When self-similar pulses are generated in the gain fiber, the effect of gain saturation energy and gain bandwidth on pulse distortion increases with the increasing energy, resulting in the inability to obtain highenergy, highquality selfsimilar pulses. This paper focuses on the use of dispersion decreasing fiber (DDF) to further optimize the self-similarity evolution process of pulses in gain fibers, ensuring the quality of self-similarity pulses with high-energy in gain fibers. The feasibility of using DDF to optimize self-similar pulses generated in gain fibers is analyzed theoretically and verified numerically. The effect of different types of DDF on the optimization effect is also analyzed. The simulation results show that after using DDF optimization, the self-similarity evaluation factor decreases from 0.051 7 to 0.028 6, indicating that DDF effectively optimizes the self-similarity pulses generated by gain fibers. Meanwhile, by analyzing different shaped DDFs, it was found that hyperbolic shaped-DDF can achieve the best optimization results, obtaining low pedestal ultra short pulses with a peak power of 11 034 W and a full width at half maximum (FWHM) of 129 fs. This study has certain implications for obtaining self-similar pulses with high-energy and high-quality.

The design and application of metasurface is one of the hot spots in the field of optics in recent years, and it is also an interdisciplinary research field involving physics, materials, optics, quantum information and other directions. Metasurface can precisely control the phase, polarization, amplitude and other parameters of incident light field. Therefore, metasurface has a very important application prospect in the research process of experimental platform on quantum state slices. Based on the propagation phase theory and the effective medium theory, we designed a cylindrical three-dimensional metasurface phase. Blue-detuned optical was used as incident light to form a focused hollow beam to store cold Iodine (I2) molecules. To determine the parameters of the periodic structural element and the metasurface by finite element analysis software. Calculate the optical field intensity of the hollow ring, and calculate the dipole potential depth, dipole force of I2 molecules in the optical field, thus proving that the designed metasurface can trap the I2 molecules. Firstly, silicon dioxide (SiO2) with a periodic width of 110 nm was selected as the substrate, and silicon (Si) column as the peri-odic structure element on the substrate. By finite element analysis, the height range of 100 nm～150 nm silicon column was scanned to find the height value of silicon column with high transmittance and phase coverage in the range of -π～π. Then, the height value of silicon column was determined to be 132 nm. Secondly, the duty cycle of silicon column within a periodic is scanned, ranging from 10%～90%, and then the functional relationship between phase value and duty cycle is obtained. Map the phase values greater than π or less than -π to the range from -π～π. Thirdly, 81 periodic structural elements are arranged in the two-dimensional direction, the total width is 8.855 μm, and the discrete phase values required by these positions are determined by the functional relationship between phase value and duty cycle, so as to determine the width of silicon column of periodic structure elements at different positions, forming two-dimensional unit structure array, so that the incident light converges to the focal point. The expected focal length is 5.5 μm. Finally, By adding 1.045 μm SiO2 substrate with no structure element, the total length of the 2-dimensional array of structued element is 9.9 μm. The end of the unstructured element is taken as the center of the circle, and a threedimensional metasurface ring array is formed by rotating one circle. When radially polarized light with wavelength of 300 nm is incident from the direction of the substrate, hollow rings are formed at the focal plane, and the expected radius is 5.445 μm. When the incident light passes through the structure elements array, it is converged into a focused hollow beam. The actual focus is 5.6 μm, and the error is 1.8%. At the focal plane, the radius is 5.438 μm, and the error is 0.13%. The width of the hollow ring is 0.54 μm, the maximum light intensity of the hollow ring increased by 39.2 times compared with the minimum light intensity. The maximum dipole potential depth of I2 molecule was about 340 μK, and the maximum dipole force was about 2.9×10-20 N. The three-dimensional ring array metasurface designed based on periodic structure element can form hollow focusing rings, which can meet the requirements of trapping I2 molecules, and realize optical storage.

