Relation of the tomographic representation of states to the bargmann representation of states

We introduce some equivalent forms of a map realizing the connection between the Bargmann and tomographic representations of states and observables. We perform the same task for a dual tomographic map. In spite of the fact that, due to the analyticity of the Bargmann representation, there exist many forms for such a map, we restrict ourselves to integral transforms. To perform our calculations, we also introduce a new technique for disentangling the SU(1, 1)-group operators.     

Linear amplifier via the displaced Fock states superposition

The linear amplifier with the superposition of displaced Fock states (DFS’s) as an input field is discussed. The s-parameterized characteristic function (CF) of linear amplifier for the superposition of two DFS’s is considered. Several quantum statistical expectation values for the output of linear amplifier are evaluated once the time dependent CF has been computed. The Glauber secondorder coherence function is calculated. The squeezing properties of the output field are studied. The s-ordered quasiprobability distribution function (QDF) for the output of linear amplifier driven by DFS’s superposition is investigated. The phase properties of the superposition of DFS’s are studied. The s-parameterized phase distribution, obtained by integrating the s-parameterized QDF over radial variable is illustrated.     

Fock states of flavor neutrinos are unphysical

It is shown that it is possible to construct an infinity of Fock spaces of flavor neutrinos depending on arbitrary unphysical mass parameters, in agreement with the theory of Blasone and Vitiello in the version proposed by Fujii, Habe and Yabuki. However, we show by reductio ad absurdum that these flavor neutrino Fock spaces are clever mathematical constructs without physical relevance, because the hypothesis that neutrinos produced or detected in charged-current weak interaction processes are described by flavor neutrino Fock states implies that measurable quantities depend on the arbitrary unphysical flavor neutrino mass parameters. Received: 26 August 2004, Published online: 18 January 2005 PACS: 14.60.Pq, 14.60.Lm     

IWOP积分技术证明粒子数平移态的过完备性

利用正规乘积算符内的积分技术(IWOP),导出了在相干态|z＞过完备性中,积分变量z与z*可以独立地做积分变换,而保持其完备性.利用相干态的这一特点和IWOP积分技术,进而可以方便地证明粒子数平移态D(z),|n＞具有过完备性.     

Implication of the overlap representation for modelling generalized parton distributions

Based on a field theoretically inspired model of light-cone wave functions, we derive valence-like generalized parton distributions and their double distributions from the wave function overlap in the parton number conserved s-channel. The parton number changing contributions in the t-channel are restored from duality. In our construction constraints of positivity and polynomiality are simultaneously satisfied and it also implies a model dependent relation between generalized parton distributions and transverse momentum dependent parton distribution functions. The model predicts that the t  -behavior of resulting hadronic amplitudes depends on the Bjorken variable xBj$x_{\mathrm{Bj}}$. We also propose an improved ansatz for double distributions that embeds this property.     

低分析频率压缩光的实验制备

基于PPKTP晶体的阈值以下光学参量振荡(OPO)过程,制备了共振于铷原子D1线795 nm的压缩真空态光场,研究了分析频率处于千赫兹范围的主要噪声来源,特别是795 nm激光及其二次谐波397.5 nm激光在晶体内吸收引起的非线性损耗增加和系统热不稳定的问题(397.5 nm激光处于PPKTP晶体透光范围边缘,具有高于其他波长数倍的吸收系数).以795 nm和1064 nm为例,分析了非线性损耗及晶体内热效应对压缩度的影响.受限于以上因素,795 nm压缩光很难得到1064 nm波段同样的压缩度.探测系统中的噪声耦合则限制了压缩频带.实验上对分析频率为千赫兹的经典噪声进行了有效控制,通过使用真空注入的OPO、垂直偏振及反向传输的腔长锁定光、低噪声的平衡零拍探测器、高稳定度的实验系统及量子噪声锁定等方法,最终在2.6—100 kHz的分析频段得到了约2.8 dB的795 nm压缩真空.该压缩光可用作磁场测量系统的探测光以提高测量灵敏度.     

E11 as E10 representation at low levels

The Lorentzian Kac–Moody algebra E₁₁, obtained by doubly overextending the compact E₈, is decomposed into representations of its canonical hyperbolic E₁₀ subalgebra. Whereas the appearing representations at levels 0 and 1 are known on general grounds, higher level representations can currently only be obtained by recursive methods. We present the results of such an analysis up to height 120 in E₁₁ which comprises representations on the first five levels. The algorithms used are a combination of Weyl orbit methods and standard methods based on the Peterson and Freudenthal formulae. In the appendices we give all multiplicities of E₁₀ occurring up to height 340 and for E₁₁ up to height 240.     

