Correlation of quadrature amplitude fluctuations during the intracavity generation of second harmonic

For the process of intracavity generation of the second harmonic, the dynamics of correlation of quadrature amplitudes fluctuations of the fundamental and the second harmonic modes is studied depending on the nonlinear coupling coefficient between the modes. It was shown that in this system the entangled states of field related to variables of quadrature amplitudes may be obtained depending on the nonlinear coupling coefficient. It was also shown that the entanglement of the states of field modes related to one quadrature amplitude may vanish depending on the value of nonlinear coupling coefficient, whereas the states of field modes related to the other quadrature amplitude stay entangled.     

Quantum dynamics of interacting modes in the process of intracavity subharmonic generation

The dynamics of correlation between fluctuations of the number of photons of interacting modes is investigated for the process of intracavity subharmonic generation. It is demonstrated that this correlation strongly depends on the nonlinear mode coupling coefficient. For small values of the coupling coefficient, the correlation between fluctuations of the number of photons is small. With an increase in the coupling coefficient, the correlation increases (the state of subsystems becomes entangled) and, starting from a particular value of the coupling coefficient, starts to decrease with further increase in the coupling coefficient, gradually approaching zero (entanglement of subsystem states decreases). The quantum dynamics of the number of photons, quantum entropy, and Wigner function of the stationary state of the fundamental and subharmonic modes is investigated. It is demonstrated that the dynamics of these quantities also strongly depends on the coupling coefficient of the interacting modes. We show that, for large values of the mode coupling coefficient and long interaction times, the subharmonic mode becomes localized in a two-component state with equal probabilities of finding it in each component. Quantum entropy of this state is smaller than maximum entropy of the two-component state equal to ln2, which suggests that quantum-mechanical interference takes place between the subharmonic mode components.     

Bose-Hubbard模型中系统初态对量子关联的影响

量子关联是量子信息、量子计算与量子计量领域的重要资源, 在量子纠缠和贝尔非局域性中, 两子系统起着同等关键的作用, Einstein-Podolsky-Rosen (EPR)量子引导关联的强度介于量子纠缠和贝尔非局域性之间, 对单向EPR量子引导关联而言两子系统的作用不对等. 本文研究了双模Bose-Hubbard模型中模间量子关联的动态特性, 揭示了EPR量子引导关联的取向对系统初态模间交换对称性的依赖关系. 根据Hillery-Zubairy纠缠判据以及基于最大平均量子Fisher信息的纠缠判据考察了系统初态对模间量子纠缠演化规律的影响. 如果模间耦合强度远大于同一势阱内粒子间的相互作用, 初始处于SU(2)相干态的系统在具有确定的两子系统交换对称性的条件下, 其量子关联呈现简单的周期性演化规律; 当这种对称性破缺时, 模间量子关联的演化呈现较复杂的崩塌与回复现象.     

Giant violations of classical inequalities through conditional homodyne detection of the quadrature amplitudes of light

Conditional homodyne detection is proposed as an extension of the intensity correlation technique introduced by Hanbury-Brown and Twiss [Nature (London) 177, 27 (1956)]. It detects giant quadrature amplitude fluctuations for weakly squeezed light, violating a classical bound by orders of magnitude. Fluctuations of both quadrature amplitudes are anomalously large. The squeezed quadrature also exhibits an anomalous phase.     

Quantum coherence and entangled states in intracavity third subharmonic generation process

The dynamics of correlation of photon number fluctuations of interacting modes for the process of intracavity third subharmonic generation is investigated. It is shown that the entangled field states by the variables of photon number can be obtained in this system. The quantum dynamics of the photons number, the quantum entropy and the Wigner function of the stationary states of the fundamental mode and the third subharmonic mode have also been studied. It is found that the dynamics of these quantities depends highly on the value of the coupling coefficient of the interacting modes. It is shown that at long interaction times and for the large values of the coupling coefficient of the modes, the mode of the third subharmonic is localized in the three-component state with the same probability of detection of the mode in each component of the state. The quantum entropy of the state is less than the maximal entropy of the three-component state ln3, which points out the presence of quantum mechanical interference between the components of the state of third subharmonic mode.     