Semiconductor lasers have been widely used in quantum information, precision measurement, optical sensing and other fields due to the advantages of large wavelength coverage, easy tuning, small size, light weight, simple structure, low power consumption and long working lifetime. Since the output frequency of free-running semiconductor laser fluctuates widely, it is necessary to stabilize its frequency by feedback control. However, the traditional feedback control system has some disadvantages, such as complex structure, large size and poor stability, so we construct a stabilization system of external cavity diode laser based on a Field Programmable Gate Array (FPGA) module. In this paper we use PyRPL, an open-source software package, to provide an arbitrary signal generator, a lock-in amplifier, a Proportional-Integral-Differential (PID) controller and an oscilloscope based on STEM125-14. And the saturated absorption spectrum of cesium atoms is used as the reference frequency for the stabilization system to lock a semiconductor laser. The arbitrary signal generator is used to generate sawtooth signal to scan the external cavity length of the semiconductor laser, thus realizing the tuning of the laser frequency. The lock-in amplifier module is used to generate sinusoidal signal to modulate laser current and to demodulate the modulated signal of the saturated absorption spectrum, and then error signal through filtering is generated. The PID module is used to employ the feedback signal to control the laser current, which makes the laser frequency be stabilized to the atomic transition lines. Using the FPGA module as a core circuit device, the frequency of laser is stabilized to the frequency of crossover line of |62S1/2,F=4>→|62P3/2,F=4,5> and the transition line of |62S1/2,F=4>→|62P3/2,F=5>. The frequency fluctuation of the locking laser within 80 s is 3.0(0.3) MHz. The Allan deviation and frequency spectra of the error signal when the laser is locked and unlocked are compared and the results show that frequency fluctuation can be suppressed effectively when the feedback is applied. The system with advantages of high integration, compact and easy to use, can be used in a variety of locking systems.

Quantum entangled states, as an important resource for quantum communication and information, can obtain relevant information about their quantum states can be measured to obtain. Projection measurement can cause the initial state to collapse to one of its eigenstate. It cannot be used to reverse the measured quantum state to its initial state. If the weak measurement operation is applied to the quantum entangled state and the corresponding reversibility operation is used to explore the elimination effect of its weak measurement on the perturbation of the quantum entangled state, it has certain significance. Therefore, the study of the reversibility of quantum entangled states under different initial conditions after weak measurement and analyzing the feasibility of inverting the quantum entangled state after weak measurement operation to its initial state after reversibility operation is significant. Using weak measurement schemes and reversible operations, numerical analysis of the weak measured quantum state is theoretically carried out, exploring the realization of the inversion of the weak measured quantum state. By implementing reversible operation on the quantum entanglement state after weak measurement operation, this work mainly explores the reversal behavior of the entanglement strength of the quantum entangled state. Concurrence is used to measure the entanglement strength of quantum entanglement states before and after weak measurement. And the entanglement strength of the initial quantum entangled state and the entanglement strength after weak measurement operation are analyzed. Taking a two-body quantum entangled state as an example, two entangled two-level atoms are respectively placed in a high-quality vacuum cavity field. By considering the weak measurement and reversible operation to one atom, we explore the dynamic characteristics of the two-body system quantum entangled state under this scheme. The numerical analysis results show that the entanglement strength of the quantum state after weak measurement can be fully reversed to its initial value through an appropriate reversibility operation. That is to say, the interference of weak measurement on quantum state can be repaired through the reversible operation.

Quantum optics theory needs an advanced method to tackle density operator’ various physical quantities, such as expec-tation value, variance, cumulant, etc. To be specific, since photon creation and annihilation operators do not commute, we need to deal with the problems of how to convert normally ordered operators into anti-normally ordered operators, and how to convert anti-normally ordered operators into normally ordered operators. In short, the operator re-ordering problem is often encountered in quantum optics theory. In this paper we employ the generating function of two-variable Hermite polynomials to derive two basic operator identities. The first basic operator identity is ana+m=(-i)m+n：Hm,n(ia+, ia): , which converts anti-normally ordered operators into normally ordered operators. As an application of the basic operator identity we compute and get am|n>=√ (n!/(n-m)!)|n-m>, meanwhile, we give the commutation relation of [am,a+n]. The second basic operator identity is a+man=Hn,m(a+,a), which converts normally ordered operators into anti-normally ordered operators. When m= n, in virtue of laguerre's polynomials we get the equality Hn,n(x,y)=(-1)nn!Ln (xy). We derive a formula for the transformation between normal product and the anti-normal product in the end. The two basic operator identities are easily remembered and useful in quantum optics. The application of two-variable Hermite polynomials, such as for studying quantum entangled state representation, is greatly developed by Fan Hong-yi in recent years. One can also apply the new basic operator identities to develop binomial and negative- binomial theory which involves twovariable Hermite polynomials.

