Geometric phase of an open double-quantum-dot system detected by a quantum point contact

doi:10.1088/1674-1056/ab6963

摘要/Abstract

摘要： We study theoretically the geometric phase of a double-quantum-dot (DQD) system measured by a quantum point contact (QPC) in the pure dephasing and dissipative environments, respectively. The results show that in these two environments, the coupling strength between the quantum dots has an enhanced impact on the geometric phase during a quasiperiod. This is due to the fact that the expansion of the width of the tunneling channel connecting the two quantum dots accelerates the oscillations of the electron between the quantum dots and makes the length of the evolution path longer. In addition, there is a notable near-zero region in the geometric phase because the stronger coupling between the system and the QPC freezes the electron in one quantum dot and the solid angle enclosed by the evolution path is approximately zero, which is associated with the quantum Zeno effect. For the pure dephasing environment, the geometric phase is suppressed as the dephasing rate increases which is caused only by the phase damping of the system. In the dissipative environment, the geometric phase is reduced with the increase of the relaxation rate which results from both the energy dissipation and phase damping of the system. Our results are helpful for using the geometric phase to construct the fault-tolerant quantum devices based on quantum dot systems in quantum information.

关键词: geometric phase, decoherence, quantum transport

Abstract: We study theoretically the geometric phase of a double-quantum-dot (DQD) system measured by a quantum point contact (QPC) in the pure dephasing and dissipative environments, respectively. The results show that in these two environments, the coupling strength between the quantum dots has an enhanced impact on the geometric phase during a quasiperiod. This is due to the fact that the expansion of the width of the tunneling channel connecting the two quantum dots accelerates the oscillations of the electron between the quantum dots and makes the length of the evolution path longer. In addition, there is a notable near-zero region in the geometric phase because the stronger coupling between the system and the QPC freezes the electron in one quantum dot and the solid angle enclosed by the evolution path is approximately zero, which is associated with the quantum Zeno effect. For the pure dephasing environment, the geometric phase is suppressed as the dephasing rate increases which is caused only by the phase damping of the system. In the dissipative environment, the geometric phase is reduced with the increase of the relaxation rate which results from both the energy dissipation and phase damping of the system. Our results are helpful for using the geometric phase to construct the fault-tolerant quantum devices based on quantum dot systems in quantum information.

Key words: geometric phase, decoherence, quantum transport

中图分类号: (Phases: geometric; dynamic or topological)

03.65.Vf

03.65.Yz (Decoherence; open systems; quantum statistical methods) 05.60.Gg (Quantum transport)

杜倩, 蓝康, 张延惠, 姜露静. Geometric phase of an open double-quantum-dot system detected by a quantum point contact[J]. 中国物理B, 2020, 29(3): 30302-030302.

Qian Du(杜倩), Kang Lan(蓝康), Yan-Hui Zhang(张延惠), Lu-Jing Jiang(姜露静). Geometric phase of an open double-quantum-dot system detected by a quantum point contact[J]. Chin. Phys. B, 2020, 29(3): 30302-030302.

