Time evolution of angular momentum coherent state derived by virtue of entangled state representation and a new binomial theorem

doi:10.1088/1674-1056/ab3a90

中国物理B ›› 2019, Vol. 28 ›› Issue (10): 100301-100301.doi: 10.1088/1674-1056/ab3a90

• SPECIAL TOPIC—Recent advances in thermoelectric materials and devices • 上一篇下一篇

Time evolution of angular momentum coherent state derived by virtue of entangled state representation and a new binomial theorem

Ji-Suo Wang(王继锁), Xiang-Guo Meng(孟祥国), Hong-Yi Fan(范洪义)

1 Shandong Provincial Key Laboratory of Laser Polarization and Information Technology, College of Physics and Engineering, Qufu Normal University, Qufu 273165, China;
2 Shandong Provincial Key Laboratory of Optical Communication Science and Technology, School of Physical Science and Information Engineering, Liaocheng University, Liaocheng 252059, China;
3 Department of Material Science and Engineering, University of Science and Technology of China, Hefei 230026, China

收稿日期:2019-05-28 修回日期:2019-07-30 出版日期:2019-10-05 发布日期:2019-10-05
通讯作者: Ji-Suo Wang E-mail:jswang@qfnu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 11347026) and the Natural Science Foundation of Shandong Province, China (Grant Nos. ZR2016AM03 and ZR2017MA011).

Time evolution of angular momentum coherent state derived by virtue of entangled state representation and a new binomial theorem

Ji-Suo Wang(王继锁)¹, Xiang-Guo Meng(孟祥国)², Hong-Yi Fan(范洪义)³

1 Shandong Provincial Key Laboratory of Laser Polarization and Information Technology, College of Physics and Engineering, Qufu Normal University, Qufu 273165, China;
2 Shandong Provincial Key Laboratory of Optical Communication Science and Technology, School of Physical Science and Information Engineering, Liaocheng University, Liaocheng 252059, China;
3 Department of Material Science and Engineering, University of Science and Technology of China, Hefei 230026, China

Received:2019-05-28 Revised:2019-07-30 Online:2019-10-05 Published:2019-10-05
Contact: Ji-Suo Wang E-mail:jswang@qfnu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 11347026) and the Natural Science Foundation of Shandong Province, China (Grant Nos. ZR2016AM03 and ZR2017MA011).

摘要/Abstract

摘要： We study how can an angular momentum coherent state |τ> keeps its form-invariant during time evolution governed by the Hamiltonian H=f(t)J₊+f^* (t)J_+ g(t)J_z. We discuss this topic in the context of boson realization of |τ>. By employing the entangled state representation |ζ> and deriving a new binomial theorem involving two-subscript Hermite polynomials, we derive the wave function <ζ|τ>, which turns out to be a single-subscript Hermite polynomial. Based on this result the maintenance of angular momentum coherent state during time evolution is examined, and the value of τ (t) is totally determined by the parameters involved in the Hamiltonian.

关键词: invariance of angular momentum coherent state, entangled state representation, new binomial theorem, time evolution

Abstract: We study how can an angular momentum coherent state |τ> keeps its form-invariant during time evolution governed by the Hamiltonian H=f(t)J₊+f^* (t)J_+ g(t)J_z. We discuss this topic in the context of boson realization of |τ>. By employing the entangled state representation |ζ> and deriving a new binomial theorem involving two-subscript Hermite polynomials, we derive the wave function <ζ|τ>, which turns out to be a single-subscript Hermite polynomial. Based on this result the maintenance of angular momentum coherent state during time evolution is examined, and the value of τ (t) is totally determined by the parameters involved in the Hamiltonian.

Key words: invariance of angular momentum coherent state, entangled state representation, new binomial theorem, time evolution

中图分类号: (Quantum mechanics)

03.65.-w

03.65.Ud (Entanglement and quantum nonlocality) 42.50.Dv (Quantum state engineering and measurements)

王继锁, 孟祥国, 范洪义. Time evolution of angular momentum coherent state derived by virtue of entangled state representation and a new binomial theorem[J]. 中国物理B, 2019, 28(10): 100301-100301.

Ji-Suo Wang(王继锁), Xiang-Guo Meng(孟祥国), Hong-Yi Fan(范洪义). Time evolution of angular momentum coherent state derived by virtue of entangled state representation and a new binomial theorem[J]. Chin. Phys. B, 2019, 28(10): 100301-100301.

