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Non-classical eigen state and the persistent current in one-dimensional mesoscopic ring with the electron-two-phonon interaction

Luo Zhi-Hua Liang Guo-Dong

Non-classical eigen state and the persistent current in one-dimensional mesoscopic ring with the electron-two-phonon interaction

Luo Zhi-Hua, Liang Guo-Dong
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  • For the one-dimensional mesoscopic ring with the ferromagnetic texture, to restrain the quantum fluctuations caused by the electron-one-phonon interaction, the non-classical correlation effects are used in our research to solve this puzzling problem, i.e. 1) the hopping electron-displaced phonon state correlation; 2) the process correlation between the phonon squeezed state, and the one-phonon coherent state, originating from the squeezed coherent state of phonon; 3) the renormalization of the phonon displacement. It is found that due to the electron-two phonon interaction, the squeezing effect of phonon is enhanced significantly. Because of the effect of the electron-displaced phonon correlation the non-classical eigen state energy declines significantly and the amplitude of the persistent current increases substantially. Particularly the process correlation between the squeezed phonon state and the one-phonon coherent state is by far the most important contribution to these non-classical effects. First of all, this effect more greatly increases the squeezing effect of phonon field in contrast to the ideal squeezed state. As a result, it will restrain effectively the Debye-Waller effect (factor wph) with wph wph(0). Furthermore, when we combine the effective renormalization of the phonon displacement with the effect of process correlation between the phonon squeezed state and the one-phonon coherent state, the phonon squeezing effect will increases substantially, at the same time, the D-W effect decreased more substantially (wph wph(0), thereby weakening the quantum fluctuation to a bigger degree. With these results, the non-classical eigen energy (En) is much lowered (En En(0)), while the amplitude of eigen persistent current is increased most significantly (In In(0)).
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 10574163).
    [1]

    Buttiker M, Imry Y, Landauer R 1983 Phys. Lett. A 96 365

    [2]

    Chandrasekhar V, Webb R A, Brady M J, Ketchen M B, GailagherW J, Kleinsasser A 1991 Phys. Rev. Lett. 67 3578

    [3]

    Cheung H F, Gefen Y, Riedel E K, Shih W H 1988 Phys. Rev. B37 6050

    [4]

    Ambegaoker V, Eckern U 1990 Phys. Lett. 65 381

    [5]

    Altshuler B L, Gelfan Y, Imry Y 1991 Phys. Rev. Lett. 66 88

    [6]

    Bouzerar G, Poilblanc D, Monlambaux G 1994 Phys. Rev. B 498258

    [7]

    Lévy L P, Dolan G, Dansmuir J, Bouchait H 1990 Phys. Rev. Lett.64 2074

    [8]

    Mailly D, Chapelier C, Benoid A 1993 Phys. Rev. Lett. 70 2120

    [9]

    Grüner G 1994 Rev. Mod. Phys. 66 1

    [10]

    Ye J F, Ye F, Ding G H 2003 Acta Phys. Sin. 52 468 (in Chinese) [叶剑斐, 叶飞, 丁国辉 2003 物理学报 52 468]

    [11]

    Giamarchi T, Shastry B S 1995 Phys. Rev. B 51 10915

    [12]

    Wang J, Ma Z S 1995 Phys. Rev. B 52 14892

    [13]

    Liang S D, Bai Y H, Beng B 2006 Phys. Rev. B 74 113304

    [14]

    Citro R, Romeo F 2007 Phys. Rev. B 75 073306

    [15]

    Sun Q F, Xie X C, Wang J 2007 Phys. Rev. Lett. 98 196801

    [16]

    Niliionl J, Eckler H P, Johanness O 2007 Phys. Rev. B 76 73408

    [17]

    Zhao H K 2005 Phys. Lett. A 342 468

    [18]

    Liang F Y, Li H M, Li Y J 2006 Acta Phys. Sin. 55 830 (in Chinese) [梁芳营, 李汉明, 李英骏 2006 物理学报 55 830]

    [19]

    Wu S Q, Sun W L, Yu W L,Wang S J 2005 Acta Phys. Sin. 542910 (in Chinese) [吴绍全, 孙威立, 余万伦, 王顺金 2005 物理学报 54 2910]

    [20]

    Chen X W, He D J, Wu S Q, Song K H 2006 Acta Phys. Sin. 554287 (in Chinese) [谌雄文, 贺达江, 吴绍全, 宋克慧 2006 物理学报 55 4287]

    [21]

    Dajkal J, Szopal M, Voardas Z 2004 Phys. Rev. B 69 45305

    [22]

    Sheng J S, Kai C 2006 Phys. Rev. B 74 235315

    [23]

    Wu J N, Chang M C 2005 Phys. Rev. B 72 172405

    [24]

    Wu H 2008 Chin. Phys. B 17 3026

    [25]

    Liu P, Xiong S J 2009 Chin. Phys. B 18 5414

    [26]

    Xu N, Ding JW,Ma M M, Jang X 2010 Chin. Phys. B 19 016101

    [27]