[1]	Berry M V 1984 Proc. R. Soc. A 392 45
[2]	Aharonov Y and Anandan J 1987 Phys. Rev. Lett. 58 1593 doi: 10.1103/PhysRevLett.58.1593
[3]	Samuel J and Bhandari R 1988 Phys. Rev. Lett. 60 2339 doi: 10.1103/PhysRevLett.60.2339
[4]	Sjöqvist E, Pati A K, Ekert A, Anandan J S, Ericsson M, Oi D K L and Vedral V 2000 Phys. Rev. Lett. 85 2845 doi: 10.1103/PhysRevLett.85.2845
[5]	Tong D M, Sjöqvist E, Kwek L C and Oh C H 2004 Phys. Rev. Lett. 93 080405 doi: 10.1103/PhysRevLett.93.080405
[6]	Uhlmann A 1986 Rep. Math. Phys. 24 229 doi: 10.1016/0034-4877(86)90055-8
[7]	Yi X X and Chang J L 2004 Phys. Rev. A 70 012108 doi: 10.1103/PhysRevA.70.012108
[8]	Tong D M, Sjöqvist E, Filipp S, Kwek L C and Oh C H 2005 Phys. Rev. A 71 032106 doi: 10.1103/PhysRevA.71.032106
[9]	Wu B, Liu J and Niu Q 2005 Phys. Rev. Lett. 94 140402 doi: 10.1103/PhysRevLett.94.140402
[10]	Carollo A, Fuentes-Guridi I, Franca S M and Vedral V 2003 Phys. Rev. Lett. 90 160402 doi: 10.1103/PhysRevLett.90.160402
[11]	Cai X J and Zheng Y J 2016 Phys. Rev. A 94 042110 doi: 10.1103/PhysRevA.94.042110
[12]	Cai X J and Zheng Y J 2017 Phys. Rev. A 95 052104 doi: 10.1103/PhysRevA.95.052104
[13]	Cai X J and Zheng Y J 2018 J. Chem. Phys. 149 094107 doi: 10.1063/1.5039891
[14]	Cai X J 2019 Entropy 21 1040 doi: 10.3390/e21111040
[15]	Cai X J 2020 Sci. Rep. 10 88 doi: 10.1038/s41598-019-57081-8
[16]	Wang Y M, Du G and Liang J Q 2012 Chin. Phys. B 21 044207 doi: 10.1088/1674-1056/21/4/044207
[17]	Li Z L, Bi J J, Liu R, Yi X H, Fu H Y, Sun F, Wei M Z and Wang C K 2017 Chin. Phys. B 26 098508 doi: 10.1088/1674-1056/26/9/098508
[18]	Chiao R Y and Wu Y S 1986 Phys. Rev. Lett. 57 933 doi: 10.1103/PhysRevLett.57.933
[19]	Tomita A and Chiao R Y 1986 Phys. Rev. Lett. 57 937 doi: 10.1103/PhysRevLett.57.937
[20]	Jones J A, Vedral V, Ekert A and Castagnoli G 2000 Nature 403 869 doi: 10.1038/35002528
[21]	Ekert A, Ericsson M, Hayden P, Inamori H, Jones J A, Oi D K L and Vedral V 2000 J. Mod. Opt. 47 2501 doi: 10.1080/09500340008232177
[22]	Zanardi P and Rasetti M 1999 Phys. Lett. A 264 94 doi: 10.1016/S0375-9601(99)00803-8
[23]	Fuentes-Guridi I, Girelli F and Livine E 2005 Phys. Rev. Lett. 94 020503 doi: 10.1103/PhysRevLett.94.020503
[24]	Wang X B and Keiji M 2001 Phys. Rev. Lett. 87 097901 doi: 10.1103/PhysRevLett.87.097901
[25]	Huang Y Y, Wu Y K, Wang F, Hou P Y, Wang W B, Zhang W G, Lian W Q, Liu Y Q, Wang H Y, Zhang H Y, He L, Chang X Y, Xu Y and Duan L M 2019 Phys. Rev. Lett. 122 010503 doi: 10.1103/PhysRevLett.122.010503
[26]	Duan L M, Cirac J I and Zoller P 2001 Science 292 1695 doi: 10.1126/science.1058835
[27]	Falci G, Fazio R, Palma G M, Siewert J and Vedral V 2000 Nature 407 355 doi: 10.1038/35030052
