Quantum damping motion of a single trapped ion

Li Jin-Qing; Luo Yun-Rong; Hai Wen-Hua

doi:10.7498/aps.66.233701

Abstract

Classical motion of a single damped ion confined in a Paul trap is usually described by a damped harmonic oscillator model. We report the treatment of quantum damping motion of the system via a non-Hermitian Hamiltonian with dipole and quadrupole imaginary potential. By deriving and analyzing the exact solution of the system, we obtain the different real energy spectra and stable quantum states for the PT symmetry and asymmetry cases, as well as the imaginary spectrum and decaying quantum state for the PT asymmetry case. The corresponding imaginary energy parameter region and the survival probability are investigated. We find that the non-Hermitian system parameters of the external filed uniquely determine the quantum stable states and lead to the new characteristic of the morphology of wave function. Based on these properties, we propose a method of incoherently manipulating quantum transitions between the quantum stable states. By setting the decayed expectation value of ion position to be the same as the decayed displacement of the classical damped harmonic oscillator, we obtain the correspondence between the imaginary potential strength and the classical damping parameters. The results will enrich the quantum dynamics of the damped trapped ions, which may be useful in a wide application field.

Keywords:

Authors and contacts

1.
Synergetic Innovation Center for Quantum Effects and Applications of Hunan Province, Key Laboratory of Low-dimensional Quantum Structures and Quantum Control of Ministry of Education, Department of Physics, Hunan Normal University, Changsha 410081, China

Corresponding author: Hai Wen-Hua, whhai2005@aliyun.com

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11475060), the Hunan Provincial Innovation Foundation for Postgraduate and Graduate Degree Thesis, China (Grant No. CX2017B222), and the Hunan Provincial Natural Science Foundation of China (Grant No. 2017JJ3208).

References

[1]	Wineland D J 2013 Rev. Mod. Phys. 85 1103
[2]	Duan L M, Monroe C 2010 Rev. Mod. Phys. 82 1209
[3]	Singer K, Poschinger U, Murphy M, Ivanov P, Ziesel F, Calarco T, Schmidt-Kaler F 2010 Rev. Mod. Phys. 82 2609
[4]	Leibfried D, Blatt R, Monroe C, Wineland D 2003 Rev. Mod. Phys. 75 281
[5]	Soderberg K A B, Monroe C 2010 Rep. Prog. Phys. 73 036401
[6]	DeVoe R G, Hoffnagle J, Brewer R G 1989 Phys. Rev. A 39 4362
[7]	Blmel R 1995 Phys. Rev. A 51 620
[8]	Nam Y S, Jones E B, Blmel R 2014 Phys. Rev. A 90 013402
[9]	Weiss D K, Nam Y S, Blmel R 2016 Phys. Rev. A 93 043424
