Phase properties of coherent phase and generalized geometric states

Abstract

We examine some properties of a class of partial phase states of a single field mode. The quasiprobability distribution function and the phase properties of both the generalized geometric and even geometric states are investigated. The relation between the coherent phase states and the SU(1, 1) coherent states is sought.     

Partial phase state as a nonlinear coherent state and some of its properties

Abstract

One introduces the phase state as a nonlinear coherent state. Some of its properties, such as the sub-Poissonian statistics, the squeezing effects, the phase properties in the Pegg-Barnett formalism and the quasiprobability function of the nonlinear coherent states, are calculated and discussed in this paper. The results show that the phase states are squeezed.     

Estimation of nonclassical properties of multiphoton coherent states from optical tomograms

We have examined both single and entangled two-mode multiphoton coherent states and shown how the ‘Janus-faced’ properties between two partner states are mirrored in appropriate tomograms. Entropic squeezing, quadrature squeezing and higher-order squeezing properties for a wide range of nonclassical states are estimated directly from tomograms. We have demonstrated how squeezing properties of two-mode entangled states produced at the output port of a quantum beamsplitter are sensitive to the relative phase between the reflected and transmitted fields. This feature allows for the possibility of tuning the relative phase to enhance squeezing properties of the state. Finally, we have examined the manner in which decoherence affects squeezing and the changes in the optical tomogram of the state due to interaction with the environment.     

Construction of deformed photon-added nonlinear coherent states with negative m for the one-mode field in a Kerr medium

In this paper, based on the nonlinear coherent states formalism and using the Hamiltonian for a single mode field in a Kerr medium, the deformed photon-added nonlinear coherent states with negative m corresponding to the nonharmonic oscillators are constructed. In addition, some of the nonclassical properties associated with these states such as the Mandel parameter, quadrature squeezing and second-order correlation function are investigated. It is found that the deformed photon-added nonlinear coherent states with negative m for the one-mode field in a Kerr medium are nonclassical states.     

Conditional generation of non-classical states in a non-degenerate two-photon micromaser: Equal-intensity pair-Fock states preparation. I

Abstract

We present the theory underlying a new experimental scheme for the preparation of selected number states of a bimodal high-Q microcavity. The practical feasibility of this method is carefully discussed. In particular we take explicitly into account the existence of fluctuations of the atom–field interaction times as well as the possibility of imperfect atomic detection.     

Quantum phase measurements and non-classical polarization states of light

Abstract

In our paper we consider the non-classical behaviour of both the Hermitian (observable) Stokes parameters of light and the phase difference of two modes that describe the quantum polarization states of optical field. To characterize the degree of polarization of light we introduce a new quantity taking into account the quantum properties of different quantum states of two orthogonally polarized modes. The problem of determination of the phase difference in two modes of optical field for the quantum polarization states of light is discussed. To describe in general such a quantum field we introduce two pairs of the phase operators: the phase angles for the Stokes parameters of light in a three-dimensional picture of the Poincaré sphere. We also consider a special type of the eight-port polarization interferometer (polarimeter) for simultaneous homodyne detection of both the Stokes parameters of light and the polarization phase operators and their fluctuations as well. Using an anisotropic (spatioperiodic) Kerr-like nonlinear medium associated with the polarization interferometer we could generate and also observe the polarization-squeezed phase states of light. The fluctuations in the phase difference between two orthogonally polarized modes for these non-classical states are less than the fluctuations for light in coherent state.     

Conditional generation of non-classical states in a non-degenerate two-photon micromaser: Single-mode fock states preparation. II

Abstract

A conditional generation of single-mode Fock states in the framework of a non-degenerate two-photon micromaser theory is reported. The exact expression for the probability of success of the experiment is obtained. We show that it is possible to conjugate experimentally interesting values of this probability, with the generation of number states having a controllable high intensity. This objective is reached by constructing analytically detailed rules about the cavity state at t = 0 as well as the atom–field interaction times as functions of the available operating conditions. These rules play a central role in our Fock-state-building process, leading to an essential countering of the Stark-shift-induced detuning effects. The practical reliability of the proposal is carefully discussed from several points of view. Some possible applicative potentialities of our scheme are briefly pointed out.     

Nonclassical features of entangled coherent states

Nonclassical features of entangled coherent states (two-mode superposition coherent states) based on two coherent states shifted in phase by π/2 are discussed. Analysis of Cauchy–Schwartz inequality, two-mode quadrature squeezing, oscillatory and sub-Poissonian photon statistics show that nonclassicality exists for these states. Furthermore, it is also observed that special states have remarkably strong nonclassical properties than the entangled coherent states based on famous even–odd coherent states.     

On the nonlinear dynamics of a piezoelectrically tuned micro-resonator based on non-classical elasticity theories

Size dependent static and dynamic behavior of a fully clamped micro beam under electrostatic and piezoelectric actuations is investigated. The microbeam is modeled under the assumptions of Euler–Bernoulli beam theory. Viscous damping and nonlinearities due to electrostatic actuation and mid-plane stretching are considered. Residual stress and fringing field effect are taken into account as well. Governing equation of motion is derived using Hamilton’s principle along with the strain gradient theory (SGT), which is a non-classical continuum theory capable of taking size effect of elastic materials into account. Reduced order model of the partial differential equations of the system is obtained using Galerkin method. Static deflection, pull-in voltage and the primary resonance of the microbeam are examined and the effect of piezoelectric voltage and its polarization on the size dependent static and dynamic response is studied. It is found that the piezoelectric voltage can effectively change the flexural rigidity of the system which in turn affects the pull-in instability regime. The effect of material length scale parameter is examined by comparing the results of the SGT with the modified couple stress (MCST) and classical theory (CT), both of which are special cases of the former. Comparison demonstrates that the CT underestimates the stiffness and consequently the pull-in voltage and overestimates the amplitude of periodic solutions. The difference between the results of classical and non-classical theories becomes more and more as the dimensions of the system gets close to the length scale parameter. Non-classical theories predict more realistic behaviors for the micro system. The results of this paper can be used in designing microbeam based MEMS devices.     

