Since the traditional definition of single-mode phase operator is not unitary, we attempt to identify a new definition. In view of the phase measurement is always relative to another reference phase, like the potential energy is always relative to zero-point position, we select to introduce phase operator in two-mode Fock space, which is the concrete way to propose a unitary two-mode phase operator operating on the two-mode entangled state representation. Its eigenvalue is just classical phase, and whose phase angle is the conjugate to photon-difference operator. We also present the number-difference-phase uncertainty relationship as well as Weyl-Wigner classical correspondence of the phase operator, which is the phase exp［iargtanp1+p1q1-q2］ in the two variable-pair coordinate-momentum space (q1,p1;q2,p2).

Using the concepts of quantum entanglement, quantum correlations and classical correlation and the method of full quantum theory, the evolution properties of quantum entanglement, quantum discord, geometrical quantum discord and classical correlation in a system of two coupled two-level atoms interacting with a single mode electromagnetic field in a thermal state are studied under the certain conditions. When the two atoms are in the separated state at the initial time, we analyze the effects of the coupling strength between the two coupled two-level atoms and a single mode radiation field in a thermal state. At the same time, we also discuss the mean photon number on the evolution properties of quantum entanglement, quantum correlations and classical correlation between the two atoms in the system. The results show that when an atom weakly coupled to thermal field, the evolution of quantum entanglement, quantum discord and geometrical quantum discord between twocoupled two-level atoms present the phenomenon of sudden death and sudden birth with the increase of the mean photon number of a single mode radiation field in a thermal state, which exhibit a collapse-revival process with gradually decreasing amplitude in the long time scale, and the evolution of classical correlation shows a stable oscillation form. When the effective coupling constant between the atom and a single mode electromagnetic field in a thermal state is stronger, the changes of quantum entanglement and quantum correlations still show the phenomenon of sudden death and sudden birth with increase of the mean photon number of a single mode radiation field in a thermal state. The four quantities are all in the form of irregular oscillation and the values of them significantly reduce in the long time scale. It is found that the other quantum corrections remain in the absence of quantum entanglement in the observed period of time.

Compensating the environmental magnetic field strictly is necessary for the interference caused by environmental magnetic fields which cannot be ignored disturbing the spin waves for quantum memory in the process of establishing the interface between light and atom. The read efficiency of multiple spin waves generated through the spontaneous Raman process will oscillate with storage time under the interference of external magnetic field in the atomic ensemble with multi-level structure. The oscillation of the readout efficiency with the storage time of magnetic field could be eliminated by magnetic compensation, and a large amount of compensation depends on the high precision magnetic field measuring instrumentstill now. We use multiple level atom ensemble of the Raman processes occurring in the spin wave. The characteristics of the readout signal vary with magnetic field, carrying out the method of using reading efficiency of environmental magnetic field compensation research. Compensating the magnetic field noise in three directions by adjusting the current of the three pairs of coils installed around the magnetic-optical-trap (MOT), the interference disappearing time influenced by the magnetic field of the readout efficiency increases continuously until the storage life exceeds the storage life of zero magnetic, and the oscillation disappearance is the symbol of completing the compensation for the environmental magnetic field. Accurately compensating the magnetic of environmental at the location of the atom to zero is impossible with the residual of measurement and adjustment due to human operation error and external unstable factors by gauss meter. In view of the fact, the above method using atoms as reference frame can compensate the environmental magnetic field more accurately and is helpful for the quantum entanglement distribution efficiently.

Analytical expressions of the particle number density, chemical potential, total energy, specific heat and the spatial distribution of particle current density for rotating interacting Fermi gases in a harmonic trap are derived based on the local density approximation (LDA). The effect of mutual interaction between the nearby atoms plays an important impact on the thermodynamics. Especially, the spatial distribution of current density is discussed in detail. The results show that the centrifugal force caused by rotation is always competing with the binding force confined by the harmonic trap. The harmonic trap and attractive interaction tend to concentrate the particles around the center of the trap. The rotationand repulsive interaction tend to decentralize the particles away from the center, which decreases the particle number density and particle current density. Their mutual competition results in the particle distribution being more scattered. Moreover, twosharp and opposite oscillations appear in the spatial distribution of fermion current density. The numerical results indicate that the amplitude and period of oscillations in the spatial distribution of fermion current density are strongly affected by the quantum states near the Fermi surface, which play a dominant contribution to these oscillations．Compared with the case of the ideal Fermi system, the repulsive interaction increases the chemical potential and total energy while the attractive interaction decreases them. The influence of mutual interaction on the specific heat shows completely different characteristics at various temperatures. At the low temperature, repulsive (attractive) interaction makes the heat capacity larger (smaller). At the high temperature, repulsive (attractive) interaction makes the heat capacity smaller (larger) and finally tends to a constant. The results given in this paper can be treated as the general reference for the multiscale analysis of rotating ideal Fermi gases and the other Fermi system. When the mutual interaction disappears, these results completely coincide with those cases for rotating ideal Fermi gases a harmonic trap.

