Unified analytical treatments to qubit-oscillator systems

doi:10.1088/1674-1056/22/6/064205

中国物理B ›› 2013, Vol. 22 ›› Issue (6): 64205-064205.doi: 10.1088/1674-1056/22/6/064205

• ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS • 上一篇下一篇

Unified analytical treatments to qubit-oscillator systems

贺树^a, 张瑜瑜^b, 陈庆虎^{c d}, 任学藻^a, 刘涛^a, 汪克林^e

a School of Science, Southwest University of Science and Technology, Mianyang 621010, China;
b Center for Modern Physics, Chongqing University, Chongqing 400044, China;
c Department of Physics, Zhejiang University, Hangzhou 310027, China;
d Center for Statistical and Theoretical Condensed Matter Physics, Zhejiang Normal University, Jinhua 321004, China;
e Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China

收稿日期:2012-08-21 修回日期:2012-10-16 出版日期:2013-05-01 发布日期:2013-05-01
基金资助:
Project supported by the National Natural Science Foundation of China (Grants Nos. 11174254 and 11104363), the National Basic Research Program of China (Grant Nos. 2011CBA00103 and 2009CB929104), and the Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20110191120046).

Unified analytical treatments to qubit-oscillator systems

He Shu (贺树)^a, Zhang Yu-Yu (张瑜瑜)^b, Chen Qing-Hu (陈庆虎)^{c d}, Ren Xue-Zao (任学藻)^a, Liu Tao (刘涛)^a, Wang Ke-Lin (汪克林)^e

a School of Science, Southwest University of Science and Technology, Mianyang 621010, China;
b Center for Modern Physics, Chongqing University, Chongqing 400044, China;
c Department of Physics, Zhejiang University, Hangzhou 310027, China;
d Center for Statistical and Theoretical Condensed Matter Physics, Zhejiang Normal University, Jinhua 321004, China;
e Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China

Received:2012-08-21 Revised:2012-10-16 Online:2013-05-01 Published:2013-05-01
Contact: Zhang Yu-Yu E-mail:yuyuzh@cqu.edu.cn; qhchen@zju.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grants Nos. 11174254 and 11104363), the National Basic Research Program of China (Grant Nos. 2011CBA00103 and 2009CB929104), and the Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20110191120046).

摘要/Abstract

摘要： An effective scheme within two displaced bosonic operators with equal positive and negative displacements is extended to study the qubit-oscillator systems analytically in a unified way. Many previous analytical treatments, such as generalized rotating-wave approximation (GRWA) [Phys. Rev. Lett. 99, 173601 (2007)] and an expansion in the qubit tunneling matrix element in the deep strong coupling regime [Phys. Rev. Lett. 105, 263603 (2010)] can be recovered straightforwardly within the present scheme. Moreover, further improving GRWA and the extension to the finite-bias case are implemented easily. The algebraic formulae for the eigensolutions are then derived explicitly and uniquely, which work well in a wide range of the coupling strengthes, detunings, and static bias including the recent experimentally accessible parameters. The dynamics of the qubit for an oscillator in ground-state is also studied. At the experimentally accessible coupling regime, GRWA can always work well. When the coupling is enhanced to the intermediate regime, only the improving GRWA can give the correct description, while the result of GRWA shows strong deviations. The previous Van Vleck perturbation theory is not valid to describe the dynamics in the present-day experimentally accessible regime, except for the strongly biased cases.

关键词: numerical exact solution, qubit-oscillator system, dynamics

Abstract: An effective scheme within two displaced bosonic operators with equal positive and negative displacements is extended to study the qubit-oscillator systems analytically in a unified way. Many previous analytical treatments, such as generalized rotating-wave approximation (GRWA) [Phys. Rev. Lett. 99, 173601 (2007)] and an expansion in the qubit tunneling matrix element in the deep strong coupling regime [Phys. Rev. Lett. 105, 263603 (2010)] can be recovered straightforwardly within the present scheme. Moreover, further improving GRWA and the extension to the finite-bias case are implemented easily. The algebraic formulae for the eigensolutions are then derived explicitly and uniquely, which work well in a wide range of the coupling strengthes, detunings, and static bias including the recent experimentally accessible parameters. The dynamics of the qubit for an oscillator in ground-state is also studied. At the experimentally accessible coupling regime, GRWA can always work well. When the coupling is enhanced to the intermediate regime, only the improving GRWA can give the correct description, while the result of GRWA shows strong deviations. The previous Van Vleck perturbation theory is not valid to describe the dynamics in the present-day experimentally accessible regime, except for the strongly biased cases.

