The electron transfer properties of an open double quantum dot based on a quantum point contact

Lan Kang; Du Qian; Kang Li-Sha; Jiang Lu-Jing; Lin Zhen-Yu; Zhang Yan-Hui

doi:10.7498/aps.69.20191718

Abstract

We theoretically study the electron transfer properties of a double quantum dot system in dissipative and pure dephasing environments based on a quantum dot contact detector. Theoretical results show that in the dissipative environment, the decoherence caused by the detector would increase the stable value of the average current and Fano factor as functions of time. Meanwhile, we find the existence of the quantum Zeno effect during the process of dynamical evolution. In the case of symmetric DQD, the relaxation caused by the dissipative environment would decrease the amplitude of the average current with time evolution and increase the value of the Fano factor in the long time limit. In the case of asymmetric DQD, the relaxation reduces the peak value of Fano factor over time. In the pure dephasing environment, we find that the frequent measurement would hinder the switch between different current channels during the cotunneling process. This results in a high value of Fano factor. In the case of symmetric DQD, increasing the pure dephasing rate would improve the value of Fano factor. In the case of asymmetric DQD, the dynamical evolution with time is not sensitive to the pure dephasing rate. In addition, it is indicated that the transfer probability of electron in the detector is only affected by the coupling between QPC and DQD. The environments have no effect on the transfer of a single electron in the detector. Our theoretical results provide theoretical references for experimental researchers to study the electron transport properties.

Keywords:

Authors and contacts

School of Physics and Electronics, Shandong Normal University, Jinan 250014, China

