Entanglement in Coupled Mesoscopic Circuits

A common two-mode squeezed state is one of the most important resources in quantum information processing of continuous variables. In this paper, a two-mode squeezed rotation-entangled state is obtained in coupled mesoscopic circuits. It is shown that instantaneously switching on the external sources may result in a two-mode squeezed state of the system, which actually arises from the coupling effect. The entanglement of the squeezed rotation-entangled state is studied. The degree of entanglement for coupled mesoscoipc circuit was calculated by using the technique of integration within an ordered product of operators. It is shown that the entanglement of the two-mode squeezed rotation-entangled state is different from that of the common squeezed state, for example, the degree of entanglement of the system, which is in the squeezed state, exist maximum value at a very low temperature.     

含时耦合谐振子系统的时间演化与双模压缩态

运用Lewis Riesenfeld不变量理论,通过适当地选取厄米不变量,得到了含驱动项和双模耦合项的含时耦合谐振子系统薛定谔方程的封闭解,给出了系统的演化算符及其产生双模光场的压缩态的条件,并得出系统压缩态的量子涨落与驱动项无关但与系统所处的初态有关的结论. 关键词： 含时耦合谐振子系统 Lewis Riesenfeld不变量理论 双模压缩态     

Time Evolution and Squeezing of Degenerate and Non-degenerate Coupled Parametric Down-Conversion with Driving Term

By properly selecting the time-dependent unitary transformation for the linear combination of the number operators, we construct a time-dependent invariant and derive the corresponding auxiliary equations for the degenerate and non-degenerate coupled parametric down-conversion system with driving term. By means of this invariant and the Lewis-Riesenfeld quantum invariant theory, we obtain closed formulae of the quantum state and the evolution operator of the system. We show that the time evolution of the quantum system directly leads to production of various generalized one- and two-mode combination squeezed states, and the squeezed effect is independent of the driving term of the Hamiltonian. In somespecial cases, the current solution can reduce to the results of the previous works.     

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.     

Two-mode squeezed vacuum states in tomographic-probability representation

The two-mode quantum electromagnetic field in the vacuum squeezed state is considered in the tomographic-probability representation. The symplectic, center-of-mass, and photon-number tomograms for the two-mode vacuum squeezed state are obtained explicitly. The expressions for photon statistics of the squeezed light are reconsidered using the state tomograms, and some new integral relations are found for one and multimode orthogonal polynomials.     

A FULL QUANTUM THEORY OF THE THREE-MODE INTERACTIONS INSIDE AN OPO CAVITY

A full quantum treatment about the process of parametric down-conversion with frequency degenerate but polarization pon-degenerate in an optical parametric oscillator (OPO) cavity is presented. Using the linearized Langevin equations and spectral matrix, we calculated the squeezing spectra of the coupled mode in the output field. The squeezing as a function of driving field and detection frequency is obtained. The resuits obtained, which are compared with those found semiclassically by Reynaud et al., indicate that it is possible to generate a two-mode coherent squeezed state with large amplitude. The quantum correlation between the signal and the idler modes is also discussed. It is shown that there is an inseparable relationship between the two-mode squeezing and the intermode quantum correlation.     

Fast Generation of Einstein–Podolsky–Rosen States for Two Cavity Modes with a Collection of Driven Atoms

We propose an efficient scheme for realizing two-mode squeezing for two cavity modes with an atomic ensemble trapped in the cavity and driven by two classical fields. Through a suitable choice of the driving classical fields, the evolution dynamics of the two cavity modes is decoupled with the atomic system and described by a two-mode squeezing operator. We show that a highly squeezed state can be obtained at the output even with a bad cavity. The required experimental techniques are within the scope of what can be obtained in the BEG-cavity setup.     

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。     

原子间相互作用对V型三能级原子激光压缩性质的影响

研究了V型三能级原子玻色-爱因斯坦凝聚体与双模压缩相干态光场相互作用系统中原子激光的两个正交分量的压缩性质,并与三型三能级原子玻色-爱因斯坦凝聚体和双摸压缩相干态相互作用系中原子激光的压缩作了比较.结果表明:压缩相干态光场的初始压缩因子和凝聚体中原子间的相互作用强度对原子激光的两个正交分量的压缩有明显的影响,随光场压缩因子增大原子激光的压缩深度增加,而随原子间相互作用变强,对原子激光的正交分量的压缩的影响变浅.     

Experimental measurement of covariance matrix of two-mode entangled state

A two-mode entangled state was generated experimentally through mixing two squeezed lights from two optical parametric amplifiers on a 50/50 beam splitter.The entangled beams were measured by means of two pairs of balanced homodyne detection systems respectively.The relative phases between the local beams and the detected beams can be locked by using the optical phase modulation technique.The covariance matrix of the two-mode entangled state was obtained when the relative phase of the local beam and the detected beam in one homodyne detection system is locked and the other is scanned.This method provides a way by which one can extract the covariance matrix of any selected quadrature components of two-mode Gaussian state.     

Photon-number distribution of two-mode squeezed thermal states by entangled state representation

Using the entangled state representation, we convert a two-mode squeezed number state to a Hermite polynomial excited squeezed vacuum state. We first analytically derive the photon number distribution of the two-mode squeezed thermal states. It is found that it is a Jacobi polynomial; a remarkable result. This result can be directly applied to obtaining the photon number distribution of non-Gaussian states generated by subtracting from (adding to) two-mode squeezed thermal states.     