Key words: numerical exact solution, qubit-oscillator system, dynamics

中图分类号: (Cavity quantum electrodynamics; micromasers)

42.50.Pq

42.50.Lc (Quantum fluctuations, quantum noise, and quantum jumps) 03.65.Ge (Solutions of wave equations: bound states)

贺树, 张瑜瑜, 陈庆虎, 任学藻, 刘涛, 汪克林. Unified analytical treatments to qubit-oscillator systems[J]. 中国物理B, 2013, 22(6): 64205-064205.

He Shu (贺树), Zhang Yu-Yu (张瑜瑜), Chen Qing-Hu (陈庆虎), Ren Xue-Zao (任学藻), Liu Tao (刘涛), Wang Ke-Lin (汪克林). Unified analytical treatments to qubit-oscillator systems[J]. Chin. Phys. B, 2013, 22(6): 64205-064205.

参考文献 44

[1]	Buluta I and Nori F 2009 Science 326 108; Buluta I, Ashhab S and Nori F 2011 Rep. Prog. Phys. 74 104401
[2]	Raimond J M, Brune M and Haroche S 2001 Rev. Mod. Phys 73 565; Mabuchi H and Doherty A C 2002 Science 298 1372
[3]	Jaynes E T and Cummings F W 1963 Proc. IEEE 51 89
[4]	You J Q and Nori F 2009 Phys. Today 58 42
[5]	You J Q and Nori F 2011 Nature 474 589
[6]	You J Q, Tsai J S and Nori F 2003 Phys. Rev. B 68 024510
[7]	You J Q and Nori F 2003 Phys. Rev. B 68 064509
[8]	Nation P D, Johansson J R, Blencowe M P and Nori F 2012 Rev. Mod. Phys. 84 1
[9]	Shevchenko S N, Ashhab S and Nori F 2010 Phys. Rep. 492 1
[10]	Wallraff A, Schuster D I, Blais A, Frunzio L, Huang R S, Majer J, Kumar S, Girvin S M and Schoelkopf R J 2004 Nature 431 162
[11]	Chiorescu I, Bertet P, Semba K, Nakamura, Harmans C J P M and Mooij J E 2004 Nature 431 159
[12]	Johansson J, Saito S, Meno T, Nakano H, Ueda M, Semba K and Takayanagi H 2006 Phys. Rev. Lett. 96 127006
[13]	Wang H, Hofheinz M, Ansmann M, Bialczak R C, Lucero E, Neeley M, OConnell A D, Sank D, Wenner J, Cleland A N and Martinis J M 2008 Phys. Rev. Lett. 101 240401
[14]	Hofheinz M, Wang H, Ansmann M, Bialczak R C, Lucero E, Neeley M, O'Connell A D, Sank D, Wenner J, Martinis J M and Cleland A N 2009 Nature 459 546
[15]	Deppe F, Mariantoni M, Menzel E P, Marx A, Saito S, Kakuyanagi K, Tanaka H, Meno T, Semba K, Takayanagi H, Solano E and Gross R 2008 Nat. Phys. 4 686
[16]	Fink J M, Göppl M, Baur M, Bianchetti R, Leek P J, Blais A and Wallraff A 2008 Nature 454 315