Quantum coherence is one of the significant properties of quantum systems, and it is widely used in the quantum information processing and condensed matter physics. An important research topic is the correlation between the quantum coherence and the quan-tum phase transitions in the many-body system. However, most of the previous works mainly focused on the total coherence of quan-tum system, and the detection of quantum phase transitions can be hindered by some physical effects. It is well known that the total coherence and its distribution are closely related but also have their own unique properties. In order to overcome the failure of the detec-tion, it is necessary to investigate the ability of coherence distribution to detect the quantum phase transitions and the impact of some physical effects on the detection. Moreover, how to regulate and control the coherence decomposition of a quantum system is very important for performing quantum information processing tasks. Whereas, the current researches cannot give a satisfactory answer. In this work, it is chosen as the research object that two-spin system surrounded by a one-dimensional XY spin chain with a Dzyaloshinsky-Moriya (DM) interaction. Based on Jensen-Shannon entropy, the coherence distributions (localized coherence and collective coherence) and their critical behaviors are investigated. By changing spin-spin coupling and DM interaction, the con-trol of quantum coherence components in a two-spin system has been achieved. The strong spin-spin interaction increases the col-lective coherence of the two-spin system and reduces its localized coherence. The strong DM interaction increases localized coherence and reduces collective coherence. In addition, the localized coherence and collective coherence of the two-spin system can accurately characterize the first-order quantum phase transition through local extremums, but the spin-spin interaction and DM interaction seriously limit the accuracy of localized coherence in characterizing it. The first derivative of local coherence and collective coherence can accurately characterize the second-order quantum phase transitions through divergent behaviors, and is not affected by spin-spin coupling and DM interaction. Finally, it is found that the total coherence and collective coherence of long-distance spin pairs can accurately characterize first-order and second-order quantum phase transition through their critical behaviors. Especially for second-order quantum phase transition environments, the longer the lattice distance between spins, the more significant the critical behavior of the two types of coherence.

With the rapid development of quantum communication technology, quantum teleportation as an important quantum communication scheme has received widespread attention and has become one of the most important protocols in quantum information processing technology. The earliest quantum teleportation are natural two-partite processes for transferring unknown quantum states from one node to another. So far, deterministic quantum teleportation has been demonstrated in three-user networks, and as quantum information research progresses, quantum states or quantum information need to be transferred between more and more nodes. Therefore, multi-user quantum teleportation networks are considered to be the basis of the future quantum internet. However, a versatile and deterministic quantum teleportation network for different combinations of users is currently needed to meet the practical requirements, and thus the construction of continuously variable multi-user quantum teleportation networks is necessary. In this paper, we propose the construction of a multi-purpose quantum teleportation network using a four-partite Greenberger-Horn-Zeilinger (GHZ) entangled state of light, and the proposed four-partite quantum teleportation network can be constructed as a communication system containing one or two subnets. Users in this network can be flexibly associated as a subnetwork, and designated users can be selected to cooperate as needed, and different quantum teleportation networks are implemented under different cooperation methods, which realises the flexibility of network construction. Meanwhile, the physical conditions of implementing different networks are analysed in detail to provide a reference for obtaining high-fidelity and high-flexibility quantum teleportation networks. The results show that in order to ensure the efficient operation of the quantum teleportation network, it is necessary to have highquality entanglement resources, reasonable gain factors, a larger number of controllers, as well as efficient transmission and detection efficiency. With the advantages of flexibility and easy scalability, this scheme can be a useful reference for the realisation of more complex quantum computation and quantum communication networks in the future, using more components of entangled state optical fields, and will provide a general platform for the demonstration of complex quantum communication and quantum computation protocols.