Corresponding author: Zhang Yan-Hui, yhzhang@sdnu.edu.cn

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References

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[2]	Kang L S, Zhang Y H, Xu X L, Tang X 2017 Phys. Rev. B 96 235417 Google Scholar
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[5]	Cui P, Li X Q, Shao J S, Yan Y J 2006 Phys. Lett. A 357 449 Google Scholar
[6]	Gurvitz S A, Mozyrsky D 2008 Phys. Rev. B 77 075325 Google Scholar
[7]	Zhao G P, Zhang Y H, Cai X J, Xu X L, Kang L S 2016 Physica E 84 10 Google Scholar
[8]	Cai X J 2019 Entropy 21 1040 Google Scholar
[9]	Li Z L, Bi J J, Liu R, Yi X H, Fu H Y, Sun F, Wei M Z, Wang C K 2017 Chin. Phys. B 26 098508 Google Scholar
[10]	Cai X J, Zheng Y J 2018 J. Chem. Phys. 149 094107 Google Scholar
[11]	Alexander S, Uttam S, Shekhar D H, Nath B M, Gerardo A 2015 Phys. Rev. Lett. 115 020403 Google Scholar
[12]	李保民, 胡明亮, 范桁 2019 物理学报 68 030304 Google Scholar Li B M, Hu M L, Fan H 2019 Acta Phys. Sin. 68 030304 Google Scholar
[13]	Xu P, Wang D, Ye L 2013 Chin. Phys. B 22 100306 Google Scholar
[14]	Zhang Y H, Kang L S, Xu X L, Tang X, Li H B, Cai X J 2017 Mod. Phys. Lett. B 31 1730004 Google Scholar
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[16]	Gurvitz S A 1997 Phys. Rev. B 56 15215 Google Scholar
[17]	Cai X J, Zheng Y J 2016 Phys. Rev. A 94 042110 Google Scholar
[18]	Sun S N, Zheng Y J 2019 Phys. Rev. Lett. 123 180403 Google Scholar
[19]	Cai X J, Zheng Y J 2017 Phys. Rev. A 95 052104 Google Scholar
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[22]	Yang L W, Xia Y J 2016 Chin. Phys. B 25 110303 Google Scholar
[23]	杨军, 武文远, 龚艳春 2008 物理学报 57 448 Google Scholar Yang J, Wu W Y, Gong Y C 2008 Acta Phys. Sin. 57 448 Google Scholar
[24]	Li X Q, Cui P, Yan Y J 2005 Phys. Rev. Lett. 94 066803 Google Scholar
[25]	Ouyang S H, Lam C H, You J Q 2010 Phys. Rev. B 81 075301 Google Scholar
[26]	栗军, 刘玉, 平婧, 叶银, 李新奇 2012 物理学报 61 137202 Google Scholar Li J, Liu Y, Ping J, Ye Y, Li X Q 2012 Acta Phys. Sin. 61 137202 Google Scholar
[27]	Aguado R, Brandes T 2004 Phys. Rev. Lett. 92 206601 Google Scholar
[28]	Du L, Wu J H, Artoni M, Rocca G C 2019 Phys. Rev. A 100 052102 Google Scholar
[29]	Ford G W, Lewis J T, O'Connell R F 2001 Phys. Rev. A 64 032101 Google Scholar
[30]	Korotkov A N, Averin D V 2001 Phys. Rev. B 64 165310 Google Scholar
[31]	Korotkov A N 2001 Phys. Rev. B 63 085312 Google Scholar
[32]	Xu C R, Vavilov M G 2013 Phys. Rev. B 88 195307 Google Scholar
[33]	Gurvitz S A 2019 J. Phys. A: Math. Theor. 52 175301 Google Scholar
[34]	Levitov L S, Lesovik G B 1993 JETP Lett. 58 230
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[36]	Bagrets D A, Nazarov Yu V 2003 Phys. Rev. B 67 085316 Google Scholar
[37]	Flindt C, Novotný T, Braggio A, Jauho A 2010 Phys. Rev. B 82 155407 Google Scholar
[38]	Novotný T, Donarini A, Flindt C, Jauho A 2004 Phys. Rev. Lett. 92 248302 Google Scholar
[39]	Iannaccone G, Lombardi G, Macucci M, Pellegrini B 1998 Phys. Rev. Lett. 80 1054 Google Scholar
[40]	Kießlich G, Schöll E, Brandes T, Hohls F, Haug R J 2007 Phys. Rev. Lett. 99 206602 Google Scholar
[41]	Olsen M K, Corney J F 2013 Phys. Rev. A 87 033839 Google Scholar
[42]	鹿博, 韩成银, 庄敏, 柯勇贯, 黄嘉豪, 李朝红 2019 物理学报 68 040306 Google Scholar Lu B, Han C Y, Zhuang M, Ke Y G, Huang J H, Li C H 2019 Acta Phys. Sin. 68 040306 Google Scholar
[43]	Albert M, Haack G, Flindt C, Büttiker M 2012 Phys. Rev. Lett. 108 186806 Google Scholar
[44]	Tang G M, Xu F M, Wang J 2014 Phys. Rev. B 89 205310 Google Scholar
[45]	Gurvitz S A, Prager Y S 1996 Phys. Rev. B 53 15932 Google Scholar
[46]	Bagrets D A, Utsumi Y, Golubev D S, Schön G 2006 Fortschr. Phys. 54 917 Google Scholar
[47]	Emary C, Marcos D, Aguado R, Brandes T 2007 Phys. Rev. B 76 161404 Google Scholar
[48]	Zheng Y J, Brown F L H 2003 Phys. Rev. Lett. 90 238305 Google Scholar
[49]	Luo J Y, Jiao H J, Shen Y, Cen G, He X L, Wang C R 2011 J. Phys. Condens. Matter 23 145301 Google Scholar
[50]	Pfeifer P 1982 Phys. Rev. A 26 701 Google Scholar
[51]	Gurvitz S A 2003 Quantum. Inf. Process. 2 15 Google Scholar
[52]	Carmi A, Oreg Y 2012 Phys. Rev. B 85 045325 Google Scholar
[53]	Kok P, Munro W J, Nemoto K, Ralph T C, Dowling J P, Milburn G J 2007 Rev. Mod. Phys. 79 135 Google Scholar
[54]	Sukhorukov E V, Burkard G, Loss D 2001 Phys. Rev. B 63 125315 Google Scholar
[55]	Xue H B, Zhang Z X, Fei H M 2012 Eur. Phys. J. B 85 336 Google Scholar
[56]	Thielmann A, Hettler M H, König J, Schön G 2005 Phys. Rev. Lett. 95 146806 Google Scholar
[57]	Flindt C, Novotný T, Jauho A P 2004 Phys. Rev. B 70 205334 Google Scholar

Cited By

图 1 量子点接触探测器测量的双量子点　(a)电子处在左侧的量子点会增大探测器的势垒, 减小探测器中电子的隧穿几率; (b) 电子处在右侧量子点会减小探测器势垒, 增大探测器中电子的隧穿几率. $\mu_{\rm l}$和$\mu_{\rm r}$表示探测器左侧和右侧的电子库, $V=\mu_{\rm l}-\mu_{\rm r}$是探测器的偏压. $\varOmega_{ {lr}}$ 和$\varOmega^{'}_{ {lr}}$分别是电子处于左侧和右侧量子点时探测器两端能级$E_{\rm l}$与$E_{\rm r}$之间的跳跃振幅