[28]	Xie H, Li H C, Yang R C, Lin X and Huang Z P 2007 Chin. Phys. 16 3382 doi: 10.1088/1009-1963/16/11/039
[29]	Jin X R, Zhang Y Q, Zhang S and Jin D Z 2007 Chin. Phys. 16 1220 doi: 10.1088/1009-1963/16/5/008
[30]	Zhang Y Q, Jin X R and Zhang S 2008 Chin. Phys. B 17 424 doi: 10.1088/1674-1056/17/2/013
[31]	Yang R C, Li H C, Lin X and Huang Z P 2008 Chin. Phys. B 17 180 doi: 10.1088/1674-1056/17/1/031
[32]	Zhang L B, Song C, Wang H and Zheng S B 2018 Chin. Phys. B 27 070303 doi: 10.1088/1674-1056/27/7/070303
[33]	Zhu A D, Zhang S, Yeon K H, Yu S C and Um C I 2007 Chin. Phys. B 16 1559 doi: 10.1088/1009-1963/16/6/011
[34]	Zhou H, Li Z K, Wang H Y, Chen H W, Peng X H and Du J F 2016 Chin. Phys. Lett. 33 060301 doi: 10.1088/0256-307X/33/6/060301
[35]	Loss D and DiVincenzo D P 1998 Phys. Rev. A 57 120 doi: 10.1103/PhysRevA.57.120
[36]	Burkard G, Loss D and DiVincenzo D P 1999 Phys. Rev. B 59 2070 doi: 10.1103/PhysRevB.59.2070
[37]	Zanardi P and Rossi F 1999 Phys. Rev. B 59 8170 doi: 10.1103/PhysRevB.59.8170
[38]	Zanardi P and Rossi F 1998 Phys. Rev. Lett. 81 4752 doi: 10.1103/PhysRevLett.81.4752
[39]	Brum J A and Hawrylak P 1997 Superlattice. Microst. 22 431 doi: 10.1006/spmi.1996.0263
[40]	Gurvitz S A, Fedichkin L, Mozyrsky D and Berman G P 2003 Phys. Rev. Lett. 91 066801 doi: 10.1103/PhysRevLett.91.066801
[41]	Kang L S, Zhang Y H, Xu X L and Tang X 2017 Phys. Rev. B 96 235417 doi: 10.1103/PhysRevB.96.235417
[42]	Levinson Y 1997 Europhys. Lett. 39 299 doi: 10.1209/epl/i1997-00351-x
[43]	van der Wiel W G, De Franceschi S, Elzerman J M, Fujisawa T, Tarucha S and Kouwenhoven L P 2002 Rev. Mod. Phys. 75 1 doi: 10.1103/RevModPhys.75.1
[44]	Yi X X, Wang L C and Wang W 2005 Phys. Rev. A 71 044101 doi: 10.1103/PhysRevA.71.044101
[45]	Lombardo F C and Villar P I 2010 Phys. Rev. A 81 022115 doi: 10.1103/PhysRevA.81.022115
[46]	Rezakhani A T and Zanardi P 2006 Phys. Rev. A 73 052117 doi: 10.1103/PhysRevA.73.052117
[47]	Luo D W, You J Q, Lin H Q, Wu L A and Yu T 2018 Phys. Rev. A 98 052117 doi: 10.1103/PhysRevA.98.052117
[48]	Sjöqvist E, Yi X X and Åberg J 2005 Phys. Rev. A 72 054101 doi: 10.1103/PhysRevA.72.054101
[49]	Villar P I and Lombardo F C 2011 Phys. Rev. A 83 052121 doi: 10.1103/PhysRevA.83.052121
[50]	Cai X J, Meng R, Zhang Y H and Wang L 2019 Europhys. Lett. 125 30007 doi: 10.1209/0295-5075/125/30007
[51]	Dajka J, Mierzejewski M and Łuczka J 2007 J. Phys. A 41 012001
[52]	Fujikawa K and Hu M G 2009 Phys. Rev. A 79 052107 doi: 10.1103/PhysRevA.79.052107
[53]	Berger S, Pechal M, Pugnetti S, Abdumalikov A A, Steffen L, Fedorov A, Wallraff A and Filipp S 2012 Phys. Rev. B 85 220502 doi: 10.1103/PhysRevB.85.220502
[54]	Guo W, Ma J, Yin X, Zhong W and Wang X 2014 Phys. Rev. A 90 062133 doi: 10.1103/PhysRevA.90.062133
