Generation of displaced squeezed superpositions of coherent states

We study the method of generation of states that approximate superpositions of large-amplitude coherent states (SCSs) with high fidelity in free-traveling fields. Our approach is based on the representation of an arbitrary single-mode pure state, and SCSs in particular, in terms of displaced number states with an arbitrary displacement amplitude. The proposed optical scheme is based on alternation of photon additions and displacement operators (in the general case, N photon additions and N − 1 displacements are required) with a seed coherent state to generate both even and odd displaced squeezed SCSs regardless of the parity of the used photon additions. It is shown that the optical scheme studied is sensitive to the seed coherent state if the other parameters are unchanged. Output states can approximate either even squeezed SCS or odd SCS shifted relative to each other by some value. This allows constructing a local rotation operator, in particular, the Hadamard gate, which is a mainframe element for quantum computation with coherent states. We also show that three-photon additions with two intermediate displacement operators are sufficient to generate even displaced squeezed SCS with the amplitude 1.7 and fidelity more than 0.99. The effects deteriorating the quality of output states are considered.     

Nonclassical properties and algebraic characteristics of negative binomial states in quantized radiation fields

We study the nonclassical properties and algebraic characteristics of the negative binomial states introduced by Barnett recently. The ladder operator formalism and displacement operator formalism of the negative binomial states are found and the algebra involved turns out to be the SU(1,1) Lie algebra via the generalized Holstein-Primarkoff realization. These states are essentially Perelomov's SU(1,1) coherent states. We reveal their connection with the geometric states and find that they are excited geometric states. As intermediate states, they interpolate between the number states and geometric states. We also point out that they can be recognized as the nonlinear coherent states. Their nonclassical properties, such as sub-Poissonian distribution and squeezing effect are discussed. The quasiprobability distributions in phase space, namely the Q and Wigner functions, are studied in detail. We also propose two methods of generation of the negative binomial states. d 32.80.Pj Optical cooling of atoms; trapping Received 8 May 1999 and Received in final form 8 November 1999     

Schemes for performance of displacing Hadamard gate with coherent states

We propose an approach with displaced states to use it for rotations of base coherent states and squeezed coherent states. Our approach is based on representation of the coherent states in free-traveling fields in terms of displaced number states with arbitrary amplitude of displacement. Two optical schemes are developed for construction of Hadamard gate for the base states. One of the optical schemes is based on alternation of photon additions and displacement operators (in general case, N-photon additions and N?1-displacements are required) to generate displaced squeezed even/odd superposition of coherent states (SCSs) with high fidelity in dependency on type (computational zero or one) of the base input state. Another optical scheme uses two-photon subtracted squeezed coherent states to approximate outcome of the Hadamard gate for the base squeezed coherent states. Output states approximate with high fidelity either even squeezed SCS or odd SCS shifted relative to each other by some value. It enables to adjust the optical scheme for construction of the Hadamard gate being mainframe element for quantum computation with basic squeezed coherent states.     

Even and Odd Nonlinear Negative Binomial States

In this paper the even and odd nonlinear negative binomial states of the radiation field are introduced. These states interpolates between even (odd) number states and the even (odd) nonlinear coherent states. The Glauber second-order correlation function is calculated for these states. The squeezing phenomenon (normal and amplitude-squared squeezing), the quasi-probability distribution function Q-function, Wigner-function and the phase properties, are also discussed. Examination of the resonance fluorescence against the present state is given. It has been shown that the atomic inversion is sensitive to any variation in the even and odd nonlinear negative binomial number M and the nonlinearity parameter η.     

Exact and approximate results for the Anderson impurity model

This paper provides exact and rigorous upper and lower bounds to the ground state energy of the Single Impurity Anderson Model in the limit of infiniteU. The upper bound approximates the ground state energy very well and the corresponding state may be used as a starting point for further investigations. The energy spectrum of the Single Impurity Anderson Model is calculated exactly for a special non-trivial model density of states describing the bare band electrons. All approaches introduced here are compared to this exact result and to other ground state energy calculations.     

一类q变形广义相干叠加态的量子统计性质

研究了一类q变形广义相干态叠加态|ψ>=a|β>+be^iφ|βe^iδ>的量子统计性质，结果表明此种叠加态普遍存在压缩效应和光子反群聚效应.相干态间的位相差，叠加系数的位相差和广义相干态之间内积的幅值和位相的变化对迭加态的压缩效应和反群聚效应起着重要的作用. 关键词： q变形')" href="#">q变形 广义相干态 压缩效应 反群聚效应     

Reduction of quantum phase fluctuations in intermediate states

Recently we have shown that the reduction of the Carruthers-Nieto symmetric quantum phase fluctuation parameter (U) with respect to its coherent state value corresponds to an antibunched state, but the converse is not true. Consequently reduction of U is a stronger criterion of nonclassicality than the lowest order antibunching. Here we have studied the possibilities of reduction of U in intermediate states by using the Barnett-Pegg formalism. We have shown that the reduction of phase fluctuation parameter U can be seen in different intermediate states, such as binomial state, generalized binomial state, hypergeometric state, negative binomial state, and photon added coherent state. It is also shown that the depth of nonclassicality can be controlled by various parameters related to intermediate states. Further, we have provided specific examples of antibunched states, for which U is greater than its Poissonian state value.     

Concurrence, tangle and fully entangled fraction

We show that although we cannot distil a singlet from many pairs of bound entangled states, the concurrence and the tangle of two entangled quantum states are always strictly larger than those of one of them, even both entangled quantum states are bound entangled. We present a relation between the concurrence and the fidelity of optimal teleportation. We also give new upper and lower bounds for concurrence and tangle.     

The dependence of fidelity on the squeezing parameter in teleportation of the squeezed coherent statesvglue4pt

This paper investigates an analytical expression of teleportation fidelity in the teleportation scheme of a single mode of electromagnetic field. The fidelity between the original squeezed coherent state and the teleported one is expressed in terms of the squeezing parameter r and the quantum channel parameter (two-mode squeezed state) p. The results of analysis show that the fidelity increases with the increase of the quantum channel parameter p, while the fidelity decreases with the increase of the squeezing parameter r of the squeezed state. Thus the coherent state (r=0) is the best quantum signal for continuous variable quantum teleportation once the quantum channel is built.     

内禀退相干下二项式光场与原子互作用的场熵演化

通过求解系统的Milburn 方程,研究了二项式光场与二能级原子相互作用系统中的场熵演化特性,讨论了内禀退相干、二项式光场系数和场的最大光子数对场熵演化的影响.结果表明二项式光场处于中间态时,由于内禀退相干,场熵振荡准周期性减弱,并随着时间的演化,场与原子纠缠逐渐趋近于一个定值,说明存在內禀退相干时,场与原子仍能纠缠;当內禀退相干因子不变时,二项式光场从相干态过渡到中间态,直至数态过程中,场熵值减小,场与原子的纠缠减弱.     

Quantum Teleportation in Thermal Fluctuating Electromagnetic Field

In this paper, we study the quantum teleportation protocol in fluctuating electromagnetic field. The noisy model of quantum teleportation is constructed and the master equation that governs the evolution is solved. We analyze the effect of temperature and noisy parameter on fidelity and quantum coherence, which give us more freedom in controlling the quantum teleportation. We find that the fidelity has some relations with quantum coherence. Fidelity decay rate is dependent on the atom spontaneous emission rate and temperature. When teleporting a non-maximally coherent state, for different ranges of noisy parameter, fidelity has different variations with temperature, and evolves to different values, higher temperature leading to higher fidelity at last; when teleporting a maximally coherent state, fidelity decays to a fixed value with increasing noisy parameter and temperature.

     

非旋波近似下二项式光场与V型三能级原子相互作用的量子特性

采用相干态正交化展开方法,研究了非旋波近似下V型三能级原子与单模腔场的相互作用,并且利用保真度对能级的交叉问题进行了判断.研究了在二项式光场作用下,V型三能级原子初始状态以及二项式态光场的光场系数对光场二阶相干度的影响.数值计算结果表明|原子初始时刻处于基态时,随着η的增大光场呈现聚束效应的持续时间先增大后减小|原子初始时刻处于叠加态时,随着参量η的增大光场呈现聚束效应的持续时间逐渐减弱|当η的值足够大时,在这两种情况下光场都将完全呈现反聚束效应|当其它参量不变时,G2(t)的平均值会随着耦合强度的增大而增大.     

The calculation of valence shell ionization potentials by the ΔSCF method

Valence shell ionization potentials for several small molecules (HF, H₂O, CH₄, CO, H₂S, PH₃, SiH₄, SO₂ and F₂CO) are calculated by means of ab initio ΔSCF calculations on all the valence hole states of each molecule. The results are compared with the experimental low energy photoelectron spectra. In the case of the higher energy ion states, particular attention is paid to finding practical means for obtaining convergence of the ΔSCF iterations, and numerical evidence is presented, indicating that the ΔSCF procedure provides upper bounds to the energy of such states, at least for the cases studied herein. A new procedure, the ‘ combined ΔSCF ’ method, for the determination of a common set of molecular orbitals for use in the construction of wavefunctions for a number of ion states is described.     