[10]	Hai W H, Duan Y W, Zhu X W, Shi L, Luo X L, He C S 1997 Acta Phys. Sin. 46 2217 (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 2217]
[11]	Mihalcea B M, Vişan G G 2010 Phys. Scr. T 140 014057
[12]	Peng H W 1980 Acta Phys. Sin. 29 1084 (in Chinese)[彭桓武 1980 物理学报 29 1084]
[13]	Gzyl H 1983 Phys. Rev. A 27 2297
[14]	Akerman N, Kotler S, Glickman Y, Dallal Y, Keselman A, Ozeri R 2010 Phys. Rev. A 82 061402
[15]	Fidio C D, Vogel W 2000 Phys. Rev. A 62 031802
[16]	Gong S J, Zhou F, Wu H Y, Wan W, Chen L, Feng M 2015 Chin. Phys. Lett. 32 013201
[17]	Bazrafkan M R, Ashrafi S M, Naghdi F 2014 Chin. Phys. Lett. 31 070303
[18]	Klimov A B, Romero J L, Delgado J, Sánchez-Soto L L 2004 Opt. Commun. 230 393
[19]	Jiang Z, Chen P X 2012 Acta Phys. Sin. 61 014209 (in Chinese)[蒋智, 陈平形 2012 物理学报 61 014209]
[20]	Bushev P, Rotter D, Wilson A, Dubin F, Becher C, Eschner J, Blatt R, Steixner V, Rabl P, Zoller P 2006 Phys. Rev. Lett. 96 043003
[21]	Eleuch H, Rotter I 2017 Phys. Rev. A 95 022117
[22]	Dattoli G, Torre A, Mignani R 1990 Phys. Rev. A 42 1467
[23]	Li J H, Yu R, Ding C L, Wu Y 2016 Phys. Rev. A 93 023814
[24]	Santra R, Cederbaum L S 2002 Phys. Rep. 368 1
[25]	Longhi S 2016 Europhys. Lett. 115 61001
[26]	Jin L, Song Z 2009 Phys. Rev. A 80 052107
[27]	Jin L, Song Z 2010 Phys. Rev. A 81 032109
[28]	Zhong H H, Hai W H, Lu G B, Li Z J 2011 Phys. Rev. A 84 013401
[29]	Xiao K W, Hai W H, Liu J 2012 Phys. Rev. A 85 013410
[30]	Bender C M, Brody D C, Jones H F 2002 Phys. Rev. Lett. 89 270401
[31]	Chen Z J, Ning X J 2003 Acta Phys. Sin. 52 2683 (in Chinese)[陈增军, 宁西京 2003 物理学报 52 2683]
[32]	Baradaran M, Panahi H 2017 Chin. Phys. B 26 060301
[33]	Wang X Y, Chen H Z, Li Y, Li B, Ma R M 2016 Chin. Phys. B 25 124211
[34]	Graefe E M, Höning M, Korsch H J 2010 J. Phys. A:Math. Theor. 43 075306
[35]	Caldeira A O, Leggett A J 1985 Phys. Rev. A 31 1059
[36]	Gu Y 1996 Quantum Chaos (Shanghai:Shanghai Scientific and Technological Education Press) (in Chinese)[顾雁 1996 量子混沌 (上海:上海科技教育出版社)]
[37]	Casati G, Guarneri I, Maspero G 2000 Phys. Rev. Lett. 84 63
[38]	Wimberger S, Krug A, Buchleitner A 2002 Phys. Rev. Lett. 89 263601
[39]	Mizrahi J, Senko C, Neyenhuis B, Johnson K G, Campbell W C, Conover C W S, Monroe C 2013 Phys. Rev. Lett. 110 203001
[40]	Chen Q, Hai K, Hai W H 2010 J. Phys. A:Math. Theor. 43 455302
[41]	Hai K, Luo Y R, Chong G S, Chen H, Hai W H 2017 Quantum Inf. Comput. 17 456
[42]	Chen Y H, She L, Wang M, Yang Z H, Liu H, Li J M 2016 Chin. Phys. B 25 120601
[43]	Yang M R, Hai W H, Lu G B, Zhong H H 2010 Acta Phys. Sin. 59 2406 (in Chinese)[杨美蓉, 海文华, 鲁耿彪, 钟宏华 2010 物理学报 59 2406]