Electronic structure and spin fluctuations in the helical ferromagnet MnSi

The influence of spin fluctuations on the magnetic properties of the ferromagnetic helimagnet MnSi has been studied in the Hubbard model taking into account the antisymmetric relativistic Dzyaloshinskii–Moriya interaction for band electrons. The obtained equations of the magnetic state indicate the correlation between the fine structure of the density of electronic states and the magnetization and coefficient of mode–mode coupling. It has been shown that the position of the Fermi energy in the immediate proximity on the point of the local minimum of the density of electronic states leads to large zero spin fluctuations at low magnetization of the helimagnet. When approaching from down the Néel point (approximately, at 0.9T_N), the zero fluctuation disappear, and the temperature rise of thermal spin fluctuation is accompanied by the change in the sign of the coefficient of mode–mode coupling. A magnetic field perpendicular to the helicoids plane brings about the formation and subsequent “collapse” of the helimagnetic cone. However, the condition of the change in the sign of the coefficient of mode–mode coupling divides the MnSi phase diagram into two parts, one of which corresponds to the ferromagnetic state induced by the field, and the other corresponding to the paramagnetic state. In this case, the h–T diagram has a specific region, inside which the paramagnetic and the ferromagnetic state are instable. The boundaries of the region agree with the experimental data on the boundaries of the anomalous phase (a phase). It has been found that the results of calculations of the temperature dependence of the magnetic susceptibility agree with the experimental data.     

Intensity fluctuations in a ring laser taking into consideration a spatial population-inversion grating

The correlation functions of the intensity fluctuations are calculated by use of a linearization procedure for the equations of motion which include the coupling of the counter-rotating travelling waves of the ring laser in the cases of Doppler broadening, of homogeneous broadening with a self-induced population-inversion grating, and in intermediate cases. Depending on the strength of the mode competition various stable stationary solutions exist for the amplitudes. The transition between these stable states shows phenomena closely resembling phase transitions such as critical fluctuations, critical slowing down, etc. In particular, when the system passes from the state where both modes are above threshold to the state where one mode is below threshold, the negative cross-correlation of the fluctuations also becomes critical. In the case of the transient behaviour of the ring laser in the unstable region the time development of the amplitudes and the correlation functions are described in a short-time approximation.     

Successively Squeezed States Studied by Virtue of the IWOP Technique

Two kinds of successively squeezed states which are generated by re-squeezing two single mode squeezed states by the two-mode squeezing operator, or by re-squeezing a two-mode squeezed state by two single-mode squeezing operators, are studied in terms of the newly developed technique of integration within an ordered product (IWOP) of operators. The fluctuations in quadrature phases for the resqueezed states are analyzed.     

Squeezed states in resonance fluorescence of two interacting atoms

The possible existence of so-called “squeezed” states in two-atom resonance fluorescence is discussed in Lehmberg's master equation approach. It is shown that squeezing strongly depends on interatomic separations r₁₂. For large r₁₂ one of the quadrature components is squeezed, and as r₁₂ decreases its squeezing decreases in order to appear in the other quadrature component for certain value of r₁₂. For very small r₁₂ fluctuations in both components tend to zero.     

玻璃陶瓷PWG中的喇曼耦合系数对Raman散射的影响

应用修正的无序诱导散理论模型讨论了玻璃陶瓷（PbF2 WO3 GeO(PWG)中的喇曼耦合系数对Raman散射过程的影响。虽然普遍认为喇曼耦合系数是随频率而变化,但实际上它是空间相关函数的Furier分量,因此,严格地讲喇曼耦合系数是随动量（波矢q)而变化的,因而,玻璃陶瓷中的喇曼耦合系数描述了在Raman散射过程中发生在玻璃陶瓷中的动量交换相互作用。对于PWG中热活性拓动态的光谱分布曲线分析说明：指数衰减关系的卷积定性地表示了这个耦合系数。证明了简谐势与耦合系数有关的空间相关函数之和给出了非常类似于双阱势的畸变谐函数,根据弛豫模行为讨论了结合势的相关性。     

