Two-Mode Wigner Operator in 〈ξ| Representation and 〈τ| Representation

We derive the two-mode Wigner operator in the 〈ξ| representation and 〈τ| representation, where |ξ〉 is common eigenvector of the mass-weighted relative coordinate and the mass-combinatorial momentum.and |τ〉 common eigenvector of the mass-weighted relative coordinate and the mass-combinatorial momentum. As an application,we calculate the Wigner function of some two-mode state.     

New theorem relating two-mode entangled tomography to two-mode Fresnel operator

Based on the Fan-Hu's formalism, i.e., the tomogram of two-mode quantum states can be considered as the module square of the states' wave function in the intermediate representation, which is just the eigenvector of the Fresnel quadrature phase, we derive a new theorem for calculating the quantum tomogram of two-mode density operators, i.e., the tomogram of a two-mode density operator is equal to the marginal integration of the classical Weyl correspondence function of F₂⁺ρF₂, where F₂ is the two-mode Fresnel operator. An application of the theorem in evaluating the tomogram of an optical chaotic field is also presented.     

On the Bosonic Phase Operator Realization for Josephson Hamiltonian Model

On the assumption that a Cooper pair acts as a Bose particle and based on the newly estabished (η|representation,which is the common eigenvector of two particles‘ relative position and total momentum,we introduce a mesoscopic Josephson junction Hamiltonian constituted by two-mode Bose phase operator and number-difference operator,The number-difference-phase uncertainty relation can then be set up,which implies the existence of Josephson current.     

Uncertainty relation and photon-number distribution for one-and two-mode squeezed light

We study the one-and two-mode photon distribution functions for Gaussian quantum states. The dependence on the photon-quadrature parameters is discussed within the framework of violation of the uncertainty relation. We derive the one-and two-mode photon distribution functions and present plots demonstrating that the expressions for the distribution functions take negative or complex values in the domain of quadrature parameters violating the uncertainty relation.     

New approach for solving the Wigner function from the Husimi function in the two-mode entangled state representation

We introduce a new method to calculate the Wigner function when its corresponding Husimi function is given. A new formula is derived for calculating conveniently the Wigner function in two-mode entangled state representation. As application, we derive Wigner functions of some quantum states, such as two-mode entangled state, the electron's two-mode squeezed canonical coherent state, and the electron's coordinate eigenstate.     

Multiple-Photon-Added and -Subtracted Two-Mode Binomial States:Nonclassicality and Entanglement *

We theoretically analyze the nonclassicality and entanglement of two new non-Gaussian entangled states generated by applying multiple-photon addition and subtraction to a two-mode binomial state. The nonclassical properties are investigated in terms of the partial negativity of the Wigner functions, whose results show that their nonclassicality can be enhanced via one-mode even-number photon operations and two-mode symmetrical operations for the initial two-mode binomial state. We also find that there exists some enhancement in the entanglement properties in certain parameter ranges via one-mode photon-addition and two-mode symmetrical operations.     

新纠缠态表象对耦合2谐振子系统的应用

我们研究一个耦合2谐振子系统的本征态问题。我们构造了由算子（x1+p2）和（x2+p1）的共同本征态组成的新纠缠态表象︱γ>。在︱γ>表象得到了系统哈密顿的本征值和本征态。同样的问题用二次量子化表象进行了研究。我们发现在Fock空间，二次量子化表象可以被用来推得本征态的正规积表示。特别是发现了系统基态为广义2模压缩态     

Effective two-mode description of a few ultra-cold bosons in a double-well potential

We present a construction of an improved two-mode model for modeling the dynamics of interacting ultra-cold bosons confined in a one-dimensional double well trap. Unlike in the typically used two-mode model based on the lowest single-particle eigenstates of the external potential, the improved model uses a basis of properly chosen effective wave functions originating in the many-body model. Accuracy of the improved model is examined and it is shown that within a certain limit of inter-particle interaction strength, the model recovers an exact evolution of the wells' populations much more closely than the traditional two-mode model.     

Creation and Destruction of Entanglement via Fourier Multiport Devices

We study entangling and disentangling functions of optical Fourier multiport devices in which input-output relation for the creation and annihilation operators is given by a finite Fourier transform. It is shown that these Fourier multiport devices can act as entanglement converters which can not only create entanglement from an unentangled state at the input but also destroy entanglement in an entangled state at the input. Creation and destruction of two-mode and three-mode entangled coherent states （ECSs） are investigated in detail. The creation and destruction of Bell-type two-mode ECS, GHZ-type and W-type three-mode ECSs are indicated explicitly through using Fourier four-port and six-port devices, respectively.     

Nonclassical effects in a two-photon laser

The steady state quantum statistical properties of light in a two-mode two-photon laser are presented. It is shown that the second-order coherence functions violate a classical inequality.     

利用置于光腔中的非线性耦合器制备压缩和连续变量纠缠光

利用置于光腔中的非线性耦合器制备了压缩和连续变量纠缠光.通过特征函数方法解析求解了双模腔场满足的主方程.分析发现：在一定的条件下,此系统能产生稳定的双模压缩和连续变量纠缠光,且压缩和纠缠的强度与系统的耦合参量及腔场损耗系数密切相关.     