    Ma M M, Ding J W, Chen H B, Xu N 2009 Acta Phys. Sin. 582726 (in Chinese) [马明明, 丁建文, 陈宏波, 徐宁 2009 物理学报 58 2726]

    [28]

    Xu N, Ding JW, Chen H B, MaM M2009 Chin. Phys. B 18 2030

    [29]

    Xu N, Ding JW,MaM M, Tang X 2010 Chin. Phys. B 19 016101

    [30]

    Du J, Wang S X, Yuan A G 2010 Acta Phys. Sin. 59 2767 (inChinese) [杜坚, 王素新, 袁爱国 2010 物理学报 59 2767]

    [31]

    Chen X W, Chen B J, Shi Z G, Song K H 2009 Acta Phys. Sin. 592767 (in Chinese)[谌雄文, 谌宝菊, 施振刚, 宋克慧 2009 物理学报 58 2720]

    [32]

    Luo Z H, Cao X J, Yu C F 2011 Chin. Phys. B 20 067103

    [33]

    Hamutal B S, Ora E W, Imryl Y 2009 Phys. Rev. B 80 02459

    [34]

    Bouchiat H 2008 Mesoscop. Phys. 1 7

    [35]

    Zelgak O M 2008 Phys. Rev. B 78 125305

    [36]

    Feilhauer J, Mo?sko M 2008 Physica E 40 1582

    [37]

    Luo Z H, Liang G D 2011 Acta Phys. Sin. 60 037303 (in Chinese) [罗质华, 梁国栋 2011 物理学报 60 037303]

    [38]

    Loss D, Goldbart P 1992 Phys. Rev. B 45 13544

    [39]

    Kusakabe K, Aoki H 1994 Phys. Rev. Lett. 72 144

    [40]

    Ivanov V A, Zhuravlev MY, Murayama Y, Nakajima S 1996 JETPLett. 64 148

    [41]

    Majernikava E, Koval J 1998 Physica 37 23

    [42]

    Mandel L, Wolf E 1995 Optical Coherence and Guantum Optics(Cambridge University Press) pp1042-1047

    [43]

    Yu C F, Liang G D, Cao X J 2008 Acta Phys. Sin. 4402 (in Chinese) [余超凡, 梁国栋, 曹锡金 2008 物理学报 57 4402]

    [44]

    Wu S S, Ma Z S 1996 Phys. Rev. B 53 16372

  • [1]

    Buttiker M, Imry Y, Landauer R 1983 Phys. Lett. A 96 365

    [2]

    Chandrasekhar V, Webb R A, Brady M J, Ketchen M B, GailagherW J, Kleinsasser A 1991 Phys. Rev. Lett. 67 3578

    [3]

    Cheung H F, Gefen Y, Riedel E K, Shih W H 1988 Phys. Rev. B37 6050

    [4]

    Ambegaoker V, Eckern U 1990 Phys. Lett. 65 381

    [5]

    Altshuler B L, Gelfan Y, Imry Y 1991 Phys. Rev. Lett. 66 88

    [6]

    Bouzerar G, Poilblanc D, Monlambaux G 1994 Phys. Rev. B 498258

    [7]

    Lévy L P, Dolan G, Dansmuir J, Bouchait H 1990 Phys. Rev. Lett.64 2074

    [8]

    Mailly D, Chapelier C, Benoid A 1993 Phys. Rev. Lett. 70 2120

    [9]

    Grüner G 1994 Rev. Mod. Phys. 66 1

    [10]

    Ye J F, Ye F, Ding G H 2003 Acta Phys. Sin. 52 468 (in Chinese) [叶剑斐, 叶飞, 丁国辉 2003 物理学报 52 468]

    [11]

    Giamarchi T, Shastry B S 1995 Phys. Rev. B 51 10915

    [12]

    Wang J, Ma Z S 1995 Phys. Rev. B 52 14892

    [13]

    Liang S D, Bai Y H, Beng B 2006 Phys. Rev. B 74 113304

    [14]

    Citro R, Romeo F 2007 Phys. Rev. B 75 073306

    [15]

    Sun Q F, Xie X C, Wang J 2007 Phys. Rev. Lett. 98 196801

    [16]

    Niliionl J, Eckler H P, Johanness O 2007 Phys. Rev. B 76 73408

    [17]

    Zhao H K 2005 Phys. Lett. A 342 468

    [18]

    Liang F Y, Li H M, Li Y J 2006 Acta Phys. Sin. 55 830 (in Chinese) [梁芳营, 李汉明, 李英骏 2006 物理学报 55 830]

    [19]

    Wu S Q, Sun W L, Yu W L,Wang S J 2005 Acta Phys. Sin. 542910 (in Chinese) [吴绍全, 孙威立, 余万伦, 王顺金 2005 物理学报 54 2910]

    [20]

    Chen X W, He D J, Wu S Q, Song K H 2006 Acta Phys. Sin. 554287 (in Chinese) [谌雄文, 贺达江, 吴绍全, 宋克慧 2006 物理学报 55 4287]