[55]	Li X and Shi Y 2013 Europhys. Lett. 103 20005 doi: 10.1209/0295-5075/103/20005
[56]	De Chiara G and Palma G M 2003 Phys. Rev. Lett. 91 090404 doi: 10.1103/PhysRevLett.91.090404
[57]	Abdel-Khalek S, Berrada K, El-Sayed M A and Abel-Aty M 2013 Chin. Phys. B 22 100301 doi: 10.1088/1674-1056/22/10/100301
[58]	Li Z J, Cheng L and Wen J J 2010 Chin. Phys. B 19 010305 doi: 10.1088/1674-1056/19/1/010305
[59]	Tian L J, Zhu C Q, Zhang H B and Qin L G 2011 Chin. Phys. B 20 040302 doi: 10.1088/1674-1056/20/4/040302
[60]	Wang L C, Yan J Y and Yi X X 2010 Chin. Phys. B 19 040512 doi: 10.1088/1674-1056/19/4/040512
[61]	Zhang A P and Li F L 2013 Chin. Phys. B 22 030308 doi: 10.1088/1674-1056/22/3/030308
[62]	Jia X Y, Li W D and Liang J Q 2007 Chin. Phys. 16 2855 doi: 10.1088/1009-1963/16/10/005
[63]	Zhong W X, Cheng G L and Chen A X 2010 Chin. Phys. B 19 110310 doi: 10.1088/1674-1056/19/11/110310
[64]	Yuan Z G and Zhang P 2015 Chin. Phys. Lett. 32 060301 doi: 10.1088/0256-307X/32/6/060301
[65]	Sun S N and Zheng Y J 2019 Phys. Rev. Lett. 123 180403 doi: 10.1103/PhysRevLett.123.180403
[66]	Chen J J, An J H, Tong Q J, Luo H G and Oh C H 2010 Phys. Rev. A 81 022120 doi: 10.1103/PhysRevA.81.022120
[67]	Yi X X, Tong D M, Wang L C, Kwek L C and Oh C H 2006 Phys. Rev. A 73 052103 doi: 10.1103/PhysRevA.73.052103
[68]	Yuan X Z and Zhu K D 2006 Phys. Rev. B 74 073309 doi: 10.1103/PhysRevB.74.073309
[69]	Liu B, Zhang F Y, Chen Z H and Song H S 2013 Int. J. Theor. Phys. 52 1877 doi: 10.1007/s10773-012-1296-2
[70]	Liu B, Zhang F Y, Song J and Song H S 2015 Sci. Rep. 5 11726 doi: 10.1038/srep11726
[71]	Gurvitz S A and Mozyrsky D 2008 Phys. Rev. B 77 075325 doi: 10.1103/PhysRevB.77.075325
[72]	Gilad T and Gurvitz S A 2006 Phys. Rev. Lett. 97 116806 doi: 10.1103/PhysRevLett.97.116806
[73]	Gurvitz S A and Berman G P 2005 Phys. Rev. B 72 073303 doi: 10.1103/PhysRevB.72.073303
[74]	Yin S and Tong D M 2009 Phys. Rev. A 79 044303 doi: 10.1103/PhysRevA.79.044303
[75]	Yin S and Tong D M 2010 J. Phys. A 43 305303 doi: 10.1088/1751-8113/43/30/305303
[76]	Gurvitz S A and Prager Y S 1996 Phys. Rev. B 53 15932 doi: 10.1103/PhysRevB.53.15932
[77]	Xu C and Vavilov M G 2013 Phys. Rev. B 88 195307 doi: 10.1103/PhysRevB.88.195307
[78]	Luo J Y, Jiao H J, Shen Y, Cen G, He X L and Wang C R 2011 J. Phys. Condens. Mat. 23 145301 doi: 10.1088/0953-8984/23/14/145301
[79]	Nazir A, Spiller T P and Munro W J 2002 Phys. Rev. A 65 042303 doi: 10.1103/PhysRevA.65.042303
[80]	Wang H and Zhu K D 2008 Europhys. Lett. 82 60006 doi: 10.1209/0295-5075/82/60006
[81]	Wu S L, Huang X L, Wang L C and Yi X X 2010 Phys. Rev. A 82 052111 doi: 10.1103/PhysRevA.82.052111