参考文献 20

[1]	Glauber R J 1963 Phys. Rev. 130 2529 doi: 10.1103/PhysRev.130.2529
[2]	Klauder J R and Sudarshan E C G 1968 Fundamentals of Quantum Optics (New York: Benjamin)
[3]	Wang J S, Meng X G, Liang B L and Yan K Z 2016 J. Mod. Opt. 63 2367 doi: 10.1080/09500340.2016.1203464
[4]	Zhou J, Fan H Y and Song J 2017 Chin. Phys. B 26 070301 doi: 10.1088/1674-1056/26/7/070301
[5]	Radcliffe J M 1971 J. Phys. A: Math. Gen. 4 313 doi: 10.1088/0305-4470/4/3/009
[6]	Meng X G, Wang J S and Liang B L 2010 Chin. Phys. B 19 124205 doi: 10.1088/1674-1056/19/12/124205
[7]	Wang J S, Meng X G and Liang B L 2010 Chin. Phys. B 19 014207 doi: 10.1088/1674-1056/19/1/014207
[8]	Holtz R and Hanus J 1974 J. Phys. A: Math. Nucl. Gen. 7 L37
[9]	Honarasa G 2017 Chin. Phys. B 26 114202 doi: 10.1088/1674-1056/26/11/114202
[10]	Fan H Y and Klauder J R 1994 Phys. Rev. A 49 704 doi: 10.1103/PhysRevA.49.704
[11]	Meng X G, Wang J S, Liang B L, and Han C X 2018 Front. Phys. 13 130322 doi: 10.1007/s11467-018-0856-1
[12]	Meng X G, Wang Z, Wang J S, Fan H Y and Yang Z S 2012 J. Opt. Soc. Am. B 29 1844 doi: 10.1364/JOSAB.29.001844
[13]	Meng X G, Wang J S and Liang B L 2013 Chin. Phys. B 22 030307 doi: 10.1088/1674-1056/22/3/030307
[14]	Hu L Y, Wu J N, Liao Z Y and Zubairy M S 2016 J. Phys. B: At. Mol. Opt. Phys. 49 175504 doi: 10.1088/0953-4075/49/17/175504
[15]	Meng X G, Wang J S, Liang B L and Du C X 2018 J. Exp. Theor. Phys. 154 NN8-9
[16]	Hu L Y, Liao Z Y and Zubairy M S 2017 Phys. Rev. A 95 012310 doi: 10.1103/PhysRevA.95.012310
[17]	Meng X G, Wang Z, Fan H Y and Wang J S 2012 J. Opt. Soc. Am. B 29 3141 doi: 10.1364/JOSAB.29.003141
[18]	Zhang R, Meng X G, Du C X and Wang J S 2012 J. Phys. Soc. Jpn. 87 024001
[19]	Wang Z, Meng X G and Fan H Y 2012 J. Opt. Soc. Am. B 29 397 doi: 10.1364/JOSAB.29.000397
[20]	Meng X G, Wang J S and Liang B L 2010 Opt. Commun. 283 4025 doi: 10.1016/j.optcom.2010.05.058

Time evolution of angular momentum coherent state derived by virtue of entangled state representation and a new binomial theorem

Time evolution of angular momentum coherent state derived by virtue of entangled state representation and a new binomial theorem

RichHTML

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献 20

相关文章 15

Metrics

本文评价

推荐阅读 0

[1]	Hai-Jun Yu(余海军) and Hong-Yi Fan(范洪义). Time evolution law of a two-mode squeezed light field passing through twin diffusion channels[J]. 中国物理B, 2022, 31(2): 20301-020301.
[2]	吕翠红, 张苏青, 许雯. Fractional squeezing-Hankel transform based on the induced entangled state representations[J]. 中国物理B, 2018, 27(9): 94206-094206.
[3]	孟祥国, 王继锁, 范洪义, 夏承魏. Kraus operator solutions to a fermionic master equation describing a thermal bath and their matrix representation[J]. 中国物理B, 2016, 25(4): 40302-040302.
[4]	刘堂昆, 吴盼盼, 单传家, 刘继兵, 范洪义. Time evolution of negative binomial optical field in a diffusion channel[J]. 中国物理B, 2015, 24(9): 90302-090302.
[5]	许雪芬, 范洪义. A new optical field generated as an output of the displaced Fock state in an amplitude dissipative channel[J]. 中国物理B, 2015, 24(1): 10301-010301.
[6]	Seyed Mahmoud Ashrafi, Mohammad Reza Bazrafkan. New approach to solving master equations of density operator for the Jaynes Cummings model with cavity damping[J]. , 2014, 23(9): 90303-090303.
[7]	陈锋, 范洪义. Evolution law of a negative binomial state in an amplitude dissipative channel[J]. 中国物理B, 2014, 23(3): 30304-030304.
[8]	范洪义, 何锐, 笪诚, 梁祖峰. Optical field’s quadrature excitation studied by new Hermite-polynomial operator identity[J]. 中国物理B, 2013, 22(8): 80301-080301.
[9]	袁洪春, 李恒梅, 许雪芬. New operator identities regarding to two-variable Hermite polynomial by virtue of entangled state representation[J]. 中国物理B, 2013, 22(6): 60301-060301.
[10]	杨阳, 范洪义. Squeezing entangled state of two particles with unequal masses[J]. 中国物理B, 2013, 22(3): 30306-030306.
[11]	孟祥国, 王继锁, 梁宝龙. New approach for deriving the exact time evolution of density operator for diffusive anharmonic oscillator and its Wigner distribution function[J]. Chin. Phys. B, 2013, 22(3): 30307-030307.
[12]	龚黎华, 周南润, 胡利云, 范洪义 . New approach for obtaining the time-evolution law of chaotic light field in damping–gaining process[J]. 中国物理B, 2012, 21(8): 80302-080302.
[13]	李学超, 谢传梅, 范洪义 . Squeeze-swapping by Bell measurement studied in terms of the entangled state representation[J]. 中国物理B, 2012, 21(8): 80304-080304.
[14]	胡利云, 王帅, 张智明. Photon-number distribution of two-mode squeezed thermal states by entangled state representation[J]. 中国物理B, 2012, 21(6): 64207-064207.
[15]	贾宁, 马寿峰, 钟石泉. Analytical investigation of the boundary-triggered phase transition dynamics in a cellular automata model with a slow-to-start rule[J]. 中国物理B, 2012, 21(10): 100206-100206.