Figure 1. A double quantum dot detected by a quantum point contact: (a) The electron occupies the left quantum dot increases the potential barrier of the detector and reduces the tunneling of electrons in the detector; (b) the electron occupies the right quantum dot reduces the potential barrier of the detector and increases the tunneling of electrons in the detector. $\mu_{\rm l}$ and $\mu_{\rm r}$ represent the chemical potentials in the left and right reservoirs of the detector, $V=\mu_{\rm l}-\mu_{\rm r}$ is the bias voltage of the detector, $\varOmega_{{lr}}$ and $\varOmega^{'}_{ {lr}}$ are the hopping amplitudes between the states $E_{\rm l}$ and $E_{\rm r}$ of the detector for electron in the left and right quantum dots, respectively.

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图 2 耗散环境中不同退相干速率影响下平均电流和Fano factor随时间的演化　(a) 对称DQD($\varepsilon=0$)时的平均电流; (b) 非对称DQD($\varepsilon=10\varDelta$)时的平均电流; (c) 对称DQD($\varepsilon=0$)时的Fano factor; (d) 非对称DQD($\varepsilon=10\varDelta$)时的Fano factor

Figure 2. Distributions of the average current and the Fano factor versus t for different values of $\varGamma_{\rm d}$ in the dissipative environment: (a) The average current in symmetric case ($\varepsilon=0$); (b) the average current in asymmetric case ($\varepsilon=10\varDelta$); (c) the Fano factor in symmetric case ($\varepsilon=0$); (d) the Fano factor in asymmetric case ($\varepsilon=10\varDelta$).

DownLoad: Full-Size Img PowerPoint

图 3 耗散环境中不同弛豫速率影响下平均电流和Fano factor随时间的演化　(a) 对称DQD($\varepsilon=0$)时的平均电流; (b) 非对称DQD($\varepsilon=10\varDelta$)时的平均电流; (c) 对称DQD($\varepsilon=0$)时的Fano factor; (d) 非对称DQD($\varepsilon=10\varDelta$)时的Fano factor

Figure 3. Distributions of the average current and the Fano factor versus t for different values of $\varGamma_{\rm r}$ in the dissipative environment: (a) The average current in symmetric case ($\varepsilon=0$); (b) the average current in asymmetric case ($\varepsilon=10\varDelta$); (c) the Fano factor in symmetric case ($\varepsilon=0$); (d) the Fano factor in asymmetric case ($\varepsilon=10\varDelta$).

DownLoad: Full-Size Img PowerPoint

图 4 耗散环境中不同退相干速率和弛豫速率影响下电子转移几率随时间的演化, $\varepsilon=0$　(a) 不同退相干速率下转移$0$个电子的几率; (b) 不同弛豫速率下转移$0$个电子的几率; (c) 不同退相干速率下转移$1$个电子的几率; (d) 不同弛豫速率下转移$1$个电子的几率; (e) 不同退相干速率下转移$2$个电子的几率; (f) 不同弛豫速率下转移$2$个电子的几率

Figure 4. Distribution of the electron transfer probability versus t for different values of $\varGamma_{\rm d}$ and $\varGamma_{\rm r}$ in the dissipative environment, $\varepsilon=0$: (a) The probability of $0$ electron transfer at different values of $\varGamma_{\rm d}$; (b) the probability of $0$ electron transfer at different values of $\varGamma_{\rm r}$; (c) the probability of $1$ electron transfer at different values of $\varGamma_{\rm d}$; (d) the probability of $1$ electron transfer at different values of $\varGamma_{\rm r}$); (e) the probability of $2$ electrons transfer at different values of $\varGamma_{\rm d}$; (f) the probability of $2$ electrons transfer at different values of $\varGamma_{\rm r}$.