Global rate equation description of a laser

The global integro-differential rate equations describing a multimode laser are analyzed. Expressions for the relaxation oscillation frequencies and their damping rates in the single-mode and two-mode regimes are obtained without specifying either the cavity geometry or the longitudinal pump profile. On the same level of generality, we prove the existence of universal relations relating the peaks of the power spectra in the two-mode regime. For a Fabry-Perot with arbitrary longitudinal pump profile, series expansions of all the physical functions are derived in powers of the pump moments. These moments are averages of the pump profile over cavity modes at linear combinations of the lasing frequencies and their harmonics. These results apply to end-pumped and/or partially filled lasers. For a single mode Fabry-Perot laser, we prove that the contribution to the steady state intensity from the lasing mode varies from 75% close to the lasing threshold to zero at high intensity. The remainder comes from the harmonics of the lasing mode. Analyzing the steady state single mode intensity equation in terms of the pump gratings, we prove that close to the lasing threshold only the space average of the pump and its grating oscillating at twice the lasing wave number do not vanish. This provides a hint towards the justification of the usual modal rate equations which retain only these two functions in the dynamical evolution of a laser. For a Fabry-Perot with constant pump profile, an exact expression for the upper boundary of the stable single mode regime is derived. In that two-mode regime, we prove that there is a critical value of the pump at which the ratio of the two relaxation oscillation frequencies is 2, leading to an internal resonance.     

量子光学理论中双模厄米多项式的新应用

强调双模厄米多项式在量子光学理论中的地位,认为它是研究连续变量纠缠态和压缩态的必要函数,具有明确的物理意义。利用双模厄米多项式,结合有序算符内的积分技术,给出了若干新的算符恒等式和互逆的积分变换公式,证明了压缩双模粒子数态恰好是双变量厄米多项式激发压缩真空态。     

基于四波混频过程的纠缠光放大

双模纠缠态是量子信息领域一种重要的量子资源,本文基于四波混频过程从理论上提出了对双模纠缠态的单个模式(单模放大方案)和对双模纠缠态的两个模式(双模放大方案)的放大.利用光学分束器模型来模拟在光学传输过程中损耗引入的真空场噪声,利用部分转置正定判据分析了两种不同的放大方案中四波混频过程的增益对初始双模纠缠态的纠缠程度的影响.结果表明,在特定的损耗情况下,两个方案中初始双模纠缠态的纠缠度都随增益的增大而减小,直至消失,且双模放大方案中初始双模纠缠态纠缠消失得比单模放大方案中更快.本文的理论结果为实验上实现基于四波混频过程的双模纠缠态的放大奠定了理论基础.     

Quantum mechanical pure states with gaussian wave functions

This paper examines single-mode and two-mode Gaussian pure states (GPS), quantum mechanical pure states with Gaussian wave functions. These states are produced when harmonic oscillators in their ground states are exposed to potentials, or interaction Hamiltonians, that are linear or quadratic in the position and momentum variables (i.e., annihilation and creation operators) of the oscillators. The physical and group theoretical properties of these Hamiltonians and the unitary operators they generate are discussed. These properties lead to a natural classification scheme for GPS. Important properties of single-mode and two-mode GPS are discussed. An efficient vector notation is introduced, and used to derive many of the important properties of GPS and of the Hamiltonians and unitary operators associated with them.     

Strong-Driving-Assisted Preparation of Superpositions of Two-Mode Coherent States in Cavity QED

A scheme is proposed for preparing the superposition of two-mode coherent states with controllable weighting factors along a straight line for two-mode cavity field. In this scheme two-level atoms driven by classical field are sent through a two-mode cavity initially in the vacuum state. Then the detection of the atoms make the cavity field be in a two-mode superpositions of coherent states.     

Generation of pair cat states through two-mode degenerate Raman process

We propose a scheme for generating superpositions of two pair coherent states of a two-mode field. In the scheme an atom is sent through a cavity initially in a pair coherent state. The state-selective measurement following the two-mode Raman process projects the two-mode field to a pair cat state.     

双模激发压缩真空态的维格纳函数

利用纠缠态表象下的维格纳(Wigner)算符,构造了双模激发压缩真空态的维格纳函数,并根据该函数在相空间ρ-γ中随参量m,n和r的变化关系,讨论了双模激发压缩真空态的量子干涉特性和压缩效应。结果表明,对于参量m,n不同的取值,双模激发压缩真空态的量子干涉效应的强弱不同;而对于不同的压缩参量r,双模激发压缩真空态呈现出不同程度的压缩效应。最后,根据双模激发压缩真空态的维格纳函数的边缘分布,阐明了此维格纳函数的物理意义。     

Emission Spectrum of Two Atoms in Two-mode Multiphoton Raman Coupled Model

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Efficient scheme for the preparation of arbitrary anticorrelated states of a two-mode field

A scheme is presented for generating any anticorrelated state of a two-mode field. In the scheme a sequence of suitably prepared three-level V-type atoms are sent across a two-mode cavity initially in the vacuum state. The detection of all the atoms in the ground state collapses the two-mode field to the desired state.