Optical wavelet-fractional squeezing combinatorial transform

doi:10.1088/1674-1056/ac1e1c

Abstract By virtue of the method of integration within ordered product (IWOP) of operators we find the normally ordered form of the optical wavelet-fractional squeezing combinatorial transform (WFrST) operator. The way we successfully combine them to realize the integration transform kernel of WFrST is making full use of the completeness relation of Dirac's ket-bra representation. The WFrST can play role in analyzing and recognizing quantum states, for instance, we apply this new transform to identify the vacuum state, the single-particle state, and their superposition state.

Keywords: wavelet transform fractional squeezing transform combinatorial transform IWOP technique

Received: 09 June 2021
Revised: 01 August 2021
Accepted manuscript online: 17 August 2021

PACS:	03.65.-w	(Quantum mechanics)
	03.65.Db	(Functional analytical methods)
	02.30.Uu	(Integral transforms)

Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11304126) and the College Students' Innovation Training Program (Grant No. 202110299696X).

Corresponding Authors: Cui-Hong Lv
E-mail: lvch@mail.ujs.edu.cn

Cite this article:

Cui-Hong Lv(吕翠红), Ying Cai(蔡莹), Nan Jin(晋楠), and Nan Huang(黄楠) Optical wavelet-fractional squeezing combinatorial transform 2022 Chin. Phys. B 31 020303

[1] Tang B and Bian L 2019 J. Opt. Soc. Am. A 36 1624
[2] Namias V 1980 J. Inst. Math. Appl. 25 241
[3] McBride A C and Kerr F H 1987 IMA J. Appl. Math. 39 159
[4] Mecdlovic D and Ozatkas H M 1993 J. Opt. Soc. Am. A 10 1875
[5] Ozatkas H M and Mecdlovic D 1993 J. Opt. Soc. Am. A 10 2522
[6] Chen S, Yuan Y, Xu H L, Zhang S N and Zhao H C 2021 Sig. Pro. 178 894
[7] Zhou G Q 2009 Chin. Phys. B 18 2779
[8] Cai L and Zhu X L 2021 J. Phys. Con. Ser. 1820 012008
[9] Loudon R and Knight P L 1987 J. Mod. Opt. 34 709
[10] Fan H Y, Lou S Y and Hu L Y 2013 Chin. Phys. Lett. 30 090304
[11] Du J M and Fan H Y 2013 Chin. Phys. B 22 060302
[12] Lv C H, Fan H Y and Li D W 2015 Chin. Phys. B 24 020301
[13] Wu M T, Zhang Y, Tang M Y, Duan Z Y, Ma F Y, Du Y L, Liang E J and Gong Q X 2020 Chin. Phys. B 29 124201
[14] Jaffard S, Meyer Y and Ryan R D 2001 SIAM Rev. 44 302
[15] Chatterjee P 1992 Introduction to wavelets (New York:Academic Press)
[16] Daubechies I 1993 J. Acoust. Soc. Am. 93 1671
[17] Lv C H, Zhang S Q and Xu W 2018 Chin. Phys. B 27 094206
[18] Fan H Y and Hu L Y 2012 Front. Phys. 7 261
[19] Fan H Y, Lu H L and Fan Y 2006 Ann. Phys. 321 480
[20] Song J and Fan H Y 2010 Chin. Phys. Lett. 27 024210
[21] Fan H Y and Lu H L 2006 Phys. Lett. 31 3432