[1]	Huan Yang(杨欢), Ling-Ling Xing(邢玲玲), Zhi-Yong Ding(丁智勇), Gang Zhang(张刚), and Liu Ye(叶柳). Steering quantum nonlocalities of quantum dot system suffering from decoherence[J]. 中国物理B, 2022, 31(9): 90302-090302.
[2]	Jun Feng(冯俊), Jing-Jun Zhang(张精俊), and Qianyi Zhang(张倩怡). Geometric phase under the Unruh effect with intermediate statistics[J]. 中国物理B, 2022, 31(5): 50312-050312.
[3]	Yang-Yan Guo(郭仰岩), Wei-Hua Han(韩伟华), Xiao-Di Zhang(张晓迪), Jun-Dong Chen(陈俊东), and Fu-Hua Yang(杨富华). Observation of source/drain bias-controlled quantum transport spectrum in junctionless silicon nanowire transistor[J]. 中国物理B, 2022, 31(1): 17701-017701.
[4]	Bao-Min Li(李保民), Ming-Liang Hu(胡明亮), and Heng Fan(范桁). Nonlocal advantage of quantum coherence and entanglement of two spins under intrinsic decoherence[J]. 中国物理B, 2021, 30(7): 70307-070307.
[5]	Sai Li(李赛), Tao Chen(陈涛), Jia Liu(刘佳), and Zheng-Yuan Xue(薛正远). Interaction induced non-reciprocal three-level quantum transport[J]. 中国物理B, 2021, 30(6): 60314-060314.
[6]	Da-Jian Zhang(张大剑), Qing-hai Wang(王清海), and Jiangbin Gong(龚江滨). Geometry of time-dependent $\mathcal{PT}$-symmetric quantum mechanics[J]. 中国物理B, 2021, 30(10): 100307-100307.
[7]	赵文垒, 揭泉林. Quantum to classical transition induced by a classically small influence[J]. 中国物理B, 2020, 29(8): 80302-080302.
[8]	王晨, 徐大智. A polaron theory of quantum thermal transistor in nonequilibrium three-level systems[J]. 中国物理B, 2020, 29(8): 80504-080504.
[9]	牛真霞, 邰永航, 石俊生, 张威. Bose-Einstein condensates in an eightfold symmetric optical lattice[J]. 中国物理B, 2020, 29(5): 56103-056103.
[10]	马刘红, 韩伟华, 杨富华. Coulomb blockade and hopping transport behaviors of donor-induced quantum dots in junctionless transistors[J]. 中国物理B, 2020, 29(3): 38104-038104.
[11]	张子静, 王峰, 宋杰, 赵远. The effect of phase fluctuation and beam splitter fluctuation on two-photon quantum random walk[J]. 中国物理B, 2020, 29(2): 20503-020503.
[12]	Munsif Jan, 许小冶, 王琴琴, 陈哲, 韩永建, 李传锋, 郭光灿. Dipole-dipole interactions enhance non-Markovianity and protect information against dissipation[J]. 中国物理B, 2019, 28(9): 90303-090303.
[13]	陈许敏, 王晨. Unifying quantum heat transfer and superradiant signature in a nonequilibrium collective-qubit system:A polaron-transformed Redfield approach[J]. 中国物理B, 2019, 28(5): 50502-050502.
[14]	向左鲜, 唐传祥, 颜立新. A primary model of decoherence in neuronal microtubules based on the interaction Hamiltonian between microtubules and plasmon in neurons[J]. 中国物理B, 2019, 28(4): 48701-048701.
[15]	张显扬, 张双根, 张化迪, 马秀荣. Controllable photon echo phase induced by modulated pulses and chirped beat detection[J]. 中国物理B, 2019, 28(2): 24207-024207.