Based on the fractional Schrdinger equation with variable coefficients, the influence of chirp on the propagation characteristics of Airy beams is studied analytically and numerically. When the initial Airy beam has no chirp, it splits into two Airy-like wave packets with equal intensity. For the action of the longitudinal periodic modulation, the beam presents a periodic focusing behavior. When the initial Airy beam has a quadratic chirp, it causes the Airy beam to split into two wave packets with unequal intensities. Under the action of the longitudinal periodic modulation, it exhibits periodic oscillation behavior, and the Airy beam is restored at the focus point of the two beams. Then the influence of related parameters on the dynamics of the second chirped Airy beam is analyzed. The results show that the existence of a chirp has an inhibitory effect on the split beam, and the larger the value of the chirp, the more obvious the inhibitory effect on the split beam. Different signs of the chirp have different effects on the transmission of the light beam. The positive chirp inhibits the right split, and the negative chirp inhibits the left split. It is because of this suppression that interference fringes become less and less obvious. When the chirp parameter is constant, as the Lévy index increases until α=2, Airy beam appears to be inverted. In addition, the influence of related parameters on the interaction of the double Airy beams is also considered. We find that the focal positions of the two beams change with the distance between the two Airy beams, and the number of focal points of the two beams increases with the increase of the Lévy index. The results show that the Airy beams can be controlled by adjusting the parameters to realize the beam management in the fractional Schrdinger equation.

In this paper, based on the potential-free Schrdinger equation, the dynamic solution describing the evolution of the Pearcey-Gaussian beam is obtained. It is found that each lobe of the Pearcey-Gaussian beam isaccelerated in the transverse direction, and the farther away from the main lobe, the greater the acceleration of these side lobes. Eventually, the side lobes and the main lobe reach the same position at the same time. When passing this position, the direction of acceleration changes, so they slow down in the transverse direction. The difference in acceleration of the lobes leads to the separation of the lobes and the invertion of the profile of the Pearcey-Gaussian beam. Thus a focusing and inverting behavior forms. According to the analytical result, the analytical expression governing the focusing distance of the Pearcey-Gaussian beam with a small truncation coefficient is given and verified by numerical simulation. Moreover, the effect of the truncation coefficient on the dynamic behavior of the Pearcey-Gaussian beam is studied numerically by means of a symmetrized split-step Fourier scheme. The results show that the focusing behavior of the Pearcey-Gaussian beam weakens with the increasing of the truncation coefficient. When the truncation coefficient is large, the focusing behavior of the Pearcey-Gaussian beam disappears completely and is replaced by the diffusion behavior. Finally, the dependences of the focusing distance and the peak power at the focusing position on the truncation coefficient are investigated in detail. The results show that with the increasing of the truncation coefficient, the focusing distance decreases gradually, while the peak power at the focusing position decreases rapidly. The results have an important application value for generating an optical beam with high peak power by adjusting the truncation coefficient.

In the last few years, the fractional Schrdinger equation (FSE) received a lot of attention in various areas of physics. In particular, since Longhi suggested a scheme to explore the FSE in optics, the propagation of light beams in the framework of the FSE has been investigated extensively. Also, the beams described by special functions, such as Airy beam, Gaussian beam and Bessel beam, were paid much attention due to their novel properties and potential applications in the related physical fields. However, among the investigations, the propagation dynamics of Airy beam in the framework of the FSE with a combined potential was rarely involved.In the paper, based on the FSE with a combined potential consisted of periodic potential and linear potential, the optical Bloch oscillation and Zener tunneling of Airy beam are studied by numerical simulation. It is found that under the condition of weak transverse force, the initial incident Airy beam first reaches the edge of Brillouin region due to the refractive index gradient, and then be reflected to the center of Brillouin region due to the Bragg reflection, at which the total internal reflectionof the beam occurs. This eventually leads to periodic oscillation of the Airy beam alternating between Bragg reflection and total internal reflection, i.e., optical Bloch oscillation. Different from the propagation in free space and uniform space, the Airy beam with Bloch oscillation can well maintain the Airy shape even after propagating for a long distance. It is related to the energy band structure of the system, i.e., with the decrease of the Lévy index, the energy band width and oscillation amplitude decrease. In this case, the Lévy index can not only change the energy band structure of the fractional system, but also effectively control the optical Bloch oscillation. Furthermore, increasing the linear potential transverse force would lead the appearance of optical Zener tunneling at the edge of Brillouin region, but the decreasing of the Lévy index could suppress this phenomenon effectively.

