Geometry and dynamics of squeezing in finite systems

Squeezing and its inverse magnification form a one-parameter group of linear canonical transformations of continuous signals in paraxial optics. We search for corresponding unitary matrices to apply on signal vectors in N-point finite Hamiltonian systems. The analysis is extended to the phase space representation by means of Wigner quasi-probability distribution functions on the discrete torus and on the sphere. Together with two previous studies of the fractional Fourier and Fresnel transforms, we complete the finite counterparts of the group of linear canonical transformations.     

The Statistical Properties of a Generalized Two-mode Squeezed Operator

Abstract

In this paper we have employed the generalized two-mode squeeze operator to discuss the effect of squeezing on two-mode coherent states, number states and thermal states. By using the Glauber second-order correlation function we examined the statistical properties of these various squeezed states. The statistical investigations are carried out for the quasi-probability distribution functions (Wigner function and Q function). The P representation is also considered.     

Excited atomic coherent states

Abstract

The excited atomic coherent (EAC) states are introduced and some of their statistical properties are discussed. When the Holstein-Primakoff transformations are used then these states become intermediate states interpolating between Fock and displaced Fock states. A generation scheme is discussed. The quasi-probability distribution functions (QDF) for these states are investigated. The Pegg-Barnett phase distribution of these states is studied.     

X-ray imaging: a generalized approach using phase-space tomography

We discuss the role of coherence in x-ray imaging and consider how phase-space tomography can be used to extract information about partial coherence. We describe the application of phase-space tomography to x-ray imaging and recover the spatial coherence properties of a one-dimensional soft (1.5 keV) x-ray beam from a synchrotron undulator source. We present phase-space information from a Young's experiment and observe negative regions in the quasi-probability distribution. We show that, given knowledge of the coherence of the beam, we can use partially coherent diffraction data to recover fully coherent information, and we present some simple experimental demonstrations of this capability.     

Fractional Fourier transforms in two dimensions

We analyze the fractionalization of the Fourier transform (FT), starting from the minimal premise that repeated application of the fractional Fourier transform (FrFT) a sufficient number of times should give back the FT. There is a qualitative increase in the richness of the solution manifold, from U(1) (the circle S1) in the one-dimensional case to U(2) (the four-parameter group of 2 x 2 unitary matrices) in the two-dimensional case [rather than simply U(1) x U(1)]. Our treatment clarifies the situation in the N-dimensional case. The parameterization of this manifold (a fiber bundle) is accomplished through two powers running over the torus T2 = S1 x S1 and two parameters running over the Fourier sphere S2. We detail the spectral representation of the FrFT: The eigenvalues are shown to depend only on the T2 coordinates; the eigenfunctions, only on the S2 coordinates. FrFT's corresponding to special points on the Fourier sphere have for eigenfunctions the Hermite-Gaussian beams and the Laguerre-Gaussian beams, while those corresponding to generic points are SU(2)-coherent states of these beams. Thus the integral transform produced by every Sp(4, R) first-order system is essentially a FrFT.     

Statistical Properties of a New Squeezed Operator Model

Abstract

We introduce a new squeezed operator which is a combination of the two-mode squeezed operator and the two single photon squeezed operator. Here we study the effects of this operator on the photon number sum and difference. The squeezing in the frequency converter model has been examined, and statistical investigations are carried out for the quasi-probability distribution functions (Wigner function and Q-function). An application to the parametric amplifier is given.     

SU(2) and SU(1,1) Rotation Transformation and Pseudo-vector Model in Quantum Optics

Abstract

We construct a pseudo-vector model and realize the rotation transformation for the SU(2) and SU(1,1) dynamics. We introduce concepts of the pseudo-scalar and the scalar product in quantum optics. Several equivalents of the SU(2) and SU(1,1) unified rotation operator are given. By using this method, the two- and three-level Jaynes-Cummings model is discussed in the non-rotating wave approximation.     

Quantum Phase in Nanoscopic Superconductors

Using the pseudospin representation and the SU(2) phase operators we introduce a complex parameter to characterize both infinite and finite superconducting systems. While in the bulk limit the parameter becomes identical to the conventional order parameter, in the nanoscopic limit its modulus reduces to the number parity effect parameter and its phase takes discrete values. We evaluate the Josephson coupling energy and show that in bulk superconductor it reproduces the conventional expression and in the nanoscopic limit it leads to quantized Josephson effect. Finally, we study the phase flow or dual Josephson effect in a superconductor with fixed number of electrons.     

Rotation and gyration of finite two-dimensional modes

Hermite-Gauss and Laguerre-Gauss modes of a continuous optical field in two dimensions can be obtained from each other through paraxial optical setups that produce rotations in (four-dimensional) phase space. These transformations build the SU(2) Fourier group that is represented by rigid rotations of the Poincaré sphere. In finite systems, where the emitters and the sensors are in NxN square pixellated arrays, one defines corresponding finite orthonormal and complete sets of two-dimensional Kravchuk modes. Through the importation of symmetry from the continuous case, the transformations of the Fourier group are applied on the finite modes.     

SU(1, 1) and SU(2) Squeezing in Trilinear Optical Processes

Abstract

The squeezing properties in terms of SU(1, 1) and SU(2) operators for the case of trilinear processes are studied. The initial state of the system is supposed to be a coherent state in one of the modes and number states in the remaining modes. It is pointed out that in several cases a considerable amount of squeezing can be achieved. Due to the common mathematical structure the case of a two-mode coupler with intensity dependent coupling is also analysed.     

Emergence of Pairing Interaction in the Hubbard Model in the Strong Coupling Limit

We implement the rotationally-invariant formulation of the two-dimensional Hubbard model, with nearest-neighbors hopping t, which allows for the analytic study of the system in the low-energy limit. Both U(1) and SU(2) gauge transformations are used to factorize the charge and spin contribution to the original electron operator in terms of the corresponding gauge fields. The Hubbard Coulomb energy U-term is then expressed in terms of quantum phase variables conjugate to the local charge and variable spin quantization axis, providing a useful representation of strongly correlated systems. It is shown that these gauge fields play a similar role as phonons in the BCS theory: they act as the “glue” for fermion pairing. By tracing out gauge degrees of freedom the form of paired states is established and the strength of the pairing potential is determined. It is found that the attractive pairing potential in the effective low-energy fermionic action is non-zero in a rather narrow range of U/t.     

Study of Hole Pair Condensation based on the SU(2) Slave-Boson Approach to the t-J Hamiltonian; Temperature, Momentum and Doping Dependences of Spectral Functions

Based on the U(1) and SU(2) slave-boson approaches to the t-J Hamil-tonian, we evaluate the one electron spectral functions for the hole doped high T _c cuprates for comparison with the angle resolved photoemission spectroscopy(ARPES) data. We find that the observed quasiparticle peak in the superconducting state is correlated with the hump which exists in the normal state. We find that the spectral weight of the quasiparticle peak increases as doping rate increases, which is consistent with observation. As a conse-quence of the phase fluctuation effects of the spinon and holon pairing order parameters the spectral weight of the predicted peak obtained from the SU(2) theory is found to be smaller than the one predicted from U(1) mean field theory.     

Interaction of a System of Initially Unexcited Two-level Atoms with a Weak Cavity Field

Abstract

Using a perturbation method, constructed in terms of SU(2) group representations, the interaction of N initially unexcited two-level atoms and a weak single-mode cavity field is studied. The field is assumed to be initially either in a Fock state with a number of photons equal to n or in a coherent state. In the case of the photon-number state with n  3, the pure phenomenon of collective collapses and revivals manifests itself. For the initially coherent field the phenomenon of collapses and revivals arising from the photon number distribution mechanism is additionally modulated by this collective mechanism. The problem of the interaction of excited atoms with an initially coherent field has already been solved numerically by Barnett and Knight. For n=1 2 and 3 the approximate solution is compared with the exact solutions also given in this paper and the limit of applicability of our approach is established.     

Generalized Wigner distributions,moments and conditional correspondence rules

Methods are presented to generate conditional moments for all quasi-probability distributions, and explicit expressions for all conditional moments are given. In analogy to the generalized characteristic function operator, which generates all joint quasi-distribution functions, the conditional characteristic function operator which generates all conditional quasi-distributions is defined. This allows one to introduce the concept of conditional correspondence rules; formulations are given for all such rules.     

Quantum Dynamics of a Nonlinear Birefringent Model with Anticorrelated Field States

Abstract

In this paper, anticorrelated field states with a binomial distribution over orthogonal polarizations, interacting with a nonlinear birefringent medium, are discussed. The field states are the SU(2) coherent states, where the angular momentum operators are realized as bilinear products of the boson operators associated with the two polarizations. The system discussed here provides an optical realization of a nonlinear rotator. We study the quantum dynamics of the statistical properties of the field and the evolution of the degree of polarization.     

Dihedral representations and statistical geometric optics. I. Spherocylindrical lenses

The linear 2-dim irreducible representations of the dihedral groups (Dn) are interpreted as classical linear operators of geometrical optics. It is shown that the 2-dim irreducible representation of D4 is simply the refractive group described by Campbell [Optom. Vision Sci. 74, 381 (1997)]. The dihedral Fourier-inverse mechanism is introduced and shown to provide a systematic connection between the standard refractive data and their vector space representation, as proposed by Thibos et al. [Vision Sci. Appl. 2, 14 (1994)].     

SU(1,1) Squeezing of SU(1,1) Generalized Coherent States

Abstract

In this paper we have introduced a new class of the SU(1,1) coherent states which are the eigenstates of the generalized annihilation operator K_. We have also studied the SU(1,1) squeezing of the SU(1,1) generalized coherent states interacting with a nonlinear medium modelled as an anharmonic oscillator.     

高温多元醇法制备超顺磁CoFe2O4纳米颗粒磁共振造影剂

以FeCl₃·6H₂O、CoCl₂·6H₂O和HOOC-PEG-COOH为反应物, 利用高温多元醇法制备了核心粒径为5~10nm的超顺磁CoFe₂O₄纳米颗粒, 样品在水溶液中具有良好分散性. 通过改变修饰剂的种类和用量、反应温度及反应时间可以对纳米颗粒的尺寸、水中分散性及磁性能产生影响. 研究表明：选用带有强极性基团的修饰剂, 增加修饰剂的用量, 提高反应温度和延长反应时间, 可以增大颗粒的尺寸, 改善颗粒的分散性, 窄化粒径分布. 实验获得的最佳生长条件为：金属盐总量与修饰剂质量比为1∶10, 在210~220℃之间反应2h. 磁性能研究表明所得样品在室温下具有超顺磁性, 其饱和磁化强度与尺寸有关.     

基于DILL模型的SU8厚胶曝光仿真

基于DILL经典曝光模型,对其分别在深度轴和时间轴上进行扩展:在深度轴上,以基尔霍夫衍射公式为基础,引入复折射率,利用光束传输法的思想计算了某曝光时刻下胶体内部的光场分布;在时间轴上,分析SU8光刻胶的特点及曝光反应过程,建立合适的光交联反应动力学模型,计算不同曝光时刻下的光场分布,通过整个曝光模型的建立,最终给出一定曝光时间后的光场分布;结果表明,在曝光阶段,胶内深层光场整体分布随时间变化不大,曝光时间对曝光阶段光场分布的影响较小,这种影响将在后烘阶段得以放大.     

Fabrication of Hierarchical Pillar Arrays from Thermoplastic and Photosensitive SU‐8

By exploiting the thermoplastic and photosensitive nature of SU‐8 photoresists, different types of hierarchical pillar arrays with variable aspect ratios are fabricated through capillary force lithography (CFL), followed by photopatterning. The thermoplastic nature of SU‐8 enables the imprinting of micropillar arrays with variable aspect ratios by CFL using a single poly(dimethylsiloxane) mold, simply by tuning the initial film thickness of SU‐8 on a substrate. The pillar array is subsequently photopatterned through a photomask, followed by post‐exposure baking above the glass transition temperature (T_g) of SU‐8. The pillars in the exposed region become highly crosslinked and, therefore, neither soluble nor able to reflow above T_g, whereas the pillars in the unexposed regions can reflow and flatten out. Two developing strategies are investigated after UV exposure of the SU‐8 pillar arrays including i) solvent development and drying and ii) thermal reflow to create bilevel hierarchical structures with short pillars and single‐level, dual‐scaled, high‐aspect‐ratio (up to 7.7) pillars in a microdot array, respectively.