In this study, the temporal characteristics of the polarization process of rubidium atoms in a laser pumping magnetic resonance system under the influence of a constant magnetic field and radiofrequency (RF) field are analyzed both theoretically and experimentally. A simple optical magnetic resonance experiment platform has been established based on rubidium atoms in our experiment. By applying a constant magnetic field along the z-direction, Zeeman splitting was induced in rubidium atoms. The frequency of the laser propagating along the z-direction was locked to the saturated absorption spectrum of 85Rb atoms' D1 line transition 52S1/2, Fg=3→52P1/2, Fe=2, and converted into left circularly polarized beam to polarize the atoms. This laser beam was also used as a probe beam to detect the polarization state of rubidium atoms. Meanwhile, a switch-controlled resonant RF field was applied along the x-direction to induce transitions between atomic polarization states. Here, we monitored the polariza-tion state of rubidium atoms by recording the transmission intensity of the probe beam. When the RF field is turned off, rubidium atoms are polarized solely by absorbing left circularly polarized probe beam. The maximum intensity of the transmitted beam indicates that maximum polarization can be achieved in the experiment. When the resonant RF field is activated, the polarization state is disrupted, causing the atoms to depolarize and reabsorb the probe beam, resulting in a decrease in the intensity of the transmitted beam. The minimum intensity of the transmitted beam indicates an equilibrium between the magnetic resonance depolarization process and the optical pumping polarization process. The RF current amplitude was set to 1.8 mA, and the probe beam power increased from 70 μW to 200 μW. The time evolution of transmission beam was observed by periodically switching the current amplitude of the RF coil. Experimental results showed that the power of the probe beam influenced the polarization process of rubidium atoms, with higher probe beam power resulting in shorter polarization completion time. Numerical analysis based on density matrix theory for a three-level system strongly supported the provided experimental data, aiding further investigation into the dynamic evolution of the magnetic resonance system.

Optically levitated micro- and nano-particle system is an important platform for the study of many-body physics. However, the previous studies are mainly implemented in the liquid. Recently, due to the obvious advantages, the technique of optical levitation in a vacuum has attracted much attention. In this paper, we experimentally trap two nanoparticles using two individual strongly focused lasers in a vacuum and study the light-induced dipole-dipole interaction of the nanoparticles due to the scattering. In the experiment, a laser beam is directly divided into parts to individually trap two silica nanoparticles. The system is analogous to a Mach Zehnder interferometer (MZI), in which the two nanoparticles are sensitive to the interference intensity of the light fields and therefore can be regarded as reflective mirrors. The constructive or destructive interference of the light fields at the nanoparticles' positions directly determines the strength of the dipole-dipole interaction. This system reduces the noise caused by the phase flicker and improves the trapping stability compared to using a spatial light modulator. The light-induced dipole-dipole interaction is measured by adjusting the relative frequencies of the center-of-mass (CoM) motions (or torsional vibrations) of two nanoparticles near the frequency degeneracy point under different linear polarization conditions. The interaction of the torsional vibrations is not observed in this experiment, which indicates that the dipole scattering almost can't influence this motion mode. While a strong coupling between the CoM motions occurs when the polarizations of the trapping beams are perpendicular to the line between the two particles. The measured coupling strength is 1.6 kHz. This work is helpful for further studies of the non-reciprocal interaction between two nanoparticles via adjusting the distance between the nanoparticles and the phase difference of trapping beams, the collective motion of light-induced dipole-dipole interaction of nanoparticles, collaborative cooling and manipulation of multi-particle systems at the single-particle level. It provides a new technical route for studying the multi-particle system.

