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研究驻波型激光脉冲作用下，囚禁于Paul阱中的单离子在Lamb-Dicke区域的久期运动.通过试探解方法，得到系统的量子力学精确解.基于精确解描述的概率波包串，发现：1）波包串中心以及波包串的高度和宽度受激光脉冲强度的控制，通过调节激光强度可以控制波包串的形变和传播；2）在激光脉冲作用瞬间，离子的能量期待值发生跳变，而在激光关闭时段，有窄的能带形成；3）存在一个激光脉冲强度的临界值，在临界点附近，系统的稳定性发生变化.
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关键词:
- 囚禁离子 /
- 激光脉冲 /
- Lamb-Dicke近似 /
- 精确解
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:
- trapped ion /
- laser pulse /
- Lamb-Dicke approximation /
- exact solution
[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 57 5589］
[2] ［2］Protsenko I E, Reymond G, Schlosser N, Grangier P 2002 Phys. Rev. A 66 062306
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[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］Ngerl 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
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[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 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 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 55 3438］
[15] ］Fang M F, Liu X 2001 Acta Phys. Sin. 50 2363 (in Chinese) ［方卯发、 刘翔 2001 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 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 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 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 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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[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 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, Rtteler 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］Ngerl 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 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 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 55 3438］
[15] ］Fang M F, Liu X 2001 Acta Phys. Sin. 50 2363 (in Chinese) ［方卯发、 刘翔 2001 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 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 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 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 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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