Detecting the inseparability and distillability of continuous variable states in Fock space

The partial transposition (PT) operation is an efficient tool in detecting the inseparability of a mixed state. We give an explicit formula for the PT operation for the continuous variable states in Fock space. We then give the necessary and sufficient condition for the positivity of Gaussian operators. Based on this, a number of criteria on the inseparability and distillability for the multimode Gaussian states are naturally drawn. We finally give an explicit formula for the state in a subspace of a global Gaussian state. This formula, together with the known results for Gaussian states, gives the criteria for the inseparability and distillability in a subspace of the global Gaussian state.     

Exact broken-symmetry states and Hartree–Fock solutions for quantum dots at high magnetic fields

Wigner molecules formed at high magnetic fields in circular and elliptic quantum dots are studied by exact diagonalization (ED) and unrestricted Hartree–Fock (UHF) methods with multicenter basis of displaced lowest Landau level wave functions. The broken symmetry states with semi-classical charge density constructed from superpositions of the ED solutions are compared to the UHF results. UHF overlooks the dependence of the few-electron wave functions on the actual relative positions of electrons localized in different charge puddles and partially compensates for this neglect by an exaggerated separation of charge islands which are more strongly localized than in the exact broken-symmetry states.     

The hidden phase of Fock states; quantum non-local effects

We revisit the question of how a definite phase between Bose-Einstein condensates can spontaneously appear under the effect of measurements. We first consider a system that is the juxtaposition of two subsystems in Fock states with high populations, and assume that successive individual position measurements are performed. Initially, the relative phase is totally undefined, and no interference effect takes place in the first position measurement. But, while successive measurements are accumulated, the relative phase becomes better and better defined, and a clear interference pattern emerges. It turns out that all observed results can be interpreted in terms of a pre-existing, but totally unknown, relative phase, which remains exactly constant during the experiment. We then generalize the results to more condensates. We also consider other initial quantum states than pure Fock states, and distinguish between intrinsic phase of a quantum state and phase induced by measurements. Finally, we examine the case of multiple condensates of spin states. We discuss a curious quantum effect, where the measurement of the spin angular momentum of a small number of particles can induce a big angular momentum in a much larger assembly of particles, even at an arbitrary distance. This spin observable can be macroscopic, analogous to the pointer of a measurement apparatus, which illustrates the non-locality of standard quantum mechanics with particular clarity. The effect can be described as the teleportation at arbitrary distances of the continuous classical result of a local experiment. The EPR argument, transposed to this case, takes a particularly convincing form since it does not involve incompatible measurements and deals only with macroscopic variables.     

Generation of motional Fock states of a trapped ion in the mediate-excitation regime

We propose a scheme to prepare Fock states for the vibrational motion of a trapped ion. Unlike previous schemes, the present scheme works in the mediate-excitation regime, in which the corresponding Rabi frequency is equal to the trap frequency. Thus, the required time is greatly shortened, which is important in view of decoherence.     

Contextuality and the probability representation of quantum states

We consider the notions of contextuality and noncontextuality within the framework of the probability representation of quantum states. We present an example of qutrit states and violation of the noncontextuality inequalities using the spin tomogram and tomographic symbols of the observables.     

Covariant description of the spin states of a fermi particle moving in external fields

Covariant operators for the spin of a Fermi particle are considered. The choice of spin integrals of motion is determined for motion in steady isotropie electromagnetic fields. The spin integrals in the presence of an anomalous magnetic moment are examined.     

Gaussian representation of extended quantum states

Excited energy eigenstates and their superpositions typically exhibit a fine oscillatory structure near caustics. Semiclassical theory accesses these, but depends on detailed geometrical knowledge of the caustics. Here we show that a finite placement of coherent states on the classical region efficiently fits such extended states, reproducing structures that are much finer than the Gaussian width of the basis states. An extended state, evolved such that it becomes fully distinguishable from the original state, can also be faithfully reproduced by this finite basis. The ideal fitting follows from the projection of the extended state on the finite Hilbert space spanned by the Gaussians, rather than any discretization of the continuous (overcomplete) coherent state representation.     

Analysis of a teleportation scheme involving cavity field states in a linear superposition of Fock states

We analyse a teleportation scheme of cavity field states. The experimental sketch discussed makes use of cavity quantum electrodynamics involving the interaction of Rydberg atoms with superconducting (micromaser) cavities as well as with classical microwave (Ramsey) cavities. In our scheme the Ramsey cavities and the atoms play the role of auxiliary systems used to teleport a field state, which is formed by a linear superposition of vacuum |∅〉 and the one-photon state |1〉, from a micromaser cavity to another.     

Covariant polarization density matrix for pure states of particles with integral spin

A closed expression is obtained for the covariant polarization density matrix of pure states of particles with integral spin. The application of the results to the decay f⁰ is considered.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 111–115, August, 1977.I am very grateful to A. B. Govorkov for his interest in the work and valuable comments. I am also very grateful to B. Z. Kopeliovich for a helpful discussion.