[17]	Niemczyk T, Deppe F, Huebl H, Menzel E P, Hocke F, Schwarz M J, Garcia-Ripoll J J, Zueco D, Hmmer T, Solano E, Marx A and Gross R 2010 Nat. Phys. 6 772
[18]	Forn-Díaz P, Lisenfeld J, Marcos D, García-Ripoll J J, Solano E, Harmans C J P M and Mooij J E 2010 Phys. Rev. Lett. 105 237001
[19]	Fedorov A, Feofanov A K, Macha P, Forn-Díaz P, Harmans C J P M and Mooij J E 2010 Phys. Rev. Lett. 105 060503
[20]	Werlang T, Dodonov A V, Duzzioni E I and Villas-Bôas C J 2008 Phys. Rev. A 78 053805
[21]	Zueco D, Reuther G M, Kohler S and Hänggi P 2009 Phys. Rev. A 80 033846
[22]	Ashhab S and Nori F 2010 Phys. Rev. A 81 042311
[23]	Hausinger J and Grifoni M 2010 Phys. Rev. A 80 062320
[24]	Chen Q H, Li L, Liu T and Wang K L 2012 Chin. Phys. Lett. 29 014208
[25]	Irish E K 2007 Phys. Rev. Lett. 99 173601
[26]	Irish E K 2007 Phys. Rev. Lett. 99 259901
[27]	Chen Q H, Zhang Y Y, Liu T and Wang K L 2008 Phys. Rev. A 78 051801
[28]	Liu T, Wang K L and Feng M 2009 Europhys. Lett. 86 54003
[29]	Chen Q H, Yang Y, Liu T and Wang K L 2010 Phys. Rev. A 82 052306
[30]	Gan C J and Zheng H 2010 Eur. Phys. J. D 59 473
[31]	Casanova J, Romero G, Lizuain I, García-Ripoll J J and Solano E 2010 Phys. Rev. Lett. 105 263603
[32]	Chen Q H, Liu T, Zhang Y Y and Wang K L 2011 Europhys. Lett. 96 14003
[33]	Braak D 2011 Phys. Rev. Lett. 107 100401
[34]	Cao X, You J Q, Zheng H, Kofman A G and Nori F 2010 Phys. Rev. A 82 022119
[35]	Cao X, Ai Q, Sun C P and Nori F 2012 Phys. Lett. A 376 349
[36]	Cao X, You J Q, Zheng H and Nori F 2011 New. J. Phys. 13 073002
[37]	Albert V V, Scholes G D and Brumer P 2011 Phys. Rev. A 84 042110
[38]	Jonasson1 O, Tang C S, Goan H S, Manolescu A and Gudmundsson V 2012 New J. Phys. 14 013036
[39]	Gudmundsson V, Jonasson O, Tang C S, Goan H S and Manolescu A 2012 Phys. Rev. B 85 075306
[40]	Albert V V Phys. Rev. Lett. 108 180401
[41]	Feranchuk I D, Komarov L I and Ulyanenkov A P 1996 J. Phys. A: Math. Gen. 29 4035
[42]	Amniat-Talab M, Guerin S and Jauslin H R 2005 J. Math. Phys. 46 042311
[43]	Zhang Y, Chen G, Yu L, Liang Q, Liang J Q and Jia S 2011 Phys. Rev. A 83 065802
[44]	Fraleigh J B 1994 A First Course in Abstract Algebra 5th edn. (Reading, MA: Addison-Wesley)

