在与原子相互作用中光偏振态的量子描述及其演化

应用偏振光的量子理论和斯托克斯算符研究了无克尔媒质和存在克尔媒质情况下，光在与原子相互作用过程中偏振态的演化.研究了偏振光中斯托克斯参量的涨落及其压缩的非经典行为.偏振椭圆、量子光学中的偏振度和斯托克斯参量的信噪比也得到了讨论.结果表明斯托克斯参量及其涨落在时间演化中呈现出被调制的振荡，这些振荡表现出间歇地崩塌和恢复.在与原子的相互作用过程中，光的偏振椭圆不随时间变化，但偏振度却随时间出现振荡.克尔媒质对这些振荡演化有很大影响. 关键词： 斯托克斯算符 斯托克斯参量 量子偏振态 量子涨落     

Degree of polarization for single-photon beam in a turbulent atmosphere

The polarization fluctuations of single-photon beam propagation through the slant path turbulent atmosphere are studied. The Stokes operators and the degree of polarization of single-photon beam in a turbulent atmosphere are obtained. It is shown by analytical calculations, that the quantum degree of polarization of linearly polarization light is a decrease function of the atmospheric turbulence strength and the propagation distance for lower detection photon number.     

Optical experiments beyond the quantum limit: Squeezing,entanglement, and teleportation

Results of experiments recently performed are reported, in which two optical parametric amplifiers were set up to generate two independently quadrature squeezed continuous wave laser beams. The transformation of quadrature squeezed states into polarization squeezed states and into states with spatial quantum correlations is demonstrated. By utilizing two squeezed laser beams, a polarization squeezed state exhibiting three simultaneously squeezed Stokes operator variances was generated. Continuous variable polarization entanglement was generated and the Einstein-Podolsky-Rosen paradox was observed. A pair of Stokes operators satisfied both the inseparability criterion and the conditional variance criterion. Values of 0.49 and 0.77, respectively, were observed, with entanglement requiring values below unity. The inseparability measure of the observed quadrature entanglement was 0.44. This value is sufficient for a demonstration of quantum teleportation, which is the next experimental goal of the authors.     

多个量子节点确定性纠缠的建立

量子纠缠是一种重要的量子资源,在多个空间分离的量子存储器间建立确定性的量子纠缠,然后在用户控制的时刻将所存储的量子纠缠转移到量子信道中进行信息的分发和传送,这对于实现量子信息网络是至关重要的.本文介绍了用光学参量放大器制备与铷原子D1吸收线对应的非经典光场,而且在三个空间分离的原子系综中确定性量子纠缠的产生、存储和转移.利用电磁感应透明光和原子相互作用的原理,将制备的多组分光场纠缠态模式映射到三个远距离的原子系综以建立原子自旋波之间的纠缠.然后,存储在原子系综中的纠缠态通过三个量子通道,纠缠态的量子噪声被转移到三束空间分离的正交纠缠光场.三束释放的光场间纠缠的存在验证了该系统具有保持多组分纠缠的能力.这个方案实现了三个量子节点间的纠缠,并且可以直接扩展到具有更多节点的量子网络,为未来实现大型量子网络通信奠定了基础.     

Quantum measurements of the parameters of the Gell-Mann optical field with an SU(3) interferometer

The SU(3) polarization theory in the Hilbert space is developed for quantum Bose systems with Gell-Mann symmetry. The degrees of polarization and isopolarization are determined. An original SU(3) interferometer for measuring the phase-dependent Gell-Mann parameters of an optical field is considered, and the signal-to-noise measurements limiting in quantum noises and based on the use of entangled and squeezed states of light at the entrance of the optical system are analyzed. A new type of quantum (helical) states of optical radiation for which the correlation between the Hermitian quadratures and isospin operators plays a crucial role is revealed for one of these modes in the classical-field approximation.     

A two-step quantum secure direct communication protocol with hyperentanglement

We propose a two-step quantum secure direct communication (QSDC) protocol with hyperentanglement in both the spatial-mode and the polarization degrees of freedom of photon pairs which can in principle be produced with a beta barium borate crystal. The secret message can be encoded on the photon pairs with unitary operations in these two degrees of freedom independently. This QSDC protocol has a higher capacity than the original two-step QSDC protocol as each photon pair can carry 4 bits of information. Compared with the QSDC protocol based on hyperdense coding, this QSDC protocol has the immunity to Trojan horse attack strategies with the process for determining the number of the photons in each quantum signal as it is a one-way quantum communication protocol.     

