLGBs through turbulent ocean are explored numerically.It is shown that the propagation properties of the PCLGBs are as same as that of the PCBGBs, but the continuously variable orbital angular momentum make it more superior to the latter. The properties of the PCLGBs depend on the oceanic parameters. As relative strength of temperature and salinity fluctuation, and the rate of dissipation of mean-square temperature are smaller, or the rate of dissipation of turbulent kinetic energy per unit mass of fluid is larger, the effective radius of curvature is larger and the propagation factor is smaller, namely, the effect of turbulence on the beam is smaller. The work can provide theoretical and experimental basis for practical applications of underwater laser communication and laser weapons.

This paper proposes a gold nanocross bi-layer Plasmonic Nanostructure Array (BPNA). This structural array consists of gold nano-cross hole array, silica array, and gold nano-cross thin sheet array unit structure.In order to explore the causes of Localized Surface Plasmon (LSP) and its transmission performance of this bilayer structure, observe the resonant coupling effect of plasma, The Finite-Difference Time-Domain (FDTD) method is used to calculate the electric field pattern of the transmission spectrum and x direction of this structure under different parameters.The increase of the cross hole width D can improve the transmission intensity and make the peak position of LSP blue shift, the increase of the thickness of the cross hole H can reduce the transmission intensity and slightly shift the LSP peak position, the increase of the length L of the cross hole can improve the transmission intensity and redshift the peak position of LSP. The increase of the width d of the cross lamella can increase the inhibition intensity and allow the LSP peak position to shift blue, the increase of the thickness h of the cross sheet can improve the inhibition strength and shift the peak position of LSP blue, the increase of the length l of the cross lamella can increase the inhibition intensity and redshift the peak position of LSP. The change of period T can shift the peak position of LSP blue.When the upper and lower layers exist, we obtain a new LSP peak and analyze its cause by electric field. By changing the thickness of the silica layer, it was found that the intensity and position changes of the two LSP peaks were related to the resonance coupling effect between the cross hole slit, and the cross sheet, where the first LSP peak was dominated by the cross hole slit and the second LSP peak was dominated by the cross lamina, but both peaks were affected by the resonance coupling between thecross hole and the cross sheet. In addition, the ideal medium also has an impact on its transmission propertiesIn order to obtain the high-performance transmission effect, we changed the structural parameters and calculated the Full Width Half Maxima (FWHM) and Figure Of Merit (FOM), and obtained higher FOM values and special transmission conditions. It has certain reference significance for the realization of high-performance LSP sensors and optics.

Low noise all-solid-state single-frequency Nd:YVO4 lasers are important for applications in quantum precision measurement, atomic frequency standard, non-classical state preparation and gravitational wave detection. The laser’s intensity noise has become a crucial parameter since it can directly affect measurement accuracy or experimental results. By altering laser parameters such as the intensity noise of the pump, intracavity losses, and the transmissionof output coupler, the intensity noise of the all-solid-state single-frequency Nd:YVO4 laser is fully investigated. The intensity noise can only be slightly improved by optimizing these parameters. The main factor affecting noise level is relaxation oscillation, thus changing the state of relaxation oscillation is an efficient method for reducing the intensity noise. By altering the gain and phase of the noise transfer function, the photoelectronic negative feedback technique can effectively suppress the intensity noise. The intensity noise is reduced by about 5 dB in the audio frequency region and by about 36 dB at the relaxation oscillation frequency with the support of reflectivity of beam splitter ε=10%, DC gain g=15xtdB, the amount of phase advance φ=60° and the pump noise VP=15dB. By using a low noise injection field, the injection locking technology can modify the relaxation oscillation’s state and effectively suppress the noise in the relaxation oscillation frequency region. The maximum intensity noise is decreased by around 31 dB with the help of injection laser noise Vin=5dB, injection locking power amplification ratio H=50 and the pump noise VP=15dB. The photoelectric negative feedback technique may reduce noise in both the audio frequency region and the relaxation oscillation frequency region, the injection locking technique can only do so in the relaxation oscillation frequency region. The noise in the relaxation oscillation zone can be suppressed more strongly by combining the two techniques. The intensity noise of the all-solid-state single-frequency Nd:YVO4 laser is reduced by about 5 dB in the audio frequency region andby about 39 dB around the peak of the relaxation oscillation with the feasible parameters of ε=10%, g=15dB, φ=60°, H=20 and the real injection laser noise. The theoretical analysis in this paper will aid in the creation of an all-solid-state low noise Nd:YVO4 laser.