Exact quantum motion of a single trapped ion interacting with standing laser pulses in Lamb-Dicke regime

Yang Mei-Rong; Hai Wen-Hua; Lu Geng-Biao; Zhong Hong-Hua

doi:10.7498/aps.59.2406

Abstract

We investigate the secular motion of a single Paul-trapped ion in the Lamb-Dicke regime, which interacts with a sequence of standing laser pulses. By using the ansatz method, we get an exact quantum solution of the system. Based on the wave-packet trains described by the exact solution, we find that: i) The center, height and width of the wave-packet trains depend on the strength of laser pulses, the deformation and spread of the wave-packet trains can be controlled by adjusting the strength of laser. ii) Energy expectation values of the ion show jumps at the instantaneous switching on of the laser pulses. In the time intervals when the laser pulses are switched off some narrow energy bands are generated. iii) When the strength of laser pulses reaches a critical value, the system changes its stability.

Keywords:

Authors and contacts

1.
湖南师范大学物理系，长沙 410081

References

[1]	［1］Ai L Y, Yang J, Zhang Z M 2008 Acta Phys. Sin. 57 5589 (in Chinese) ［艾凌艳、杨健、张智明 2008 物理学报 57 5589］
[2]	［2］Protsenko I E, Reymond G, Schlosser N, Grangier P 2002 Phys. Rev. A 66 062306
[3]	［3］Childs A M, Chuang I L 2000 Phys. Rev. A 63 012306
[4]	［4］Klappenecker A, Rtteler M 2003 Phys. Rev. A 67 010302
[5]	［5］Lévi B, Georgeot B, Shepelyansky D L 2003 Phys. Rev. E 67 046220
[6]	［6］Steane A, Roos C F, Stevens D, Mundt A, Leibfried D, Schmidt-Kaler F, Blatt R 2000 Phys. Rev. A 62 042305
[7]	［7］Ngerl H C, Leibfried D, Rohde H, Thalhammer G, Eschner J, Schmidt-Kaler F, Blatt R 1999 Phys. Rev. A 60 145
[8]	［8］Feng M, Wang X G 2002 J. Opt. B: Quantum Semiclass. Opt. 4 283
[9]	［9］
[10]	Feng M, Luo X L, Zhu X W, Shi L, Yan M 1998 Acta Phys. Sin. (Oversea) 7 488
[11]	］Wu Y, Yang X X 1997 Phys. Rev. Lett. 78 3086
[12]	］Shi L, Duan Y W, Feng M, Zhu X W, Fang X M 1998 Acta Phys. Sin. 47 1248 (in Chinese) ［施磊、段宜武、冯芒、朱熙文、方细明 1998 物理学报 47 1248］