Power fluctuations in a closed turbulent shear flow

We study experimentally the power consumption P of a confined turbulent flow at constant Reynolds number Re. We analyze in details its temporal dynamics and statistical properties, in a setup that covers two decades in Reynolds numbers. We show that nontrivial power fluctuations occur over a wide range of amplitudes and that they involve coherent fluid motions over the entire system size. As a result, the power fluctuations do not result from averaging of independent subsystems and its probability density function Pi(P) is strongly non-Gaussian. The shape of Pi(P) is Reynolds number independant and we show that the relative intensity of fluctuations decreases very slowly as Re increases. These results are discussed in terms of an analogy with critical phenomena.     

三层弱循环耦合可激发介质中螺旋波动力学

采用Bär模型研究了具有循环反馈耦合的三层可激发介质中的螺旋波动力学行为,数值模拟结果显示: 在耦合强度较小时, 在各子系统中可观察到螺旋波漂移或漫游; 当耦合强度稍大时, 相互作用既可以使螺旋波漫游或漂移出系统边界而使子系统回到静息态,还可以使子系统的螺旋波态转变为靶波或湍流态, 并观察到子系统的渐近态依赖初值现象; 继续增大耦合强度, 三个子系统的螺旋波可达到近似广义同步; 当耦合强度更大时, 螺旋波演化为湍流态.     

The quantum-fluctuations of the optical parametric oscillator. I

Our treatment is based on a microscopically correct Hamiltonian which contains the Bose-operators of the light modes and the Fermi-operators of the optically active electrons in the medium. The coupling between modes and atoms is taken from quantum-electrodynamics. Besides that, the light modes may interact with external “heat baths” like the mirrors, scattering centers etc., while the atoms interact with lattice vibrations, incoherent light fields etc. Using recently developed methods the effect of these heatbaths is taken into account in a quantum mechanically consistent fashion. In the present paper we apply quantum mechanical Langevin equations for the field and electron operators which contain dissipation and fluctuation terms. The elimination of the electron operators by an iteration procedure finally leaves us with a set of coupled nonlinear field equations which are shown to be quantum mechanically consistent. They are solved in the Heisenberg picture below threshold by linearization and well above threshold by quantum mechanical quasi-linearization. The solutions show that the line width of the signal mode below threshold is due to the vacuum fluctuations in the idler and vice versa, whereas the thermal noise of the resonator and the spontaneous emission noise of the medium may be neglected. Above threshold the linewidth is caused by the undamped diffusion of the phase difference between signal and idler, to which the vacuum fluctuations of both modes contribute in equal parts. The phase sum of both modes adiabatically follows the slow phase diffusion of the external pump light, produced by a laser, and therefore contributes to the linewidth too. Well above threshold the amplitudes are stable. Correlation and cross-correlation functions of their small residual fluctuations are calculated.     

Quantum properties of nonclassical states generated by an optomechanical system with catalytic quantum scissors

A scheme is proposed to investigate the non-classical states generated by a quantum scissors device (QSD) operating on the the cavity mode of an optomechanical system. When the catalytic QSD acts on the cavity mode of the optomechanical system, the resulting state contains only the vacuum, single-photon and two-photon states depending upon the coupling parameter of the optomechanical system as well as the transmission coefficients of beam splitters (BSs). Especially, the output state is just a class of multicomponent cat state truncations at time t=2π by choosing the appropriate value of coupling parameter. We discuss the success probability of such a state and the fidelity between the output state and input state via QSD. Then the linear entropy is used to investigate the entanglement between the two subsystems, finding that QSD operation can enhance their entanglement degree. Furthermore, we also derive the analytical expression of the Wigner function (WF) for the cavity mode via QSD and numerically analyze the WF distribution in phase space at time t=2π. These results show that the high non-classicality of output state can always be achieved by modulating the coupling parameter of the optomechanical system as well as the transmittance of BSs.     

Quantum atomic-fluctuations reduction and squeezed-state generation via forward degenerate four-wave mixing

It is shown that correlation of quantum atomic fluctuations for coupled modes at forward degenerate four-wave mixing leads to atomic noise reduction from the in-phase quadrature variance of the mode which is a linear combination of the coupled signal and probe modes. Thus, quantum atomic fluctuations are not an obstacle for the squeezed-state generation via degenerate four-wave mixing.     