Polarization squeezing of continuous variable stokes parameters

We report the first direct experimental characterization of continuous variable quantum Stokes parameters. We generate a continuous wave light beam with more than 3 dB of simultaneous squeezing in three of the four Stokes parameters. The polarization squeezed beam is produced by mixing two quadrature squeezed beams on a polarizing beam splitter. Depending on the squeezed quadrature of these two beams the quantum uncertainty volume on the Poincaré sphere becomes a "cigarlike" or "pancakelike" ellipsoid.     

Cross-spectral purity of the Stokes parameters

We extend the concept of cross-spectral purity from the spectral density to the polarization properties of electromagnetic fields by considering the polarization Stokes parameters. We show that purity conditions similar to those in the case of electromagnetic cross-spectral purity can be derived for all the Stokes parameters. Furthermore, we introduce a situation of strict cross-spectral purity which leads to the equality of the degrees of coherence for electromagnetic fields in the space–time and space–frequency domains.     

Vector and tensor polarizations of light beams

Generalized Stokes vectors consisting of nine real parameters in terms of irreducible spherical and Cartesian tensor operators are considered to describe the 3D electromagnetic field. Vector and tensor polarization degrees are introduced to characterize the polarized beam. It is shown that the degree of a pure vector polarized light beam is less than 1, i.e., vector polarized light beam is only partially polarized. The geometrical interpretation of vector and tensor polarizations is presented.     

Macroscopic pure state of light free of polarization noise

The preparation of completely nonpolarized light is seemingly easy; an everyday example is sunlight. The task is much more difficult if light has to be in a pure quantum state, as required by most quantum-technology applications. The pure quantum states of light obtained so far are either polarized or, in rare cases, manifest hidden polarization; even if their intensities are invariant to polarization transformations, higher-order moments are not. We experimentally demonstrate the preparation of the macroscopic singlet Bell state, which is pure, is completely nonpolarized, and has no polarization noise. Simultaneous fluctuation suppression in three Stokes observables below the shot-noise limit is demonstrated, opening perspectives for noiseless polarization measurements. The state is shown to be invariant to polarization transformations. This robust highly entangled isotropic state promises to fuel important applications in photonic quantum technologies.     

Role of the null space of the DRM in the performance of modulated polarimeters

Imaging polarimeters infer the spatial distribution of the polarization state of the optical field as a function of time and/or wavelength. A polarimeter indirectly determines the polarization state by first modulating the intensity of the light field and then demodulating the measured data to infer the polarization parameters. This Letter considers passive Stokes parameter polarimeters and their inversion methods. The most widely used method is the data reduction matrix (DRM), which builds up a matrix equation that can be inverted to find the polarization state from a set of intensity measurements. An alternate strategy uses linear system formulations that allow band limited reconstruction through a filtering perspective. Here we compare these two strategies for overdetermined polarimeters and find that design of the null space of the inversion operator provides degrees of freedom to optimize the trade off between accuracy and signal-to-noise ratio. We further describe adaptive filtering techniques that could optimize the reconstruction for a particular experimental configuration. This Letter considers time-varying Stokes parameters, but the methods apply equally to polarimeters that are modulated in space or in wavelength.     

Experimental demonstration of continuous variable polarization entanglement

We report the experimental transformation of quadrature entanglement between two optical beams into continuous variable polarization entanglement. We extend the inseparability criterion proposed by Duan et al. [Phys. Rev. Lett. 84, 2722 (2000)]] to polarization states and use it to quantify the entanglement. We propose an elaboration utilizing two quadrature entangled pairs for which all three Stokes operators between a pair of beams are entangled.     

Operatorial form of the theory of polarization optical devices: I. Spectral theory of the basic devices

While the theory of operators in quantum mechanics is expressed nowadays in a pure operatorial form (wrapped mostly in Dirac's symbolic language), in optics the polarization device operators and their action are analyzed yet in the old matrix (Jones or Muller) formalism. The theory of polarization device operators has not taken systematically advantage of the very general, fundamental and deep results of the spectral theory of operators, on the basis of which it can be structured in an elegant deductive and physically expressive form. In this paper we apply the spectral theorem to the polarization device operators, we calculate their expansions in a pure operatorial Dirac-dyadic form and give some examples which illustrate the advantages from the physical insight viewpoint of such an approach. We are concerning here only with the basic polarization devices, to which correspond normal operators.     