Cited By

[1]	Wineland D J 2013 Rev. Mod. Phys. 85 1103
[2]	Duan L M, Monroe C 2010 Rev. Mod. Phys. 82 1209
[3]	Singer K, Poschinger U, Murphy M, Ivanov P, Ziesel F, Calarco T, Schmidt-Kaler F 2010 Rev. Mod. Phys. 82 2609
[4]	Leibfried D, Blatt R, Monroe C, Wineland D 2003 Rev. Mod. Phys. 75 281
[5]	Soderberg K A B, Monroe C 2010 Rep. Prog. Phys. 73 036401
[6]	DeVoe R G, Hoffnagle J, Brewer R G 1989 Phys. Rev. A 39 4362
[7]	Blmel R 1995 Phys. Rev. A 51 620
[8]	Nam Y S, Jones E B, Blmel R 2014 Phys. Rev. A 90 013402
[9]	Weiss D K, Nam Y S, Blmel R 2016 Phys. Rev. A 93 043424
[10]	Hai W H, Duan Y W, Zhu X W, Shi L, Luo X L, He C S 1997 Acta Phys. Sin. 46 2217 (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 2217]
[11]	Mihalcea B M, Vişan G G 2010 Phys. Scr. T 140 014057
[12]	Peng H W 1980 Acta Phys. Sin. 29 1084 (in Chinese)[彭桓武 1980 物理学报 29 1084]
[13]	Gzyl H 1983 Phys. Rev. A 27 2297
[14]	Akerman N, Kotler S, Glickman Y, Dallal Y, Keselman A, Ozeri R 2010 Phys. Rev. A 82 061402
[15]	Fidio C D, Vogel W 2000 Phys. Rev. A 62 031802
[16]	Gong S J, Zhou F, Wu H Y, Wan W, Chen L, Feng M 2015 Chin. Phys. Lett. 32 013201
[17]	Bazrafkan M R, Ashrafi S M, Naghdi F 2014 Chin. Phys. Lett. 31 070303
[18]	Klimov A B, Romero J L, Delgado J, Sánchez-Soto L L 2004 Opt. Commun. 230 393
[19]	Jiang Z, Chen P X 2012 Acta Phys. Sin. 61 014209 (in Chinese)[蒋智, 陈平形 2012 物理学报 61 014209]
[20]	Bushev P, Rotter D, Wilson A, Dubin F, Becher C, Eschner J, Blatt R, Steixner V, Rabl P, Zoller P 2006 Phys. Rev. Lett. 96 043003
[21]	Eleuch H, Rotter I 2017 Phys. Rev. A 95 022117
[22]	Dattoli G, Torre A, Mignani R 1990 Phys. Rev. A 42 1467
[23]	Li J H, Yu R, Ding C L, Wu Y 2016 Phys. Rev. A 93 023814
[24]	Santra R, Cederbaum L S 2002 Phys. Rep. 368 1
[25]	Longhi S 2016 Europhys. Lett. 115 61001
[26]	Jin L, Song Z 2009 Phys. Rev. A 80 052107
[27]	Jin L, Song Z 2010 Phys. Rev. A 81 032109
[28]	Zhong H H, Hai W H, Lu G B, Li Z J 2011 Phys. Rev. A 84 013401
[29]	Xiao K W, Hai W H, Liu J 2012 Phys. Rev. A 85 013410
[30]	Bender C M, Brody D C, Jones H F 2002 Phys. Rev. Lett. 89 270401
[31]	Chen Z J, Ning X J 2003 Acta Phys. Sin. 52 2683 (in Chinese)[陈增军, 宁西京 2003 物理学报 52 2683]
[32]	Baradaran M, Panahi H 2017 Chin. Phys. B 26 060301
[33]	Wang X Y, Chen H Z, Li Y, Li B, Ma R M 2016 Chin. Phys. B 25 124211
[34]	Graefe E M, Höning M, Korsch H J 2010 J. Phys. A:Math. Theor. 43 075306
[35]	Caldeira A O, Leggett A J 1985 Phys. Rev. A 31 1059
[36]	Gu Y 1996 Quantum Chaos (Shanghai:Shanghai Scientific and Technological Education Press) (in Chinese)[顾雁 1996 量子混沌 (上海:上海科技教育出版社)]
[37]	Casati G, Guarneri I, Maspero G 2000 Phys. Rev. Lett. 84 63
[38]	Wimberger S, Krug A, Buchleitner A 2002 Phys. Rev. Lett. 89 263601
[39]	Mizrahi J, Senko C, Neyenhuis B, Johnson K G, Campbell W C, Conover C W S, Monroe C 2013 Phys. Rev. Lett. 110 203001
[40]	Chen Q, Hai K, Hai W H 2010 J. Phys. A:Math. Theor. 43 455302
[41]	Hai K, Luo Y R, Chong G S, Chen H, Hai W H 2017 Quantum Inf. Comput. 17 456
[42]	Chen Y H, She L, Wang M, Yang Z H, Liu H, Li J M 2016 Chin. Phys. B 25 120601
[43]	Yang M R, Hai W H, Lu G B, Zhong H H 2010 Acta Phys. Sin. 59 2406 (in Chinese)[杨美蓉, 海文华, 鲁耿彪, 钟宏华 2010 物理学报 59 2406]