Unified analytical treatments to qubit-oscillator systems

Unified analytical treatments to qubit-oscillator systems

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献 44

相关文章 15

Metrics

本文评价

推荐阅读 0

[1]	Liping Zhang(张丽萍), Zuyu Xu(徐祖雨), Xiaojie Li(黎晓杰), Xu Zhang(张旭), Mingyang Qin(秦明阳), Ruozhou Zhang(张若舟), Juan Xu(徐娟), Wenxin Cheng(程文欣), Jie Yuan(袁洁), Huabing Wang(王华兵), Alejandro V. Silhanek, Beiyi Zhu(朱北沂), Jun Miao(苗君), and Kui Jin(金魁). Cascade excitation of vortex motion and reentrant superconductivity in flexible Nb thin films[J]. 中国物理B, 2023, 32(4): 47302-047302.
[2]	Z W Liang(梁正伟), P Wu(吴平), L C Wang(王利晨), B G Shen(沈保根), and Zhi-Hong Wang(王志宏). Conductive path and local oxygen-vacancy dynamics: Case study of crosshatched oxides[J]. 中国物理B, 2023, 32(4): 47303-047303.
[3]	Cong-Min Ji(祭聪敏), Yusong Tu(涂育松), and Yuan-Yan Wu(吴园燕). Heterogeneous hydration patterns of G-quadruplex DNA[J]. 中国物理B, 2023, 32(2): 28702-028702.
[4]	Tao-Wen Xiong(熊涛文), Xiao-Ping Chen(陈小平), Ye-Ping Lin(林也平), Xin-Fu He(贺新福), Wen Yang(杨文), Wang-Yu Hu(胡望宇), Fei Gao(高飞), and Hui-Qiu Deng(邓辉球). Molecular dynamics study of interactions between edge dislocation and irradiation-induced defects in Fe–10Ni–20Cr alloy[J]. 中国物理B, 2023, 32(2): 20206-020206.
[5]	Peng Xu(许鹏), Ran Zhang(张然), and Sheng-Mei Zhao(赵生妹). Realization of the iSWAP-like gate among the superconducting qutrits[J]. 中国物理B, 2023, 32(2): 20306-020306.
[6]	Zilin Wang(王梓霖), Liang Yang(杨亮), Changsheng Liu(刘长生), and Shiwei Lin(林仕伟). Formation of nanobubbles generated by hydrate decomposition: A molecular dynamics study[J]. 中国物理B, 2023, 32(2): 23101-023101.
[7]	Mengjiao Wu(吴梦娇), Huishu Ma(马慧姝), Haiping Fang(方海平), Li Yang(阳丽), and Xiaoling Lei(雷晓玲). Adsorption dynamics of double-stranded DNA on a graphene oxide surface with both large unoxidized and oxidized regions[J]. 中国物理B, 2023, 32(1): 18701-018701.
[8]	Qing-Qin Zou(邹青钦), Shuang Lei(雷双), Zhang-Yong Li(李章勇), and Dui Qin(秦对). Effects of adjacent bubble on spatiotemporal evolutions of mechanical stresses surrounding bubbles oscillating in tissues[J]. 中国物理B, 2023, 32(1): 14302-014302.
[9]	Ding-Zong Zhang(张定宗), Xu-Ming Feng(冯旭铭), Jun Ma(马骏), Wen-Feng Guo(郭文峰), Yan-Qing Huang(黄艳清), and Hong-Bo Liu(刘洪波). Linear analysis of plasma pressure-driven mode in reversed shear cylindrical tokamak plasmas[J]. 中国物理B, 2023, 32(1): 15201-015201.
[10]	Long Zhou(周龙), Xu-Long Zhang(张旭龙), Yu-Ying Cao(曹玉莹), Fu Zheng(郑富), Hua Gao(高华), Hong-Fei Liu(刘红飞), and Zhi Ma(马治). Prediction of flexoelectricity in BaTiO₃ using molecular dynamics simulations[J]. 中国物理B, 2023, 32(1): 17701-017701.
[11]	Tzu-Chia Chen, Mahyuddin KM Nasution, Abdullah Hasan Jabbar, Sarah Jawad Shoja, Waluyo Adi Siswanto, Sigiet Haryo Pranoto, Dmitry Bokov, Rustem Magizov, Yasser Fakri Mustafa, A. Surendar, Rustem Zalilov, Alexandr Sviderskiy, Alla Vorobeva, Dmitry Vorobyev, and Ahmed Alkhayyat. Effect of spatial heterogeneity on level of rejuvenation in Ni₈₀P₂₀ metallic glass[J]. 中国物理B, 2022, 31(9): 96401-096401.
[12]	Long Lin(林龙), Tong-Gang Jia(贾铜钢), Zhi-Bin Wang(王志斌), and Peng-Cheng Li(李鹏程). Probing subcycle spectral structures and dynamics of high-order harmonic generation in crystals[J]. 中国物理B, 2022, 31(9): 93202-093202.
[13]	Zhen Liu(刘震), Zi-Xuan Yang(杨子萱), Chuan Xu(徐川), Jia-Ji Zhao(赵嘉佶), Lu-Junyu Wang(王陆君瑜), Yun-Qi Fu(富云齐), Xue-Lei Liang(梁学磊), Hui-Ming Cheng(成会明), Wen-Cai Ren(任文才), Xiao-Song Wu(吴孝松), and Ning Kang(康宁). Finite superconducting square wire-network based on two-dimensional crystalline Mo₂C[J]. 中国物理B, 2022, 31(9): 97404-097404.
[14]	Hanghang Chen(陈航航), Zijiang Yang(杨紫江), and Maodu Chen(陈茂笃)^†. State-to-state integral cross sections and rate constants for the N⁺(³P)+HD→NH⁺/ND⁺+D/H reaction: Accurate quantum dynamics studies[J]. 中国物理B, 2022, 31(9): 98204-098204.
[15]	Xinwen Ma(马新文), Shaofeng Zhang(张少锋), Weiqiang Wen(汶伟强), Zhongkui Huang(黄忠魁), Zhimin Hu(胡智民), Dalong Guo(郭大龙), Junwen Gao(高俊文), Bennaceur Najjari, Shenyue Xu(许慎跃), Shuncheng Yan(闫顺成), Ke Yao(姚科), Ruitian Zhang(张瑞田), Yong Gao(高永), and Xiaolong Zhu(朱小龙). Atomic structure and collision dynamics with highly charged ions[J]. 中国物理B, 2022, 31(9): 93401-093401.