Entanglement dynamics for a solid polariton system at zero and finite temperatures

The dynamics of the entanglement for a solid polariton system is investigated. The polariton system is a photon-phonon complex and its time-dependent characteristic function in the Wigner representation for the system is obtained analytically. It is found that when the photon field is initially prepared in the squeezed vacuum state, and the phonon in the thermal state, the polariton system can evolve into a two-mode Gaussian mixed state. The entanglement between photon and phonon turns out to be apparently dependent on the squeezing parameter and exhibits a critical behavior with respect to the temperature.     

纠缠微波信号的特性及表示方法

纠缠微波信号是电磁场微波频段量子特性的体现.在总结了现有纠缠微波信号产生及验证实验的基础上,针对目前没有统一的表达式来描述纠缠微波信号格式的问题,通过深入分析纠缠微波信号的特性,提出了两种纠缠微波信号的表示方法.一种是在量子框架下,利用双模压缩真空态表示,并分别在光子数表象下和Wigner分布下分析了其信号特征,刻画了正交分量之间的正反关联特性;另一种是在经典框架下,利用关联随机信号表示,刻画了测量后纠缠微波信号场幅度正交分量随时间变化的波形图.两种表示恰当合理地反映了纠缠微波信号连续变量纠缠的特性.     

Optical enhanced interferometry with two-mode squeezed twin-Fock states and parity detection

We theoretically investigate the quantum enhanced metrology using two-mode squeezed twin-Fock states and parity detection. Our results indicate that, for a given initial squeezing parameter, compared with the two-mode squeezed vacuum state, both phase sensitivity and resolution can be enhanced when the two-mode squeezed twin-Fock state is considered as an input state of a Mach–Zehnder interferometer. Within a constraint on the total photon number, although the two-mode squeezed vacuum state gives the better phase sensitivity when the phase shift φ to be estimated approaches to zero, the phase sensitivity offered by these non-Gaussian entangled Gaussian states is relatively stable with respect to the phase shift itself. When the phase shift slightly deviates from φ= 0, the phase sensitivity can be still enhanced by the two-mode squeezed twin-Fock state over a broad range of the total mean photon number where the phase uncertainty is still below the quantum standard noise limit. Finally, we numerically prove that the quantum Cramer–Rao bound can be approached with the parity detection.     

单双模连续压缩真空态及其量子统计性质

利用有序算符内的积分技术研究了通过双模压缩算符作用于两个单模压缩 态上得到的单双模 连续压缩态. 导出了单双模连续压缩算 符的正规乘积形式, 并在此基础上研究了单双模连续压缩真空态的量子统计性质. 特别是利用Weyl编 序算符在相似变换 下的不变性, 简洁地导出了单双模连续 压缩真空态的Wigner函数. 最后, 还简单地提出 了单双模连续压缩 真空态的实验产生方案.     

Two-mode squeezing in a coherently driven degenerate parametric down conversion

Squeezing properties of a two-mode radiation produced by a process of driven degenerate parametric down conversion, when the cavity is coupled to two independent squeezed vacuum reservoirs employing the linearization procedure, are analyzed. The two-mode cavity and output radiations exhibit considerable squeezing even when the oscillator is coupled to a vacuum reservoir. One of the effects of coupling the cavity to the squeezed vacuum reservoirs is to increase the degree of squeezing exponentially. For the output radiation the correlation of the quadrature operators evaluated at different times also contributes to the squeezing, which is the reason for quenching of the overall noise in one of the quadrature components of the fundamental mode.     

Engineering two-mode squeezed states of cold atomic clouds with a superconducting stripline resonator

A scheme is proposed for engineering two-mode squeezed states of two separated cold atomic clouds positioned near the surface of a superconducting stripline resonator. Based on the coherent magnetic coupling between the atomic spins and a stripline resonator mode, the desired two-mode squeezed state can be produced via precisely control on the dynamics of the system. This scheme may be used to realize scalable on-chip quantum networks with cold atoms coupling to stripline resonators.     

Single-mode quadrature-amplitude measurement for generalized two-mode squeezed states studied by virtue of the entangled state representation

The result of one-mode quadrature-amplitude measurement for some generalized two-mode squeezed states has been studied by virtue of the entangled state representation of the corresponding two-mode squeezing operators. We find that the remaining field-mode simultaneously collapses to the single-mode squeezed state with more stronger squeezing. The measurement result caused by a single-mode squeezed state projector is also calculated, which indicates quantum entanglement in squeezing.     

Preparation of Squeezed State and Entanglement State Between VibrationalMotion of Trapped Ion and Light

Several schemes have been proposed to prepare two-mode squeezed state and entanglement state between motional states of a single trapped ion and light. Preparation of two-mode squeezed state is based on interaction of a trapped ion located in light cavity with cavity field. Preparation of entanglement state is based on interaction of a trapped ion located in light cavity with cavity field and a traveling wave light field.     

Statistical properties of photon-added and photon-subtracted two-mode squeezed vacuum state

We introduce photon-added and photon-subtracted two-mode squeezed vacuum states and examine the quantum statistical properties of these states by analytic calculating. Because of the entanglement between the modes of the field in a two-mode squeezed state, photon adding (or subtracting) for one of the modes results in interesting outcome.