New approach for deriving the exact time evolution of density operator for diffusive anharmonic oscillator and its Wigner distribution function

doi:10.1088/1674-1056/22/3/030307

Chin. Phys. B ›› 2013, Vol. 22 ›› Issue (3): 30307-030307.doi: 10.1088/1674-1056/22/3/030307

New approach for deriving the exact time evolution of density operator for diffusive anharmonic oscillator and its Wigner distribution function

孟祥国^a, 王继锁^{a b}, 梁宝龙^a

a Department of Physics, Liaocheng University, Liaocheng 252059, China;
b Shandong Provincial Key Laboratory of Laser Polarization and Information Technology, College of Physics and Engineering,Qufu Normal University, Qufu 273165, China

收稿日期:2012-06-19 修回日期:2012-08-21 出版日期:2013-02-01 发布日期:2013-02-01
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11147009 and 11244005) and the Natural Science Foundation of Shandong Province, China (Grant No. ZR2012AM004).

New approach for deriving the exact time evolution of density operator for diffusive anharmonic oscillator and its Wigner distribution function

Meng Xiang-Guo (孟祥国)^a, Wang Ji-Suo (王继锁)^{a b}, Liang Bao-Long (梁宝龙)^a

a Department of Physics, Liaocheng University, Liaocheng 252059, China;
b Shandong Provincial Key Laboratory of Laser Polarization and Information Technology, College of Physics and Engineering,Qufu Normal University, Qufu 273165, China

Received:2012-06-19 Revised:2012-08-21 Online:2013-02-01 Published:2013-02-01
Contact: Meng Xiang-Guo E-mail:mengxiangguo1978@sina.com
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11147009 and 11244005) and the Natural Science Foundation of Shandong Province, China (Grant No. ZR2012AM004).

摘要/Abstract

摘要： Using the thermal entangled state representation, we solve the master equation of a diffusive anharmonic oscillator (AHO) to obtain the exact time evolution formula for the density operator in the infinitive operator-sum representation. We present a new evolution formula of the Wigner function (WF) for any initial state of the diffusive AHO by converting the calculation of the WF to an overlap between two pure states in an enlarged Fock space. It is found that this formula brings us much convenience to investigate the WF's evolution of any known initial state. As applications, this formula is used to obtain the evolution of the WF for a coherent state and the evolution of the photon-number distribution of the diffusive AHO.

关键词: diffusive anharmonic oscillator, thermal entangled state representation, infinitive operator-sum representation, Wigner function

Abstract: Using the thermal entangled state representation, we solve the master equation of a diffusive anharmonic oscillator (AHO) to obtain the exact time evolution formula for the density operator in the infinitive operator-sum representation. We present a new evolution formula of the Wigner function (WF) for any initial state of the diffusive AHO by converting the calculation of the WF to an overlap between two pure states in an enlarged Fock space. It is found that this formula brings us much convenience to investigate the WF's evolution of any known initial state. As applications, this formula is used to obtain the evolution of the WF for a coherent state and the evolution of the photon-number distribution of the diffusive AHO.

Key words: diffusive anharmonic oscillator, thermal entangled state representation, infinitive operator-sum representation, Wigner function

中图分类号: (Entanglement and quantum nonlocality)

03.65.Ud

42.50.Dv (Quantum state engineering and measurements)

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.

Meng Xiang-Guo (孟祥国), Wang Ji-Suo (王继锁), Liang Bao-Long (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.

参考文献 22

[1]	Landau L D and Lifschitz E M 1976 Mechanics (Oxford: Pergamon Press)
[2]	Wang L M, Cai J and Qiao H X 2011 Chin. Phys. B 20 073202
[3]	He L, Zhang F M, Yang Y F and Li C F 2010 Chin. Phys. B 19 040306
[4]	Tanaś R, Miranowicz A and Kielich S 1991 Phys. Rev. A 43 4014
[5]	Chung N N and Chew L Y 2007 Phys. Rev. A 76 032113
[6]	Jentschura U D, Surzhykov A and Zinn-Justin J 2009 Phys. Rev. Lett. 102 011601
[7]	Ho K C, Liu Y T, Lo C F, Liu K L, Kwok W M and Shiu M L 1996 Phys. Rev. A 53 1280
[8]	Luo H G and Wang S J 2000 Phys. Rev. B 62 5341
[9]	Abraham K J and Vary J P 2003 Phys. Rev. C 67 054313
[10]	Núñez M A 2003 Phys. Rev. E 68 016703
[11]	Claudon J, Zazunov A, Hekking F W J and Buisson O 2008 Phys. Rev. B 78 184503
[12]	Peixoto de Faria J G 2007 Eur. Phys. J. D 42 153
[13]	Daniel D J and Milburn G J 1989 Phys. Rev. A 39 4628
[14]	Oliveira A C, Peixoto de Faria J G and Nemes M C 2006 Phys. Rev. E 73 046207
[15]	Chaturvedi S and Srinivasan V 1991 Phys. Rev. A 43 4054
[16]	Jiang N Q, Fan H Y and Hu L Y 2011 J. Phys A: Math. Theor. 44 195302
[17]	Meng X G, Wang J S and Liang B L 2011 Chin. Phys. B 20 014204
[18]	Hu L Y and Fan H Y 2009 Chin. Phys. B 18 1674
[19]	Wodkiewicz K and Eberly J H 1985 J. Opt. Soc. Am. B 2 458
[20]	Moya-Cessa H 2006 Phys. Rep. 432 1
[21]	Hu L Y and Fan H Y 2009 Opt. Commun. 282 4379
[22]	Takahashi Y and Umezawa H 1975 Collect. Phenom. 2 55

New approach for deriving the exact time evolution of density operator for diffusive anharmonic oscillator and its Wigner distribution function

New approach for deriving the exact time evolution of density operator for diffusive anharmonic oscillator and its Wigner distribution function

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