Abstract:
We propose a new numerical approach to compute nonclassical solutions to hyperbolic conservation laws. The class of finite difference schemes presented here is fully conservative and keep nonclassical shock waves as sharp interfaces, contrary to standard finite difference schemes. The main challenge is to achieve, at the discretization level, a consistency property with respect to a prescribed kinetic relation. The latter is required for the selection of physically meaningful nonclassical shocks. Our method is based on a reconstruction technique performed in each computational cell that may contain a nonclassical shock. To validate this approach, we establish several consistency and stability properties, and we perform careful numerical experiments. The convergence of the algorithm toward the physically meaningful solutions selected by a kinetic relation is demonstrated numerically for several test cases, including concave-convex as well as convex-concave flux-functions.

Abstract:
In this paper, we will try to present a general formalism for the construction of {\it deformed photon-added nonlinear coherent states} (DPANCSs) $|\alpha, f, m>$, which in special case lead to the well-known photon-added coherent state (PACS) $|\alpha, m>$. Some algebraic structures of the introduced DPANCSs are studied and particularly the resolution of the identity, as the most important property of generalized coherent states, is investigated. Meanwhile, it will be demonstrated that, the introduced states can also be classified in the $f$-deformed coherent states, with a special nonlinearity function. Next, we will show that, these states can be produced through a simple theoretical scheme. A discussion on the DPANCSs with negative values of $m$, i.e., $|\alpha, f, -m>$, is then presented. Our approach, has the potentiality to be used for the construction of a variety of new classes of DPANCSs, corresponding to any nonlinear oscillator with known nonlinearity function, as well as arbitrary solvable quantum system with known discrete, nondegenerate spectrum. Finally, after applying the formalism to a particular physical system known as P\"oschl-Teller (P-T) potential and the nonlinear coherent states corresponding to a specific nonlinearity function $f(n)=\sqrt n$, some of the nonclassical properties such as Mandel parameter, second order correlation function, in addition to first and second-order squeezing of the corresponding states will be investigated, numerically.

Abstract:
本文从描述驻波激光场与囚禁离子相互作用的非线性Jaynes-Cummings模型出发，引入一种新的量子态，即非线性增光子热态。采用理论分析和数值计算相结合的方法，研究了Lamb-Dicke参数，温度和激光场的初相位等参数对这种量子态的非经典效应的影响。结果表明：非线性增光子热态的Mandel 因子随温度的变化存在一个极小值。Lamb-Dicke参数越大，非线性增光子热态的非经典效应就越强。此外驻波场的初相位也对该态的非经典效应有明显的影响。 According to the nonlinear Jaynes-Cummings model which describes the interaction of a trapped ion with a standing wave laser field, a new quantum state, so called nonlinear photon-added thermal state, is introduced. The effect of Lamb-Dicke parameter , temperature and phase of the standing field on the nonclassical effect of the quantum state is studied by using the method of theoretical analysis and numerical calculation. The results show that the change of Mandel factor of nonlinear photon-added thermal state with temperature has a minimum. The larger the Lamb-Dicke parameter is, the stronger nonclassical effects of the nonlinear photon added thermal state is. In addition, the initial phase of the standing wave field has a significant effect on the nonclassical effects of the state.

Abstract:
We experimentally demonstrate the nonclassical photon number correlations expected in tripartite continuous variable states obtained by parametric processes. Our scheme involves a single nonlinear crystal, where two interlinked parametric interactions take place simultaneously, and represents a bright and compact source of a sub-shot-noise tripartite light field. We analyze the effects of the pump intensities on the numbers of detected photons and on the amount of noise reduction in some details, thus demonstrating a good agreement between the experimental data and a single-mode theoretical description.

Abstract:
We present two linear optical schemes using nonideal photodetectors to demonstrate inseparability of W-type N-partite entangled states containing only a single photon. First, we show that the pairwise entanglement of arbitrary two modes chosen from N optical modes can be detected using the method proposed by Nha and Kim [Phys. Rev. A 74, 012317 (2006)], thereby suggesting the full inseparability among N parties. In particular, this scheme is found to succeed for any nonzero quantum efficiency of photodetectors. Second, we consider a quantum teleportation network using linear optics without auxiliary modes. The conditional teleportation can be optimized by a suitable choice of the transmittance of the beam splitter in the Bell measurement. Specifically, we identify the conditions under which maximum fidelity larger than classical bound 2/3 is achieved only in cooperation with other parties. We also investigate the case of on-off photodetectors that cannot discriminate the number of detected photons.

Abstract:
We investigate electromagnetic radiation emitted by a small voltage-biased Josephson junction connected to a superconducting transmission line. At frequencies below the well known emission peak at the Josephson frequency (2eV/h), extra radiation is triggered by quantum fluctuations in the electromagnetic environment. For weak tunneling couplings and typical ohmic transmission lines, the corresponding photon flux spectrum is symmetric around half the Josephson frequency, indicating that the photons are predominately created in pairs. By establishing an input-output formalism for the microwave field in the transmission line, we give further evidence for this nonclassical photon pair production, demonstrating that it violates the classical Cauchy-Schwarz inequality for two-mode flux cross correlations. In connection to recent experiments, we also consider a stepped transmission line, where resonances increase the signal-to-noise ratio.

Abstract:
理论上研究了联合增光子二模圆态的互相关函数，亚泊松分布等非经典特性。数值计算表明激发数和叠加态数对这些特性有明显的影响。当叠加态数 时，交叉关联函数随单模平均光子数的增大而单调减小， 并且联合增光子二模圆态存在关联效应。随着叠加态数的增加，二模光场间的关联效应将减弱。当叠加数 时，只有当激发数 时，且单模平均光子数大于某阈值时，联合增光子二模圆态才存在亚泊松分布效应。 We investigate theoretically the nonclassical properties, such as cross correlation function and sub- Poisson distribution effect, for the nonlocal coherent photon-added two-mode circular state. The results show the superposition number and excitation number have significant effect on these properties. When the superposition number , the value of cross correlation function decreases monotonously with the increasing of the average photon number of single-mode and the nonlocal coherent photon-added two-mode circular state has the cross correlation effect. Increasing the superposition number , the cross correlation effect will be reduced. When the superposition number , sub-Poissonian distribution effect of the nonlocal coherent two-mode photon-added circular state can be observed only when single-mode average photon number is greater than a certain threshold value

Abstract:
This book chapter reports on theoretical protocols for generating nonclassical states of light and mechanics. Nonclassical states are understood as squeezed states, entangled states or states with negative Wigner function, and the nonclassicality can refer either to light, to mechanics, or to both, light and mechanics. In all protocols nonclassicallity arises from a strong optomechanical coupling. Some protocols rely in addition on homodyne detection or photon counting of light.

Abstract:
We use photon counters to obtain the joint photon counting statistics from twin-beam non-degenerate parametric down conversion, and we demonstrate directly, and with no auxiliary assumptions, that these twin beams are nonclassical.

Abstract:
The nonclassical effect of photon anti-bunching is observed in the mixed field of a narrow band two-photon source and a coherent field under certain condition. A variety of different features in photon statistics are found to be the consequence of a two-photon interference effect with dependence on the relative phase of the fields. Besides the anti-bunching effect, we find another one of the features to be also nonclassical. These features emphasize the importance of quantum entanglement.