Stimulated Raman adiabatic passage in fields with stochastic amplitudes

A theoretical analysis is presented of the effect of correlation between fluctuations of laser pulse amplitudes on population transfer between the states of a three-level atom coupled by the laser field. The carrier frequencies of the pulses are tuned to resonance with the transitions between the ground and excited states, |〈 and | 2〈, and the excited and metastable states, |2〈 and |3〈, in a lambda-type configuration. The laser pulses are timed so that population transfer between states |1〈 and | 3〈 is made possible by stimulated Raman adiabatic passage (STIRAP) in the absence of fluctuations. STIRAP does not occur when the laser fields are not correlated. When the fluctuations of one pulse amplitude duplicate those of the other, STIRAP can be observed for pulse amplitudes larger than those required in the absence of fluctuations.     

Squeezing Exchange and Entanglement between Resonantly Coupled Modes

We study the problem of squeezing exchange between two modes of the electromagnetic field modeled by quantum oscillators for the most general weak bilinear resonance coupling. Also we introduce a new measure of entanglement based on the cross covariances of the quadrature components of interacting modes. We compare the covariance measure with the measures based on the von Neumann and linear entropies of the subsystems, studying their dependences on time, coupling constants, and the initial state in the cases of parametric amplification and parametric conversion. In particular, we show that coherent states remain disentagled for all times and for any choice of coupling constants in the case of parametric converter (with accuracy up to second-order terms with respect to the strength of coupling). Also, we demonstrate that no bilinear coupling can squeeze the initial coherent state or improve the squeezing of the initial squeezed state in the case of a parametric amplifier. A strong sensitivity of the character of evolution to the choice of the set of coupling constants is discovered in the case of a parametric converter.     

Scale invariance of plastic deformation of the planar and crystal subsystems of solids under superplastic conditions

The theory of structural transformations in the planar sybsystem (surface layers and internal interfaces) of solids under plastic deformation is developed. The theory is based on a consideration for local curvature of the crystal lattice, with new structural states arising in its interstices, responsible for plastic distortion. To satisfy the superplastic condition, such high-rate mechanisms should develop in both planar and 3D crystal subsystems. In a translation-invariant crystal, this condition is met by concentration fluctuations. The multiscale criterion of superplasticity is formulated based on the scale invariance of plastic deformation of the planar and crystal subsystems in a deformable solid. Beyond the criterion, superplasticity passes to the creep mode with restricted plasticity of the material.     

Fokker-Planck equation approach to fluctuations about nonequilibrium steady states

We examine the properties of steady states in systems which interact at the boundary with a nonequilibrium environment. The examination is based on a nonlinear Fokker-Planck equation, the structure of which is determined by the fact that it also governs the time evolution of the equilibrium fluctuations of the system. The nonlinearities in the Fokker-Planck equation may have two origins: thermodynamic nonlinearities which arise if the thermodynamic potential is not a bilinear function of the state variables, and nonlinear mode coupling which arises if the transport coefficients depend on the state. While these nonlinearities have only a small effect on the equilibrium fluctuations of a system away from critical points, they are shown to be important for the determination of fluctuations about nonequilibrium steady states. In particular the state dependence of the transport coefficients may lead to deviations from local equilibrium and to a breakdown of detail balance. An explicit formula for the time correlations of fluctuations about the nonequilibrium steady state is obtained. The formula leads to long-range correlations in fluids in the presence of a temperature gradient. The result is compared with earlier approaches to the same problem. Finally, we study the linear response to external forces and obtain a generalization of the fluctuation-dissipation formula relating the response functions with the nonequilibrium correlation functions.     

Two-mode coupling model in a few mode fiber

A phenomenological two-mode coupling model in few mode fibers (FMF) is developed. It uses a mode coupling coefficient and the differential modal delay as the input parameters and the split-step approach. The model is consistent with the experimental results demonstrating distributed mode coupling effects in FMF and may be used for multipath interference estimation based on statistical analysis of fluctuations.