[1]	Single pixel imaging based on semi-continuous wavelet transform Chao Gao(高超), Xiaoqian Wang(王晓茜), Shuang Wang(王爽), Lidan Gou(苟立丹), Yuling Feng(冯玉玲), Guangyong Jin(金光勇), and Zhihai Yao(姚治海). Chin. Phys. B, 2021, 30(7): 074201.
[2]	Two-step phase-shifting Fresnel incoherent correlation holography based on discrete wavelet transform Meng-Ting Wu(武梦婷), Yu Zhang(张雨), Ming-Yu Tang(汤明玉), Zhi-Yong Duan(段智勇), Feng-Ying Ma(马凤英), Yan-Li Du(杜艳丽), Er-Jun Liang(梁二军), and Qiao-Xia Gong(弓巧侠). Chin. Phys. B, 2020, 29(12): 124201.
[3]	Fractional squeezing-Hankel transform based on the induced entangled state representations Cui-Hong Lv(吕翠红), Su-Qing Zhang(张苏青), Wen Xu(许雯). Chin. Phys. B, 2018, 27(9): 094206.
[4]	Wavelet optimization for applying continuous wavelet transform to maternal electrocardiogram component enhancing Qiong Yu(于琼), Qun Guan(管群), Ping Li(李萍), Tie-Bing Liu(刘铁兵), Jun-Feng Si(司峻峰), Ying Zhao(肇莹), Hong-Xing Liu(刘红星), Yuan-Qing Wang(王元庆). Chin. Phys. B, 2017, 26(11): 118702.
[5]	Harmonic signal extraction from noisy chaotic interference based on synchrosqueezed wavelet transform Wang Xiang-Li (汪祥莉), Wang Wen-Bo (王文波). Chin. Phys. B, 2015, 24(8): 080203.
[6]	Experimental study on spectrum and multi-scale nature of wall pressure and velocity in turbulent boundary layer Zheng Xiao-Bo (郑小波), Jiang Nan (姜楠). Chin. Phys. B, 2015, 24(6): 064702.
[7]	From fractional Fourier transformation to quantum mechanical fractional squeezing transformation Lv Cui-Hong (吕翠红), Fan Hong-Yi (范洪义), Li Dong-Wei (李东韡). Chin. Phys. B, 2015, 24(2): 020301.
[8]	Extraction and verification of coherent structures in near-wall turbulence Hu Hai-Bao (胡海豹), Du Peng (杜鹏), Huang Su-He (黄苏和), Wang Ying (王鹰). Chin. Phys. B, 2013, 22(7): 074703.
[9]	Wavelet transform for Fresnel-transformed mother wavelets Liu Shu-Guang(刘述光), Chen Jun-Hua(陈俊华), and Fan Hong-Yi(范洪义) . Chin. Phys. B, 2011, 20(12): 120305.
[10]	Inversion formula and Parseval theorem for complex continuous wavelet transforms studied by entangled state representation Hu Li-Yun(胡利云) and Fan Hong-Yi(范洪义). Chin. Phys. B, 2010, 19(7): 074205.
[11]	A generalized Collins formula derived by virtue of the displacement-squeezing related squeezed coherent state representation Xie Chuan-Mei(谢传梅), Fan Hong-Yi(范洪义), and Wan Shao-Long(完绍龙). Chin. Phys. B, 2010, 19(6): 064207.
[12]	Wavelet-based multifractal analysis of DNA sequences by using chaos-game representation Han Jia-Jing(韩佳静) and Fu Wei-Juan (符维娟) . Chin. Phys. B, 2010, 19(1): 010205.
[13]	New two-mode intermediate momentum-coordinate representation with quantum entanglement and its application Xu Shi-Min(徐世民), Xu Xing-Lei(徐兴磊), Li Hong-Qi(李洪奇), and Wang Ji-Suo(王继锁). Chin. Phys. B, 2009, 18(6): 2129-2136.
[14]	Normal ordering and antinormal ordering of the operator $(fQ+gP)^n$ and some of their applications Meng Xiang-Guo(孟祥国), Wang Ji-Suo(王继锁), and Liang Bao-Long(梁宝龙). Chin. Phys. B, 2009, 18(4): 1534-1541.
[15]	Network traffic prediction by a wavelet-based combined model Sun Han-Lin(孙韩林), Jin Yue-Hui(金跃辉), Cui Yi-Dong(崔毅东),and Cheng Shi-Duan(程时端) . Chin. Phys. B, 2009, 18(11): 4760-4768.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

Optical wavelet-fractional squeezing combinatorial transform

Cite this article:

Online attention