[13]	］Gao K L, Yan M, Luo X L, Zhu X W, Huang G L, Li J M, Shi L 1995 Acta Phys. Sin. 44 43 (in Chinese)［高克林、颜旻、罗学立、朱熙文、黄贵龙、李交美、施磊 1995 物理学报 44 43］
[14]	］Wang Z Q, Duan C K, An G L 2006 Acta Phys. Sin. 55 3438 (in Chinese) ［汪仲清、段昌奎、安广雷 2006 物理学报 55 3438］
[15]	］Fang M F, Liu X 2001 Acta Phys. Sin. 50 2363 (in Chinese) ［方卯发、刘翔 2001 物理学报 50 2363］
[16]	］Hai W H, Duan Y W, Zhu X W, Luo X L, Shi L 1998 J. Phys. A 31 2991
[17]	］Hai W H, Duan Y W, Zhu X W, Shi L, Luo X L, He C S 1997 Acta Phys. Sin. 46 2117 (in Chinese) ［海文华、段宜武、朱熙文、施磊、罗学立、何春山 1997 物理学报 46 2117］
[18]	］Hai W H, Feng M, Zhu X W, Shi L, Gao K L, Fang X M 1999 J. Phys. 　A　32 8265
[19]	］Berman G P, James D F V, Hughes R J, Gulley M S, Holzscheiter M H, López G V 2000 Phys. Rev. A　61 023403
[20]	］Chacón R, Cirac J I 1995 Phys. Rev. A　51 4900
[21]	］Rabitz H, de Vivie-Riedle R, Motzkus M, Kompa K 2008 Science 288 824
[22]	］Kral P, Thanopulos I, Shapiro M 2007 Rev. Mod. Phys. 79 53
[23]	］Scott A J, Holmes C A, Milburn G J 1999 Phys. Rev. A　61 013401
[24]	］Li F, Hai W H 2004 Acta Phys. Sin. 53 1309 (in Chinese) ［李飞、海文华 2004 物理学报 53 1309］
[25]	］Chen W Q, Hai W H, Li H, Ma Z Y 2007 Acta Phys. Sin. 56 1305 (in Chinese)［陈文钦、海文华、李辉、马志英 2007 物理学报 56 1305］
[26]	］Chen W Q, Hai W H, Song J W 2008 Acta Phys. Sin. 57 1608 (in Chinese) ［陈文钦、海文华、宋建文 2008 物理学报 57 1608］
[27]	］Gardiner S A, Cirac J I, Zoller P 1997 Phys. Rev. Lett. 79 4790
[28]	］Li F, Hai W H, Chong G S, Xie Q T 2004 Commun. Theor. Phys. 42 599
[29]	］Andrér R, Carvalho, Buchleitner A 2004 Phys. Rev. Lett. 93 204101
[30]	］Lizuain I, Muga J G 2007 Phys. Rev. A　76 033808
[31]	］Leibfried D, Blatt R, Monroe C, Wineland D 2003 Rev. Mod. Phys. 75 281
[32]	］Gardiner S A, Jaksch D, Dum R, Cirac J I, Zoller P 2000 Phys. Rev. 　A　62 023612
[33]	］Hai W H, Feng M, Zhu X W, Shi L, Gao K L, Fang X M 2000 Phys. Rev. A　61 052105
[34]	］Hai W H, Zhu X W, Feng M, Shi L, Gao K L, Fang X M 2001 J. Phys. A　34 L79
[35]	］Hai W H, Huang S X, Gao K L 2003 J. Phys. B　36 3055
[36]	］Hai W H, Lee C H, Chong G S 2004 Phys. Rev. A　70 053621