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图 5 纯退相环境中不同退相干速率影响下平均电流和Fano factor随时间的分布　(a) 对称DQD($\varepsilon=0$)时的平均电流; (b) 非对称DQD($\varepsilon=10\varDelta$)时的平均电流; (c) 对称DQD($\varepsilon=0$)时的Fano factor; (d) 非对称DQD($\varepsilon=10\varDelta$)时的Fano factor

Figure 5. Distributions of the average current and the Fano factor versus t for different values of $\varGamma_{\rm d}$ in the pure dephasing environment: (a) The average current in symmetric case ($\varepsilon=0$); (b) the average current in asymmetric case ($\varepsilon=10\varDelta$); (c) the Fano factor in symmetric case ($\varepsilon=0$); (d) the Fano factor in asymmetric case ($\varepsilon=10\varDelta$).

DownLoad: Full-Size Img PowerPoint

图 6 纯退相环境中不同纯退相速率影响下平均电流和Fano factor随时间的演化　(a) 对称DQD($\varepsilon=0$)时的平均电流; (b) 非对称DQD($\varepsilon=10\varDelta$)时的平均电流; (c) 对称DQD($\varepsilon=0$)时的Fano factor; (d) 非对称DQD($\varepsilon=10\varDelta$)时的Fano factor

Figure 6. Distributions of the average current and the Fano factor versus t for different values of $\varGamma_{\phi}$ in the pure dephasing environment: (a) The average current in symmetric case ($\varepsilon=0$); (b) the average current in asymmetric case ($\varepsilon=10\varDelta$); (c) the Fano factor in symmetric case ($\varepsilon=0$); (d) the Fano factor in asymmetric case ($\varepsilon=10\varDelta$).

DownLoad: Full-Size Img PowerPoint

图 7 纯退相环境中不同退相干速率和纯退相速率影响下电子转移几率随时间的演化, $\varepsilon=10\varDelta$　(a) 不同退相干速率下转移0个电子的几率; (b) 不同纯退相速率下转移0个电子的几率; (c) 不同退相干速率下转移1个电子的几率; (d) 不同纯退相速率下转移1个电子的几率; (e) 不同退相干速率下转移2个电子的几率; (f) 不同纯退相速率下转移2个电子的几率

Figure 7. Distribution of the electron transfer probability versus t for different values of $\varGamma_{\rm d}$ and $\varGamma_{\phi}$ in the pure dephasing environment, $\varepsilon=0$: (a) The probability of 0 electron transfer at different values of $\varGamma_{\rm d}$; (b) the probability of 0 electron transfer at different values of $\varGamma_{\phi}$; (c) the probability of 1 electron transfer at different values of $\varGamma_{\rm d}$; (d) the probability of 1 electron transfer at different values of $\varGamma_{\phi}$); (e) the probability of 2 electrons transfer at different values of $\varGamma_{\rm d}$; (f) the probability of 2 electrons transfer at different values of $\varGamma_{\phi}$.

DownLoad: Full-Size Img PowerPoint

[1]	Gurvitz S A, Fedichkin L, Mozyrsky D, Berman G P 2003 Phys. Rev. Lett. 91 066801 Google Scholar
[2]	Kang L S, Zhang Y H, Xu X L, Tang X 2017 Phys. Rev. B 96 235417 Google Scholar
[3]	孙峰, 刘然, 索雨晴, 牛乐乐, 傅焕俨, 季文芳, 李宗良 2019 物理学报 68 178502 Google Scholar Sun F, Liu R, Suo Y Q, Niu L L, Fu H Y, Ji W F, Li Z L 2019 Acta Phys. Sin. 68 178502 Google Scholar
[4]	赵文垒, 王建忠, 豆福全 2012 物理学报 61 240302 Google Scholar Zhao W L, Wang J Z, Dou F Q 2012 Acta Phys. Sin. 61 240302 Google Scholar
[5]	Cui P, Li X Q, Shao J S, Yan Y J 2006 Phys. Lett. A 357 449 Google Scholar
[6]	Gurvitz S A, Mozyrsky D 2008 Phys. Rev. B 77 075325 Google Scholar
[7]	Zhao G P, Zhang Y H, Cai X J, Xu X L, Kang L S 2016 Physica E 84 10 Google Scholar
[8]	Cai X J 2019 Entropy 21 1040 Google Scholar
[9]	Li Z L, Bi J J, Liu R, Yi X H, Fu H Y, Sun F, Wei M Z, Wang C K 2017 Chin. Phys. B 26 098508 Google Scholar
[10]	Cai X J, Zheng Y J 2018 J. Chem. Phys. 149 094107 Google Scholar
[11]	Alexander S, Uttam S, Shekhar D H, Nath B M, Gerardo A 2015 Phys. