Applications of quantum Fourier transform in photon-added coherent state

Quantum Fourier transform is realized by the Hadamard gate in a quantum computer, which can also be considered as a Hadamard transform. We introduce the Hadamard transformed photon-added coherent state （HTPACS）, which is obtained by letting the photon-added coherent state （PACS） across the quantum Hadamard gate, from this result. It is found that the HTPACS can be considered as a coordinate-momentum mutual exchanging followed by a squeezing transform of the PACS. In addition, the non-classical statistical properties of HTPACS, such as squeezing coefficient, Mandel parameter, etc., are also discussed.     

Moduli and twisted sector dependence of ZN×ZM orbifold couplings

We derive the four point correlation function involving four twist fields for arbitrary even dimensional Z_N×Z_M orbifold compactifications. Using techniques from the conformal field theory the three point correlation functions with twist fields are determined. Both the choice of the modular background (compatible with the twists) and of the (higher) twisted sectors involved are fully general. Our results turn out to be target space duality invariant.     

Implementation of Quantum Fourier Transform and Its Applications via Quantum-Dot Spins and Microcavity

A scheme for implementing discrete quantum Fourier transform is proposed via quantum dots embedded in a microcavity, and then some of its applications are investigated, i.e., Deutsch 3ozsa. algorithm and Shor＇s quantum factoring. In particular, the detailed process of implementing one~qubit Deutsch Jozsa algorithm and the factorization of N = 15 are given. The microcavity mode is only virtually excited in the whole interaction, so the effective decoherent has slight effect on the current scheme. These schemes would be an important step to fabricate a solid quantum computer.     

量子离散Fourier变换在离子阱中的实现方案

在Cirac-Zoller模型的框架下,讨论在离子阱中如何利用幺正操作实施 量子离散Fourier变换的方案。由于量子离散Fourier变换可由两个基本操作组     

Implementation of Quantum Fourier Transform and Its Applications via Quantum-Dot Spins and Microcavity

A scheme for implementing discrete quantum Fourier transform isproposed via quantum dots embedded in a microcavity, and then someof its applications are investigated, i.e., Deutsch-Jozsa algorithm and Shor's quantum factoring. In particular, the detailed process of implementing one-qubit Deutsch-Jozsa algorithm and the factorization of N=15 are given. The microcavity mode is only virtually excited in the whole interaction, so the effective decoherent has slight effect on the current scheme. These schemeswould be an important step to fabricate a solid quantum computer.     

基于空域非均匀傅里叶变换的傅里叶望远镜

为了在稀疏发射阵列下清晰重构目标图像,提出了一种基于空域非均匀傅里叶变换(NDFT)的傅里叶望远镜信号处理方法。依据傅里叶望远镜的发射器位置与抽取的目标空间频率关系,结合MATLAB程序特点,完成了空域非均匀傅里叶逆变换,重构了目标图像。稀疏发射阵列配置方式为:T型阵列单臂放置11个发射望远镜,连续抽取目标的8个低频信息,再抽取3个高频分量。选择不同形状和灰度分布的4个卫星作为成像目标。与补零均匀快速傅里叶变换(FFT)方法重构的图像对比发现:信噪比为100 dB时,相比补零均匀FFT方法, NDFT方法重构图像的Strehl比都有所提升,最高提升了0.159 8。     

A geometric nonuniform fast Fourier transform

An efficient algorithm is presented for the computation of Fourier coefficients of piecewise-polynomial densities on flat geometric objects in arbitrary dimension and codimension. Applications range from standard nonuniform FFTs of scattered point data, through line and surface potentials in two and three dimensions, to volumetric transforms in three dimensions. Input densities are smoothed with a B-spline kernel, sampled on a uniform grid, and transformed by a standard FFT, and the resulting coefficients are unsmoothed by division. Any specified accuracy can be achieved, and numerical experiments demonstrate the efficiency of the algorithm for a gallery of realistic examples.     

基于空域非均匀傅里叶变换的傅里叶望远镜

为了在稀疏发射阵列下清晰重构目标图像,提出了一种基于空域非均匀傅里叶变换(NDFT)的傅里叶望远镜信号处理方法。依据傅里叶望远镜的发射器位置与抽取的目标空间频率关系,结合MATLAB程序特点,完成了空域非均匀傅里叶逆变换,重构了目标图像。稀疏发射阵列配置方式为：T型阵列单臂放置11个发射望远镜,连续抽取目标的8个低频信息,再抽取3个高频分量。选择不同形状和灰度分布的4个卫星作为成像目标。与补零均匀快速傅里叶变换(FFT)方法重构的图像对比发现：信噪比为100 dB时,相比补零均匀FFT方法, NDFT方法重构图像的Strehl比都有所提升,最高提升了0.159 8。     

Comments on the complete generalized fractional Fourier transform

In this research, we thoroughly investigate the complete generalized fractional Fourier transform (CGFRFT) and draw the following conclusions that are different from the original literature: (1) The CGFRFT is not a generalized version, but a special case that ignores the marginal postulate; (2) If the period parameter is not a multiple of four, the CGFRFT can never perform a Fourier transform regardless of the value of the transform order. The simulation results of a rectangular signal support the above conclusions.     

Fourier transform emission spectroscopy of the FΔ-XΦ system of TiF

The emission spectra of TiF have been reinvestigated in the 4200-15 000 cm⁻¹ region using the Fourier transform spectrometer associated with the National Solar Observatory at Kitt Peak. TiF was formed in a microwave discharge lamp operated with 2.5 Torr of He and a trace of TiF₄ vapor, and the spectra were recorded at a resolution of 0.02 cm⁻¹. The TiF bands observed in the 12 000-14 000 cm⁻¹ region have been assigned to a new transition, F⁴Δ-X⁴Φ. Each band consists of four sub-bands assigned as, ⁴Δ_1/2-⁴Φ_3/2, ⁴Δ_3/2-⁴Φ_5/2, ⁴Δ_5/2-⁴Φ_7/2, and ⁴Δ_7/2-⁴Φ_9/2. A rotational analysis of the 0-1, 0-0, and 1-0 bands has been obtained and spectroscopic constants have been extracted.     

不对称离散分数傅里叶变换实现数字图像的加密变换

利用不对称分数傅里叶变换的特性,提出了一种图像加密变换的新方法。对图像的x,y方向分别实施不同级次的一维分数傅里叶变换,得到加密图像。解密方法就是对变换后的图像实施对应级次的分数傅里叶逆变换,只有当x,y方向的逆变换级次分别与原变换级次都相同或者满足周期条件时,才能恢复原图像。加密变换有效地提高了图像加密和防伪力度。数值计算验证了方法的正确性和可行性。     

基于傅里叶变换红外光谱法CO2气体碳同位素比检测研究

介绍了基于傅里叶变换红外技术检测CO₂气体碳同位素比的新方法, 详细介绍了如何从HITRAN红外数据库中提取气体标准吸收截面; 介绍了基于非线性最小二乘法反演CO₂气体碳同位素比和整套实验装置的组成及实验步骤. 从理论和实验分析两方面讨论了温度和气压变化对δ¹³CO₂值的影响规律. 对于同一CO₂标准气体, 采用FTIR和同位素质谱法两种技术进行了δ¹³CO₂值对比检测, 两种测量技术的平均值差异仅为0.25%. 从实验结果可以看出, FTIR技术可以实现对CO₂气体碳同位素比的检测.     

Laser and Fourier transform emission spectroscopy of TaCl

The emission spectrum of TaCl has been recorded at high resolution in the 3000-35 000 cm⁻¹ region using a Fourier transform spectrometer. The bands were observed by microwave excitation of a mixture of TaCl₅ vapor and 3.0 Torr of He. Several TaCl bands have also been recorded using the laser ablation/molecular beam source at the University of New Brunswick. A rotational analysis of a number of bands has been obtained and the majority of the stronger bands have been classified into three groups with different lower state spectroscopic constants. The three lower states have been identified as having Ω″ = 0⁺, Ω″ = 2, and (tentatively) Ω″ = 3. The Ω″ = 0⁺ and Ω″ = 2 states are very close in energy and one of these two states is the ground state of TaCl.     

地基高分辨率傅里叶变换红外光谱反演环境大气中的CH4浓度变化

CH₄在大气中的浓度较低(～1.8 ppmv)且混合较为均匀, 不同区域浓度差较小, 其在大气中微量变化的精确观测对反演技术提出了很高要求. 基于高分辨率(0.02 cm^-1)傅里叶变换直射太阳光谱, 研究一种高精度、大尺度的CH₄浓度反演方法, 高灵敏地观测CH₄在大气强背景下的浓度变化. 先利用先验参数实现测量光谱的准确建模, 再采用非线性最小二乘光谱拟合和非线性逐次迭代相结合的方法反演CH₄的垂直柱浓度(vertical column density, VCD), 并以7885 cm^-1 O₂ 吸收窗口为参考, 反演CH₄的柱平均干空气混合比浓度(column-averaged dry air mixing ratios) XCH₄. CH₄ VCD和XCH₄拟合误差均小于1%, 且绝大多数XCH₄反演值均位于Total Carbon Column Observing Network (TCCON)规定的<0.5%区间内. 基于典型的日观测值, 研究了CH₄浓度的日变化规律, CH₄ VCD随时间变化而减少, XCH₄的日变化量小于0.02 ppmv.     

Image encryption and decryption using fractional Fourier transform and radial Hilbert transform

A technique for image encryption using fractional Fourier transform (FRT) and radial Hilbert transform (RHT) is proposed. The spatial frequency spectrum of the image to be encrypted is first segregated into two parts/channels using RHT, and image subtraction technique. Each of these channels is encrypted independently using double random phase encoding in the FRT domain. The different fractional orders and random phase masks used during the process of encryption and decryption are the keys to enhance the security of the proposed system. The algorithms to implement the proposed encryption and decryption scheme are discussed, and results of digital simulation are presented.     

用小型全息设备做傅里叶变换全息图存储资料实验

阐述了用小型全息设备做傅里叶变换全息图存储资料实验所采用的光路、详细的操作步骤和实验中的关键问题.     

Fractional Fourier transform of Lorentz beams

This paper introduces Lorentz beams to describe certain laser sources that produce highly divergent fields. The fractional Fourier transform (FRFT) is applied to treat the propagation of Lorentz beams. Based on the definition of convolution and the convolution theorem of the Fourier transform, an analytical expression for a Lorentz beam passing through a FRFT system has been derived. By using the derived formula, the properties of a Lorentz beam in the FRFT plane are illustrated numerically.     

Realization of quantum permutation algorithm in high dimensional Hilbert space

Quantum algorithms provide a more efficient way to solve computational tasks than classical algorithms. We experimentally realize quantum permutation algorithm using light's orbital angular momentum degree of freedom. By exploiting the spatial mode of photons, our scheme provides a more elegant way to understand the principle of quantum permutation algorithm and shows that the high dimension characteristic of light's orbital angular momentum may be useful in quantum algorithms. Our scheme can be extended to higher dimension by introducing more spatial modes and it paves the way to trace the source of quantum speedup.     

Displacement measurement based on joint fractional Fourier transform correlator

A displacement measurement technology based on joint fractional Fourier transform is firstly proposed. Contrast to conventional displacement measurement based on joint Fourier transform correlator, the position of cross correlation peak in the proposed technology could be fixed arbitrarily according to the order of fractional Fourier transform. The optical setup in the proposed technology is more flexible and easier to implement. Simulation and experiment results are given out to verify the analysis.