Polarization fluctuations of partially coherent Hermite–Gaussian beams in a slant turbulent channel

The propagation of a partially coherent Hermite–Gaussian beam in a slant turbulent channel is studied. The analytical formula for the quantum degree of polarization of a partially coherent Hermite–Gaussian beam is derived based on the quantum Stokes operators and the generalized Huygens–Fresnel principle. It is shown that the zenith angle slightly affects the polarization degree of partially coherent Hermite–Gaussian beams, and the changes of polarization degree are affected by the coherence length, the detection photon-number and the ground refractive index structure parameter. Furthermore, the numerical simulations show that a partially coherent Hermite–Gaussian beam with bigger coherence length, higher photon-number level, lower beam order, shorter wavelength is less affected by the turbulence. These results indicate that one can choose the partially coherent Hermite–Gaussian beam with bigger coherence length, lower beam order, shorter wavelength, higher detection photon-number and set the size of transmitting aperture w₀$w_0$ as about 0.065 m to improve the performance of a polarization-encoded free-space quantum communication system.     

Integrability of the pairing hamiltonian

We show that a many-body Hamiltonian that corresponds to a system of fermions interacting through a pairing force is an integrable problem, i.e. it has as many constants of the motion as degrees of freedom. At the classical level this implies that the time-dependent Hartree-Fock-Bogoliubov dynamics is integrable and at the quantum level that there are conserved operators of two-body character which reduce to the number operators when the pairing strength vanishes. We display these operators explicitly and study in detail the three-level example.     

On the measurability of quantum correlation functions

The concept of correlation function is widely used in classical statistical mechanics to characterize how two or more variables depend on each other. In quantum mechanics, on the other hand, there are observables that cannot be measured at the same time; the so-called incompatible observables. This prospect imposes a limitation on the definition of a quantum analog for the correlation function in terms of a sequence of measurements. Here, based on the notion of sequential weak measurements, we circumvent this limitation by introducing a framework to measure general quantum correlation functions, in principle, independently of the state of the system and the operators involved. To illustrate, we propose an experimental configuration to obtain explicitly the quantum correlation function between two Pauli operators, in which the input state is an arbitrary mixed qubit state encoded on the polarization of photons.     

Quantum reconstruction of an intense polarization squeezed optical state

We perform a reconstruction of the polarization sector of the density matrix of an intense polarization squeezed beam starting from a complete set of Stokes measurements. By using an appropriate quasidistribution, we map this onto the Poincaré space, providing a full quantum mechanical characterization of the measured polarization state.     

Assessing the polarization of a quantum field from stokes fluctuations

We propose an operational degree of polarization in terms of the variance of the Stokes vector minimized over all the directions of the Poincaré sphere. We examine the properties of this second-order definition and carry out its experimental determination. Quantum states with the same standard (first-order) degree of polarization are correctly discriminated by this new measure. We argue that a comprehensive quantum characterization of polarization properties requires a whole hierarchy of higher-order degrees.     

分振幅型全Stokes同时偏振成像系统波片相位延迟误差分析

分振幅型全Stokes同时偏振成像仪具有实时性好、空间分辨率高、精度高等优点,有很高的应用价值.分振幅型全Stokes同时偏振成像系统利用偏振分束器、1/2波片和1/4波片将入射光Stokes矢量调制在4幅图像中,可解析入射光Stokes矢量. 1/2波片和1/4波片的相位延迟误差对Stokes矢量测量精度有着不可忽略的影响.建立了包含上述两种误差的Stokes矢量测量误差方程,分析了1/2波片和1/4波片相位延迟耦合误差对自然光、0°/45°线偏光、左旋圆偏光等典型基态入射光的Stokes矢量测量误差的影响,推导了任意偏振态的Stokes矢量测量误差的表征方法.在邦加球球面和球内选取不同偏振度的Stokes矢量作为入射光进行仿真.结果表明, Stokes矢量测量误差和偏振度测量误差均随着入射光偏振度的增大而增大.选取入射光偏振度为1时的偏振测量精度评估系统.为满足2%的偏振测量精度, 1/2波片相位延迟误差应在±1.6°内, 1/4波片相位延迟误差应在±0.5°内.这对提高系统的偏振测量精度具有重要意义,为系统设计和研制提供了重要的理论指导.     

Quantum nondemolition measurements of the phase and polarization Stokes parameters of optical fields

We propose a new method for performing continuous quantum nondemolition measurements (QNDM) of the polarization characteristics of light, the signal photon number, and the Stokes parameters of light. For devices that implement such measurements we take cubically nonlinear double-filament optical fibers with tunnel coupling of the filaments. Such a system employs a four-mode mixing of the waves (two probe modes and two signal modes). Linear optical elements needed for preliminary and subsequent conversion of the Stokes parameters are also used. We show that measurements of one Stokes parameter can be used for QNDM of the phase difference between the two initial modes. Here the accuracy of such measurements is determined by the initial fluctuations of the Stokes parameters of the probe modes and by the size of the nonlinear mode conversion coefficient in the optical fibers. Zh. éksp. Teor. Fiz. 13, 1235–1252 (April 1998)