Based on the competitive nonlinear fractional Schrdinger equation, the propagation dynamics of single Gaussian beam and double Gaussian beams in nonlocal nonlinear media with cubic-quintic competition are numerically simulated by the split-step Fourier transform method. The results show that the amplitude and width of the beam have a certain effect on the evolution of the Gaussian beam into a bound soliton. For the single Gaussian beam, when the beam amplitudeor width decreases, the pulse power of the bound soliton also decreases. When other conditions are the same, the peak power of the soliton in the local medium is obviously greater than the peak power in the nonlocal medium. When the amplitude of double Gaussian beams decrease or the width increase, the soliton changes from respiratory like state to bound state, and the diffraction phenomenon increase. In local and nonlocal media, both single Gaussian beam and in-phase double Gaussian beams have certain diffraction phenomena, and the diffraction phenomenon is more obvious in nonlocal media. Moreover, the balance between the cubic and quintic nonlocal nonlinearities is also crucial to the stability of the soliton. For the interaction between double Gaussian beams, the interval between the two beams also has a certain influence on the stable transmission of the soliton. In the transmission process, the in-phase double Gaussian beams show a strong attraction. The smaller the beam interval, the greater the interaction force, the weaker the diffraction phenomenon and the smaller the respiratory cycle. And affected by the interaction force, the beam has a certain distance interval in the transmission process. The pulse width and period in nonlocal media are larger than those in local media. While out-of-phase double Gaussian beams exhibit repulsion, the larger the beam spacing, the smaller the repulsive force. The pulse width in local media is wider than that in nonlocal media, and other phenomenan are consistent.

Recently, the study of the surface acoustic wave (SAW) in an acoustic wave resonator (AWR) and its interaction with microscopic particles have caused more and more attention. This paper proposes a scheme to prepare entangled coherent states on two AWRs coupled with a nitrogen vacancy (NV) center ensemble. The two AWRs cross each other vertically, and the NV ensemble is located at the center of the crossing. We first discuss the excited-state mediated spin-phonon coupling taking place in a Λ-type three-level system for NV centers. Based on the large detuning interaction, we can achieve the maximally entangled coherent states of acoustic fields with a high probability of success and fidelity. The large detuning interaction can reduce the adverse impact from the decay process of the qubit excited state, thus improving the experimental feasibility of our scheme. The analysis results show that the fidelity of the final state can still be more than 90% under the condition of inhomogeneous qubit-resonator coupling strength. Moreover, under the existing experimental parameters, this scheme can be achieved within the coherence times of the NV centers and resonators. The NV centers in our scheme can be substituted by other emerging spin systems with spin defect centers such as quantum dots or superconducting systems, etc. Considering the macro-entangled coherent states have important applications in quantum information and quantum computing, the research results here have certain theoretical reference value for exploring the quantum acoustic properties and quantum information processing scheme with spin-phonon interaction system.

Based on the effective-mass approximation and variational approach, the ground-state exciton binding energy, the interband emission wavelength, and the radiative lifetime as functions of the quantum dot (QD) sizes (height and radius) and In content in the InxGa1-xN layer are investigated theoretically in strained wurtzite (WZ) ZnSnN2/InxGa1-xN cylindrical QDs, with considering a three-dimensional carrier confinement in QDs and a strong built-in electric field (BEF) effect due to the piezoelectricity and spontaneous polarization. The computations are performed in the case of finite band offset. Numerical results elucidate that the ground-state exciton binding energy decreases with increasing QD sizes and In content when In content x2.2?nm. and it has a red-shift with increasing QD size. In addition, the radiative lifetime increases with increasing QD size and decreases with increasing In content. The built-in electric field decreasing linearly with In content reduces the ground-state exciton binding energy, and increases the interband emission wavelength and the radiative lifetime. Because the electric field in the ZnSnN2 layer exists along the grown direction of the heterostructures, the influence on the luminescent properties from height L is more visible than the influence on the luminescent properties from radius R. So, in the investigation of the luminescent properties, the BEF and the QD height L are important. Furthermore, the ground-state exciton binding energy, the interband emission wavelength, and the radiation lifetime in ZnSnN2/InxGa1-xN QDs are all larger than those in InxGa1-xN/GaN QDs, especially for QDs with low In content.

The temperature effect of the strong coupling bound polaron in a parabolic quantum well is studied theoretically, and the expressions of the polaron ground state energy and the ground state binding energy are derived by using the linear combination operator and the unitary transformation methods. The ground state energy and ground state binding energy of polaron are functions of the vibration frequency, electron phonon coupling strength, Coulomb bound potential strength, well width and well depth, respectively. At finite temperature, the electron phonon system will no longer be complete in the ground state. The lattice vibration not only excites the real phonon, but also excites the electron. The properties of polaron are mainly determined by the statistical average of various states of electron phonon system. The expression of the average phonon number of polaron is also obtained through theoretical calculation. Combined with quantum statistics, the functional relationship between the ground state energy and ground state binding energy of polaron and temperature is obtained. By numerical calculation, the polaron ground state energy and ground state binding energy are increasing functions of temperature. When thetemperature is set to a fixed value, as the electron-phonon coupling strength, Coulomb bound potential strength and well width increase, the ground state energy of the polaron decreases and the ground state binding energy increases. With the increase of the well depth, the ground state energy of the polaron increases, and the ground state binding energy decreases.