A class of plane self-similar motions of a non-newtonian fluid with nonlinear thermophysical properties

The plane self-similar solution of a set of complete equations for the dynamics of a nonlinearly viscous fluid aad the energy equation is obtained analytically with the temperature dependence of the transfer coefficients taken into account.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 48, No. 1, pp. 129–136, January, 1985.     

复合材料梁的几何精确非线性建模及非经典效应

基于Hodges的广义Timoshenko梁理论对具有任意剖面形状、任意材料分布及大变形的复合材料梁进行几何精确非线性建模,采用旋转张量分解法计算梁内任意一点的应变,采用变分渐近法确定梁剖面的任意翘曲,采用平衡方程由二次渐近精确的应变能导出广义Timoshenko应变能,采用广义Hamilton原理建立梁的几何精确非线性运动方程。将所建模型用于复合材料梁的静动力分析,通过与实验数据的对比,验证了建模方法的准确性,并进一步研究了剖面翘曲及横向剪切变形非经典效应对复合材料梁的影响。研究表明,剖面翘曲对复合材料梁的静变形和固有频率有显著影响,横向剪切变形对复合材料梁的静变形和固有频率的影响与梁的长度/剖面高度比有关。     

Four-mode coherent entangled state as an entanglement of two bipartite coherent entangled states

By introducing a four-mode unitary operator U = exp[?iλ(X ₁ P ₂ + X ₂ P ₃ + X ₃ P ₄ + X ₄ P ₁)], we show how a four-mode coherent entangled state can be generated by entangling a two bipartite coherent entangled state. The corresponding squeezed vacuum state U|0000? in four-mode Fock space is derived by virtue of the technique of integration within ordered production of operators, which exhibits the standard squeezing for the four-mode quadratures. A new ideal quantum mechanical representation |α, β, γ? is constructed from U|0000? in the limit of infinite squeezing, which possesses the properties of both coherent and entangled states. The entanglement involved in |α, β, γ? is explained. A scheme for generating |α, β, γ? is presented.     

Generation of amplitude squeezed states of light from phase squeezed coherent states

Abstract

We propose a scheme to generate a displaced macroscopic superposition of phase squeezed coherent states by incorporating an optical parametric oscillator (OPO) and a nonlinear Kerr medium in a Mach-Zhender interferometer configuration. We show that the phase squeezed coherent state generated by the OPO evolves into a macroscopic superposition of phase squeezed coherent states on spending a specific amount of time inside a Kerr medium. The phase space displacement is achieved by the interference of the intense reference beam with the signal in the final beam splitter of the interferometer. The noise of the reference beam contaminating the signal is prevented by making this beam splitter highly reflective. We have calculated the photon number uncertainty of the outcoming beam and have shown that it is smaller than the usual amplitude squeezed coherent state's value.     

Design of a new class of microwave biasing networks with modal-matching properties

A new four-port microwave-biasing network with modal-matching properties is presented. The new network can be used to bias differential circuits and has a high common-mode rejection ratio, which is frequency-independent. It is comprised of a pair of Marchand baluns intermediated by a filtering stage with an overall physical size that can be predetermined as a design parameter. The design procedure is based on the exact synthesis of a filter prototype with a prescribed set of transmission zeros. The new network was implemented on a printed circuit board and used to bias a pseudo-differential amplifier. The measured performance of the sub-system configuration demonstrated low common-mode gain over a broad bandwidth as theoretically predicted.     

Two-photon pumped upconversion and nonlinear optical properties of a new lasing dye: HMASPS

Abstract

Two-photon pumped frequency upconversion optical properties and two-photon absorption (TPA) induced nonlinear absorption of a new dye, trans-4-[p-(N-hydroxyethyl-N-methylamino)styryl]-N-methylpyridinium ptoluene sulfonate (abbreviated to HMASPS) have been experimentally investigated. This new dye exhibits strong superradiation properties when the pumping power is above its threshold. The superradiation upconversion efficiency from 900 to 1150 nm and the nonlinear absorption from 720 to 1100 nm have been measured. The largest effective molecular TPA cross-section was measured to be 44.3 × 10^?48 cm⁴·s·photon^?1at 920 nm. At 1064 nm, it was 2.77 × 10^?48 cm⁴·s·photon^?1, much smaller than that at 920 nm. The highest conversion efficiency is 7% at 990 nm, whereas 4.2% at 1064 nm.     

Fock states generation in a kicked cavity with a nonlinear medium

Abstract

We discuss a model of a cavity filled with a passive nonlinear ?Kerr‘ medium and periodically kicked by a series of ultra-short laser pulses. The nonlinear medium is described by the (2q ? 1)th nonlinearity X ^(2q?1). We find analytical formulas describing the field states inside the cavity. We show that such a system can produce, depending on the order of the nonlinearity, superpositions of several Fock states with the small photon numbers (0,1; 0,1,2; etc). In particular, the one-photon state can be approached during the evolution of the system with X ⁽³⁾ nonlinearity provided the cavity losses are negligible. The purity of states generated in this process, however, can be seriously degraded by the cavity damping. We perform numerical calculations to validate our analytical results.