[1]	Li Jing, Ding Hai-Tao, Zhang Dan-Wei. Quantum Fisher information and parameter estimation in non-Hermitian Hamiltonians. Acta Physica Sinica, 2023, 72(20): 200601. doi: 10.7498/aps.72.20230862
[2]	Liao Qing-Hong, Deng Wei-Can, Wen Jian, Zhou Nan-Run, Liu Nian-Hua. Phonon blockade induced by a non-Hermitian Hamiltonian in a nanomechanical resonator coupled with a qubit. Acta Physica Sinica, 2019, 68(11): 114203. doi: 10.7498/aps.68.20182263
[3]	Wang Ye, Zhang Jing-Ning, Kim Kihwan. Single-ion qubit with coherence time exceeding 10 minutes. Acta Physica Sinica, 2019, 68(3): 030306. doi: 10.7498/aps.68.20181729
[4]	Liu Wang-Yun, Bi Si-Wen, Dou Xi-Bo. Evolution properties of the field quantum entropy in the nonlinear Jaynes-Cummings model of a trapped ion. Acta Physica Sinica, 2010, 59(3): 1780-1785. doi: 10.7498/aps.59.1780
[5]	Yang Mei-Rong, Hai Wen-Hua, Lu Geng-Biao, Zhong Hong-Hua. Exact quantum motion of a single trapped ion interacting with standing laser pulses in Lamb-Dicke regime. Acta Physica Sinica, 2010, 59(4): 2406-2415. doi: 10.7498/aps.59.2406
[6]	Yang Zi-Yuan. Magnetic interactions as well as microscopic origins of the spin-Hamiltonian parameters for 6S(3d5) state ions in cubic symmetry crystal filed. Acta Physica Sinica, 2008, 57(7): 4512-4520. doi: 10.7498/aps.57.4512
[7]	Zhang Miao, Jia Huan-Yu. Generations of coherent states of single trapped cold ion beyond the Lamb-Dicke limit. Acta Physica Sinica, 2008, 57(2): 880-886. doi: 10.7498/aps.57.880
[8]	Ai Ling-Yan, Yang Jian, Zhang Zhi-Ming. Generation of C-NOT gate, swap gate and phase gate based on a two-dimensional ion trap. Acta Physica Sinica, 2008, 57(9): 5589-5592. doi: 10.7498/aps.57.5589
[9]	Chen Wen-Qin, Hai Wen-Hua, Song Jian-Wen. Regular and chaotic motions of a single Paul-trapped ion interacting with double-δ-kicked pulses. Acta Physica Sinica, 2008, 57(3): 1608-1615. doi: 10.7498/aps.57.1608
[10]	Wei Qun, Yang Zi-Yuan, Wang Can-Jun, Xu Qi-Ming. Effects of excited states for d3 ions on spin-Hamiltonian parameters of the ground state 4A2 in axial-symmetrical crystal field. Acta Physica Sinica, 2007, 56(1): 507-511. doi: 10.7498/aps.56.507
[11]	Chen Wen-Qin, Hai Wen-Hua, Li Hui, Ma Zhi-Ying. Regular and chaotic motions of a single trapped ion interacting with a flashing ratchet potential. Acta Physica Sinica, 2007, 56(3): 1305-1312. doi: 10.7498/aps.56.1305
[12]	Wu Yun-Wen, Hai Wen-Hua. Exact quantum motions of two ions in a two-dimensional paul trap. Acta Physica Sinica, 2006, 55(11): 5721-5727. doi: 10.7498/aps.55.5721
[13]	Wang Zhong-Qing, Duan Chang-Kui, An Guang-Lei. Nonlinear Jaynes-Cummings model of a trapped ion and the evolution of the ion population inversion. Acta Physica Sinica, 2006, 55(7): 3438-3442. doi: 10.7498/aps.55.3438
[14]	Yang Zi-Yuan, Hao Yue. Investigations of magnetic interactions and spin-Hamiltonian parameters for 4B1(3d3) state ion in a tetragonal crystal field. Acta Physica Sinica, 2005, 54(6): 2883-2892. doi: 10.7498/aps.54.2883
[15]	Qu Zhao-Jun, Liu Sheng-Dian, Yang Chuan-Lu. Interaction between a trapped ion with a single-mode quantized radiation field. Acta Physica Sinica, 2005, 54(3): 1156-1161. doi: 10.7498/aps.54.1156
[16]	Yang Zi-Yuan. Microscopic origins of the spin-Hamiltonian parameters for 3d2 state ions in a crystal. Acta Physica Sinica, 2004, 53(6): 1981-1988. doi: 10.7498/aps.53.1981
[17]	Li Fei, Hai Wen-Hua. Regular and chaotic motions of a single trapped ion interacting with standing laser pulses. Acta Physica Sinica, 2004, 53(5): 1309-1315. doi: 10.7498/aps.53.1309
[18]	Chen Zeng-Jun, Ning Xi-Jing. Physical meaning of non-Hermitian Hamiltonian. Acta Physica Sinica, 2003, 52(11): 2683-2686. doi: 10.7498/aps.52.2683
[19]	FANG MAO-FA, LIU XIANG. PERIODIC ENTANGLEMENT BETWEEN THE INTERNAL AND EXTERANL DEGREE OF FREEDOM OF A TRAPPED ION IN A STANDING WAVE LASER. Acta Physica Sinica, 2001, 50(12): 2363-2368. doi: 10.7498/aps.50.2363
[20]	LIN FU-CHENG, ZHU JI-KANG, HUANG WU-HAN. A GENERALIZED EFFECTIVE SPIN-HAMILTONIAN. Acta Physica Sinica, 1964, 20(11): 1114-1123. doi: 10.7498/aps.20.1114

Catalog

Vol. 66, Issue 23 - 2017-12-05

Metrics

Abstract views: 6181
PDF Downloads: 193
Cited By: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

Search

Article

留言板