Photon Modulated Coherent States of a Generalized Isotonic Oscillator by Weyl Ordering and their Non-Classical Properties

We construct photon modulated coherent states of a generalized isotonic oscillator by expanding the newly introduced superposed operator through Weyl ordering method. We evaluate the parameter A ₃ and the s-parameterized quasi probability distribution function to confirm the non - classical nature of the states. We also calculate the identities related with the quadrature squeezing to explore the squeezing property of the states. Finally, we investigate the fidelity between the photon modulated coherent states and coherent states to quantify the non-Gaussianity of the states. The constructed states and their associated non - classical properties will add further knowledge on the potential.     

On the Lifschitz singularity and the tailing in the density of states for random lattice systems

We prove rigorously the existence of a Lifschitz singularity in the density of states at zero energy in some random lattice systems of noninteracting bosons and fermions in any numberv of dimensions. The basic tool is a simple modification of the method of Fukushima to yield the correct upper and lower bounds for allv. We also comment on the mathematical difference between the models treated and the system of phonons with mass disorder in the harmonic approximation, whose behavior is known to be of Debye form, not Lifschitz, at low temperatures.Supported by the Swiss National Science Foundation.On leave of absence from the Institute de Fisica, University of São Paulo, Brazil.     

Bounds on enhanced turbulent flame speeds for combustion with fractal velocity fields

Rigorous upper bounds are derived for large-scale turbulent flame speeds in a prototypical model problem. This model problem consists of a reaction-diffusion equation with KPP chemistry with random advection consisting of a turbulent unidirectional shear flow. When this velocity field is fractal with a Hurst exponentH with 0<H<1, the almost sure upper bounds suggest that there is an accelerating large-scale turbulent flame front with the enhanced anomalous propagation lawy=C _H t ^1+H for large renormalized times. In contrast, a similar rigorous almost sure upper bound for velocity fields with finite energy yields the turbulent flame propagation law within logarithmic corrections. Furthermore, rigorous theorems are developed here which show that upper bounds for turbulent flame speeds with fractal velocity fields are not self-averaging, i.e., bounds for the ensemble-averaged turbulent flame speed can be extremely pessimistic and misleading when compared with the bounds for every realization.     

类锂体系激发态的精确判据

利用Gálvez Porras关于原子体系电子在核处密度和径向期待值的精确不等式，分别建立了波函数的两套精确判据，它们是独立于能量判据之外的检验波函数精确度的判据. 以类锂体系激发态为研究对象，首先对1s2 3s态的电子在核处密度和径向期待值的上界进行了检查，然后对锂原子1s2 3s态在不同计算方法下由电子在核处密度上界定义的R6值和的上界定义的R4值分别进行了测试，同时还对锂原子双激发态的电子在核处密度和径向期待值的上界进行了检验. 研究表明这两套不等式都可作为原子体系各种能态波函数的精确判据. 关键词： 电子在核处密度 径向期待值 全实加关联 精确判据     

Pure state estimation and the characterization of entanglement

A connection between the state estimation problem and the separability problem is noticed and exploited to find efficient numerical algorithms to solve the first one. Based on these ideas, we also derive a systematic method to obtain upper bounds on the maximum local fidelity when the states are distributed among several distant parties.     

Double-Mode Excited Entangled Coherent States and Their Fidelity

In this paper, we introduce the definition of a new kind of continuous-variable-type entangled coherent states, called double-mode excited entangled coherent states through acting creation operators on the double-mode entangled coherent states. We briefly present how to produce them from the two mode ECSs through an interaction between laser and atoms. We further focus on studying the fidelity of the states and discussing the influence of photon excitations on fidelity.     

Digital Quantum Simulation and Circuit Learning for the Generation of Coherent States

Coherent states, known as displaced vacuum states, play an important role in quantum information processing, quantum machine learning, and quantum optics. In this article, two ways to digitally prepare coherent states in quantum circuits are introduced. First, we construct the displacement operator by decomposing it into Pauli matrices via ladder operators, i.e., creation and annihilation operators. The high fidelity of the digitally generated coherent states is verified compared with the Poissonian distribution in Fock space. Secondly, by using Variational Quantum Algorithms, we choose different ansatzes to generate coherent states. The quantum resources—such as numbers of quantum gates, layers and iterations—are analyzed for quantum circuit learning. The simulation results show that quantum circuit learning can provide high fidelity on learning coherent states by choosing appropriate ansatzes.