    [21]

    Dajkal J, Szopal M, Voardas Z 2004 Phys. Rev. B 69 45305

    [22]

    Sheng J S, Kai C 2006 Phys. Rev. B 74 235315

    [23]

    Wu J N, Chang M C 2005 Phys. Rev. B 72 172405

    [24]

    Wu H 2008 Chin. Phys. B 17 3026

    [25]

    Liu P, Xiong S J 2009 Chin. Phys. B 18 5414

    [26]

    Xu N, Ding JW,Ma M M, Jang X 2010 Chin. Phys. B 19 016101

    [27]

    Ma M M, Ding J W, Chen H B, Xu N 2009 Acta Phys. Sin. 582726 (in Chinese) [马明明, 丁建文, 陈宏波, 徐宁 2009 物理学报 58 2726]

    [28]

    Xu N, Ding JW, Chen H B, MaM M2009 Chin. Phys. B 18 2030

    [29]

    Xu N, Ding JW,MaM M, Tang X 2010 Chin. Phys. B 19 016101

    [30]

    Du J, Wang S X, Yuan A G 2010 Acta Phys. Sin. 59 2767 (inChinese) [杜坚, 王素新, 袁爱国 2010 物理学报 59 2767]

    [31]

    Chen X W, Chen B J, Shi Z G, Song K H 2009 Acta Phys. Sin. 592767 (in Chinese)[谌雄文, 谌宝菊, 施振刚, 宋克慧 2009 物理学报 58 2720]

    [32]

    Luo Z H, Cao X J, Yu C F 2011 Chin. Phys. B 20 067103

    [33]

    Hamutal B S, Ora E W, Imryl Y 2009 Phys. Rev. B 80 02459

    [34]

    Bouchiat H 2008 Mesoscop. Phys. 1 7

    [35]

    Zelgak O M 2008 Phys. Rev. B 78 125305

    [36]

    Feilhauer J, Mo?sko M 2008 Physica E 40 1582

    [37]

    Luo Z H, Liang G D 2011 Acta Phys. Sin. 60 037303 (in Chinese) [罗质华, 梁国栋 2011 物理学报 60 037303]

    [38]

    Loss D, Goldbart P 1992 Phys. Rev. B 45 13544

    [39]

    Kusakabe K, Aoki H 1994 Phys. Rev. Lett. 72 144

    [40]

    Ivanov V A, Zhuravlev MY, Murayama Y, Nakajima S 1996 JETPLett. 64 148

    [41]

    Majernikava E, Koval J 1998 Physica 37 23

    [42]

    Mandel L, Wolf E 1995 Optical Coherence and Guantum Optics(Cambridge University Press) pp1042-1047

    [43]

    Yu C F, Liang G D, Cao X J 2008 Acta Phys. Sin. 4402 (in Chinese) [余超凡, 梁国栋, 曹锡金 2008 物理学报 57 4402]

    [44]

    Wu S S, Ma Z S 1996 Phys. Rev. B 53 16372

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  • Received Date:  30 June 2011
  • Accepted Date:  11 July 2011
  • Published Online:  05 March 2012

Non-classical eigen state and the persistent current in one-dimensional mesoscopic ring with the electron-two-phonon interaction

  • 1. Department of Physics, Guangdong University of Education, Guangzhou 510303, China;
  • 2. Department of Optoelectronic Enginecring, Jinan University, Guangzhou 510632, China
Fund Project:  Project supported by the National Natural Science Foundation of China (Grant No. 10574163).

Abstract: For the one-dimensional mesoscopic ring with the ferromagnetic texture, to restrain the quantum fluctuations caused by the electron-one-phonon interaction, the non-classical correlation effects are used in our research to solve this puzzling problem, i.e. 1) the hopping electron-displaced phonon state correlation; 2) the process correlation between the phonon squeezed state, and the one-phonon coherent state, originating from the squeezed coherent state of phonon; 3) the renormalization of the phonon displacement. It is found that due to the electron-two phonon interaction, the squeezing effect of phonon is enhanced significantly. Because of the effect of the electron-displaced phonon correlation the non-classical eigen state energy declines significantly and the amplitude of the persistent current increases substantially. Particularly the process correlation between the squeezed phonon state and the one-phonon coherent state is by far the most important contribution to these non-classical effects. First of all, this effect more greatly increases the squeezing effect of phonon field in contrast to the ideal squeezed state. As a result, it will restrain effectively the Debye-Waller effect (factor wph) with wph wph(0). Furthermore, when we combine the effective renormalization of the phonon displacement with the effect of process correlation between the phonon squeezed state and the one-phonon coherent state, the phonon squeezing effect will increases substantially, at the same time, the D-W effect decreased more substantially (wph wph(0), thereby weakening the quantum fluctuation to a bigger degree. With these results, the non-classical eigen energy (En) is much lowered (En En(0)), while the amplitude of eigen persistent current is increased most significantly (In In(0)).

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