Cited By

[1]	［1］Ai L Y, Yang J, Zhang Z M 2008 Acta Phys. Sin. 57 5589 (in Chinese) ［艾凌艳、杨健、张智明 2008 物理学报 57 5589］
[2]	［2］Protsenko I E, Reymond G, Schlosser N, Grangier P 2002 Phys. Rev. A 66 062306
[3]	［3］Childs A M, Chuang I L 2000 Phys. Rev. A 63 012306
[4]	［4］Klappenecker A, Rtteler M 2003 Phys. Rev. A 67 010302
[5]	［5］Lévi B, Georgeot B, Shepelyansky D L 2003 Phys. Rev. E 67 046220
[6]	［6］Steane A, Roos C F, Stevens D, Mundt A, Leibfried D, Schmidt-Kaler F, Blatt R 2000 Phys. Rev. A 62 042305
[7]	［7］Ngerl H C, Leibfried D, Rohde H, Thalhammer G, Eschner J, Schmidt-Kaler F, Blatt R 1999 Phys. Rev. A 60 145
[8]	［8］Feng M, Wang X G 2002 J. Opt. B: Quantum Semiclass. Opt. 4 283
[9]	［9］
[10]	Feng M, Luo X L, Zhu X W, Shi L, Yan M 1998 Acta Phys. Sin. (Oversea) 7 488
[11]	］Wu Y, Yang X X 1997 Phys. Rev. Lett. 78 3086
[12]	］Shi L, Duan Y W, Feng M, Zhu X W, Fang X M 1998 Acta Phys. Sin. 47 1248 (in Chinese) ［施磊、段宜武、冯芒、朱熙文、方细明 1998 物理学报 47 1248］
[13]	］Gao K L, Yan M, Luo X L, Zhu X W, Huang G L, Li J M, Shi L 1995 Acta Phys. Sin. 44 43 (in Chinese)［高克林、颜旻、罗学立、朱熙文、黄贵龙、李交美、施磊 1995 物理学报 44 43］
[14]	］Wang Z Q, Duan C K, An G L 2006 Acta Phys. Sin. 55 3438 (in Chinese) ［汪仲清、段昌奎、安广雷 2006 物理学报 55 3438］
[15]	］Fang M F, Liu X 2001 Acta Phys. Sin. 50 2363 (in Chinese) ［方卯发、刘翔 2001 物理学报 50 2363］
[16]	］Hai W H, Duan Y W, Zhu X W, Luo X L, Shi L 1998 J. Phys. A 31 2991
[17]	］Hai W H, Duan Y W, Zhu X W, Shi L, Luo X L, He C S 1997 Acta Phys. Sin. 46 2117 (in Chinese) ［海文华、段宜武、朱熙文、施磊、罗学立、何春山 1997 物理学报 46 2117］
[18]	］Hai W H, Feng M, Zhu X W, Shi L, Gao K L, Fang X M 1999 J. Phys. 　A　32 8265
[19]	］Berman G P, James D F V, Hughes R J, Gulley M S, Holzscheiter M H, López G V 2000 Phys. Rev. A　61 023403
[20]	］Chacón R, Cirac J I 1995 Phys. Rev. A　51 4900
[21]	］Rabitz H, de Vivie-Riedle R, Motzkus M, Kompa K 2008 Science 288 824
[22]	］Kral P, Thanopulos I, Shapiro M 2007 Rev. Mod. Phys. 79 53
[23]	］Scott A J, Holmes C A, Milburn G J 1999 Phys. Rev. A　61 013401
[24]	］Li F, Hai W H 2004 Acta Phys. Sin. 53 1309 (in Chinese) ［李飞、海文华 2004 物理学报 53 1309］
[25]	］Chen W Q, Hai W H, Li H, Ma Z Y 2007 Acta Phys. Sin. 56 1305 (in Chinese)［陈文钦、海文华、李辉、马志英 2007 物理学报 56 1305］
[26]	］Chen W Q, Hai W H, Song J W 2008 Acta Phys. Sin. 57 1608 (in Chinese) ［陈文钦、海文华、宋建文 2008 物理学报 57 1608］
[27]	］Gardiner S A, Cirac J I, Zoller P 1997 Phys. Rev. Lett. 79 4790
[28]	］Li F, Hai W H, Chong G S, Xie Q T 2004 Commun. Theor. Phys. 42 599
[29]	］Andrér R, Carvalho, Buchleitner A 2004 Phys. Rev. Lett. 93 204101
[30]	］Lizuain I, Muga J G 2007 Phys. Rev. A　76 033808
[31]	］Leibfried D, Blatt R, Monroe C, Wineland D 2003 Rev. Mod. Phys. 75 281
[32]	］Gardiner S A, Jaksch D, Dum R, Cirac J I, Zoller P 2000 Phys. Rev. 　A　62 023612
[33]	］Hai W H, Feng M, Zhu X W, Shi L, Gao K L, Fang X M 2000 Phys. Rev. A　61 052105
[34]	］Hai W H, Zhu X W, Feng M, Shi L, Gao K L, Fang X M 2001 J. Phys. A　34 L79
[35]	］Hai W H, Huang S X, Gao K L 2003 J. Phys. B　36 3055
[36]	］Hai W H, Lee C H, Chong G S 2004 Phys. Rev. A　70 053621

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Vol. 59, Issue 4 - 2010-02-20

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