A new theorem relating quantum tomogram to the Fresnel operator

According to Fan-Hu's formalism (Fan Hong-Yi and Hu Li-Yun 2009 Opt. Commun. bf282 3734) that the tomogram of quantum states can be considered as the module-square of the state wave function in the intermediate coordinate-momentum representation which is just the eigenvector of the Fresnel quadrature phase, we derive a new theorem for calculating quantum tomogram of density operator, i.e., the tomogram of a density operator ρ is equal to the marginal integration of the classical Weyl correspondence function of F⁺ρF, where F is the Fresnel operator. Applications of this theorem to evaluating the tomogram of optical chaotic field and squeezed chaotic optical field are presented.     

The two-mode quantum Fresnel operator and the multiplication rule of 2D Collins diffraction formula

By using the two-mode Fresnel operator we derive a multiplication rule of two-dimensional (2D) Collins diffraction formula, the inverse of 2D Collins diffraction integration can also be conveniently derived in this way in the context of quantum optics theory.     

经典菲涅耳变换的量子力学对应

介绍经典菲涅耳变换的量子力学对应,它是相干态在相空间中的代表点做辛运动所对应的量子菲涅耳算符.     

New transformation of Wigner operator in phase space quantum mechanics for the two-mode entangled case

As a natural and important extension of Fan's paper (Fan Hong-Yi 2010 Chin. Phys. B 19 040305) by employing the formula of operators' Weyl ordering expansion and the bipartite entangled state representation this paper finds a new two-fold complex integration transformation about the Wigner operator Δ ( μ,v ) (in its entangled form) in phase space quantum mechanics, and its inverse transformation. In this way, some operator ordering problems regarding to ( a₁⁺-a₂) and (a₁+a₂⁺) can be solved and the contents of phase space quantum mechanics can be enriched, where a_i,a_i⁺ are bosonic creation and annihilation operators, respectively.     

Weyl Ordering Operator Formula Derived by IWOP Technique and Its Application for Fresnel Operator

Based on the technique of integration within an ordered product of operators, the Weyl ordering operator formula is derived and the Fresnel operators＇ Weyl ordering is also obtained, which together with the Weyl transformation can immediately lead to Eresnel transformation kernel in classical optics.     

Weyl Ordering Operator Formula Derived by IWOP Technique and ItsApplication for Fresnel Operator

Based on the technique of integration within an ordered product ofoperators, the Weyl ordering operator formula is derived and the Fresneloperators' Weyl ordering is also obtained, which together with the Weyltransformation can immediately lead to Fresnel transformation kernel inclassical optics.     

Quantum optical ABCD theorem in two-mode case

By introducing the entangled Fresnel operator （EFO） this paper demonstrates that there exists ABCD theorem for two-mode entangled case in quantum optics. The canonical operator method as mapping of ray-transfer ABCD matrix is explicitly shown by EFO＇s normally ordered expansion through the coherent state representation and the technique of integration within an ordered product of operators.     

New decomposition of the Fresnel operator corresponding to the optical transformation in AB CD-systems

By virtue of the coherent state representation of the newly introduced Fresnel operator and its group product property we obtain new decomposition of the Fresnel operator as the product of the quadratic phase operator, the squeezing operator, and the fractional Fourier transformation operator, which in turn sheds light on the matrix optics design of ABCD-systems The new decomposition for the two-mode Fresnel operator is also obtained by the use of entangled state representation.     

Evolution of a two-mode squeezed vacuum for amplitude decay via continuous-variable entangled state approach

Extending the recent work completed by Fan et al. [Front. Phys. 9(1), 74 (2014)] to a two-mode case, we investigate how a two-mode squeezed vacuum evolves when it undergoes a two-mode amplitude dissipative channel, with the same decay rate κ, using the continuous-variable entangled state approach. Our analytical results show that the initial pure-squeezed vacuum state evolves into a definite mixed state with entanglement and squeezing, decaying over time as a result of amplitude decay. We also investigate the time evolutions of the photon number distribution, the Wigner function, and the optical tomogram in this channel. Our results indicate that the evolved photon number distribution is related to Jacobi polynomials, the Wigner function has a standard Gaussian distribution (corresponding to the vacuum) at long periods, losing its nonclassicality due to amplitude decay, and a larger squeezing leads to a longer decay time.     

基于双模相干-纠缠态表象的算符恒等式构造法

利用最近引进的相干-纠缠态|x,α〉表象和有序算符内的积分技术,给出了关于双模光场正交分量（X₁+X₂）/2^1/2和参数化的正交分量（μX₁+νX₂）/λ的函数的若干正规乘积展开式,这对于研究场的高阶压缩行为和构建广义压缩态是有用的. 关键词： 双模相干-纠缠态 算符恒等式 有序算符内的积分技术     

New equation for deriving pure state density operators by Weyl correspondence and Wigner operator

By virtue of the completeness of Wigner operator and Weyl correspondence we construct a general equation for deriving pure state density operators. Several important examples are considered as the applications of this equation, which shows that our approach is effective and convenient for deducing these entangled state representations.     