Plasma plume produced by an atmospheric pressure plasma jet (APPJ) can be either diffuse or filamentary. Filament discharge is violent, and a large amount of joule heat generated in the filaments will damage fragile samples, so diffuse discharge can better meet application needs than filament discharge. Plasma parameters, i.e. is the representation of plasma plume state, determine whether APPJ is suitable for specific applications and its application efficiency. It is of great practical significance to study plasma parameters, including: electron temperature (is approximately equal to electron excitation temperature (Texc)), electron density, molecular vibration temperature and molecular rotation temperature (Trot) (is approximately about equal to gas temperature (Tg)), etc. In this work, an argon diffuse plasma plume is generated by a plasma jet excited by a direct current power with a needle-ring structure supply at atmospheric pressure. Optical imaging shows that the plasma plume is diffuse. Photoelectric signals indicate: depending on the voltage between the needle and the ring electrodes (Vp), the discharge may be pulsed mode or continuous mode. In the pulsed mode, Vp remains almost unchanged, while the discharge current and the total optical signal oscillate periodically. Obviously, these pulses are Trichel pulses. The difference is that, all the waveforms including Vp, discharge current and total optical signal remain almost unchanged with time in the continuous mode. Trends of the plasma plume length in two modes are different: the plasma plume length increases with the absolute value of Vp (abs (Vp)) in the pulsed mode, but remain almost constant in the whole continuous mode. The discharge frequency of the plasma plume increases as abs (Vp) increases in the pulsed mode. The plasma plume length is almost not affected by airflow, and the discharge frequency is also unaffected by airflow in the pulsed mode. Two identical photomultiplier tubes are used to collect optical signals at different locations of the plasma plume in the pulsed mode. It can be seen from the optical signal waveforms that luminescence of the discharge propagates in the form of plasma bullet, and its propagation speed is about 2.8×103 m/s. Therefore, the discharge in the pulsed mode operates in a negative streamer mechanism. Due to asymmetric of electrode structure, electric field reaches a maximum at the tip of the needle cathode, and decreases along argon stream, so discharge occurs first near the tip of the needle. Electrons in primary avalanche leave the tip of the needle and travel along the argon stream. On the other hand, the voltage-current characteristic curve has a positive slope, and the current density on the needle cathode surface is too small in the continuous mode. Therefore, the discharge in the continuous mode is probably in a Townsend discharge mechanism. Optical emission spectrum of the total discharge in both modes has been collected. Spectral lines, which including argon atom (Ar Ⅰ) and argon ion (Ar Ⅱ) appear in both discharge modes. Besides, the following spectral lines: N2, N+2, and OH Π (A2Σ+→X2Π) can also be recognized, whose intensities are much lower than that of Ar Ⅰ. Based on optical emission spectra of two modes, electron excitation temperature (ten spectral lines containing Ar Ⅰ and Ar Ⅱ are selected to estimate Texc) and gas temperature are estimated taking advantage of Boltzmann fitting and OH(A2Σ+→X2Π) free radical spectral lines fitting, respectively. Results manifest that Texc decreases as abs(Vp) increases in the pulsed mode, but remains almost unchanged with the increase of abs(Vp) in the continuous mode. Both the gas temperatures in the pulsed mode (310±20) K and the continuous mode (290±20) K are close to room temperature, in which Tg in the pulsed mode is slightly higher. A thermometer is also used to measure Tg of the plasma plume in two modes, and Tg obtained by the two methods is compared. All of the above results have been qualitatively explained. The lower gas temperature indicates that the diffuse plasma plume produced in this work is suitable for sterilization and surface treatments of biopolymers.

The study of collision of ground-state ultracold polar molecules, in particular the collision properties of two-body exchange of non-reactive molecules, is of great significance for understanding the inelastic collision of molecules, for obtaining the molecular samples with long-lived, stable chemical properties and degenerate quantum states, and carrying out moleculesbased applications. Our previous work [Phys. Chem. Chem. Phys., 20, 4893 (2018)] has achieved the short-range photo-association preparation and optical dipole capture of 85Rb133Cs molecules in the lowest vibrational state, and have measured the inelastic collision coefficients of 85Rb133Cs with 85Rb and 133Cs atoms. However, the above works have not realized the research on the collision characteristics of molecules in rotational dynamics. In this paper, the collision characteristics of different rotational dynamics on the lowest vibrational state of 85Rb133Cs molecule have been studied. In particular, the population of rotational states in the ground state ultracold 85Rb133Cs molecules prepared by directly photoassociation was measured by loss spectroscopy. The transformation of population of rotational states in the ultracold 85Rb133Cs molecules was controlled by microwave pulse technique. The collision characteristics of pure and mixed states in the lowest vibrational ground state of ultracold 85Rb133Cs molecules were studied. The evolution of population of 85Rb133Cs molecules is measured in three cases of X1Σ+(v=0,J=1), X1Σ+(v=0,J=2) and the mixed state formed by the two rotational states. The rate equation is introduced to describe the molecular dynamics in the loss process and the molecular inelastic collision coefficient is obtained. The experimental results show that the collision coefficient of the rotational mixed state is higher than the pure rotational state, which is mainly caused by the dipole-dipole interaction between the neighboring rotational states. The work provides an important reference for understanding the inelastic collision mechanism of ultracold polar molecules and obtaining ultracold polar molecules at low temperature and high density.