Optical complex integration-transform for deriving complex fractional squeezing operator

We find a new complex integration-transform which can establish a new relationship between a two-mode operator's matrix element in the entangled state representation and its Wigner function. This integration keeps modulus invariant and therefore invertible. Based on this and the Weyl–Wigner correspondence theory, we find a two-mode operator which is responsible for complex fractional squeezing transformation. The entangled state representation and the Weyl ordering form of the two-mode Wigner operator are fully used in our derivation which brings convenience.     

Bell态原子与双模纠缠相干光场相互作用的纠缠特性

运用Negativity熵研究了Bell态原子与双模纠缠相干光场相互作用系统中两个全同二能级原子之间的纠缠演化特性.分析了光场强度、光场纠缠度及原子间相互作用强度对纠缠的影响.结果表明:原子处于|β11〉时,两原子始终处于最大纠缠态;原子处于|β00〉时,初始纠缠的两原子始终较长时间处于退纠缠状态;原子处在|β10〉时,增大双模光场的平均光子数可以明显增大两原子之间的纠缠度并保持较大的纠缠状态;原子初态处在|β01〉时,原子间的相互作用强度对双原子间纠缠度有较显著的非线性调制作用.     

Bell态原子与双模纠缠相干光场相互作用的场熵演化特性

运用全量子理论研究了初始处于Bell态(对称迭加态或反对称态)的两原子与双模纠缠相干光场相互作用系统中场熵的演化特性. 分析了光场强度、光场纠缠度及原子间相互作用强度对场熵演化特性的影响. 结果表明：原子初态处于反对称态时,场熵始终为零;原子初态处在对称迭加态时,增大光场强度场熵的时间演化曲线逐渐变成较规则的振荡曲线,原子间的相互作用强度对双原子间纠缠度有显著的非线性调制作用.     

Bell态原子与双模纠缠相干光场相互作用的场熵演化特性

运用全量子理论研究了初始处于Bell态(对称迭加态或反对称态)的两原子与双模纠缠相干光场相互作用系统中场熵的演化特性. 分析了光场强度、光场纠缠度及原子间相互作用强度对场熵演化特性的影响. 结果表明：原子初态处于反对称态时,场熵始终为零;原子初态处在对称迭加态时,增大光场强度场熵的时间演化曲线逐渐变成较规则的振荡曲线,原子间的相互作用强度对双原子间纠缠度有显著的非线性调制作用.     

Bell态原子与双模纠缠相干光场相互作用的场熵演化特性

运用全量子理论研究了初始处于Bell态(对称迭加态或反对称态)的两原子与双模纠缠相干光场相互作用系统中场熵的演化特性. 分析了光场强度、光场纠缠度及原子间相互作用强度对场熵演化特性的影响. 结果表明：原子初态处于反对称态时,场熵始终为零;原子初态处在对称迭加态时,增大光场强度场熵的时间演化曲线逐渐变成较规则的振荡曲线,原子间的相互作用强度对双原子间纠缠度有显著的非线性调制作用.     

Time Evolution Caused by Hamiltonian Composed of Quadratic Combination of Canonical Operators and Time-Dependent Two-Mode Fresnel Operator

We show that the time-dependent two-mode Fresnel operator is just the time-evolutional unitary operator governed by the Hamiltonian composed of quadratic combination of canonical operators in the way of exhibiting SU（1,1） algebra. This is an approach for obtaining the time-dependent Hamiltonian from the preassigned time evolution in classical phase space, an approach which is in contrast to Lewis-Riesenfeld＇s invariant operator theory of treating timedependent harmonic oscillators.     

Bell态原子与双模纠缠相干光场相互作用的场熵演化特性

运用全量子理论研究了初始处于Bell态(对称迭加态或反对称态)的两原子与双模纠缠相干光场相互作用系统中场熵的演化特性. 分析了光场强度、光场纠缠度及原子间相互作用强度对场熵演化特性的影响. 结果表明：原子初态处于反对称态时,场熵始终为零;原子初态处在对称迭加态时,增大光场强度场熵的时间演化曲线逐渐变成较规则的振荡曲线,原子间的相互作用强度对双原子间纠缠度有显著的非线性调制作用.     

Bell态原子与双模纠缠相干光场相互作用的场熵演化特性

运用全量子理论研究了初始处于Bell态(对称迭加态或反对称态)的两原子与双模纠缠相干光场相互作用系统中场熵的演化特性. 分析了光场强度、光场纠缠度及原子间相互作用强度对场熵演化特性的影响. 结果表明：原子初态处于反对称态时,场熵始终为零;原子初态处在对称迭加态时,增大光场强度场熵的时间演化曲线逐渐变成较规则的振荡曲线,原子间的相互作用强度对双原子间纠缠度有显著的非线性调制作用.     

Bell态原子与双模纠缠相干光场相互作用的场熵演化特性

运用全量子理论研究了初始处于Bell态(对称迭加态或反对称态)的两原子与双模纠缠相干光场相互作用系统中场熵的演化特性. 分析了光场强度、光场纠缠度及原子间相互作用强度对场熵演化特性的影响. 结果表明：原子初态处于反对称态时,场熵始终为零;原子初态处在对称迭加态时,增大光场强度场熵的时间演化曲线逐渐变成较规则的振荡曲线,原子间的相互作用强度对双原子间纠缠度有显著的非线性调制作用.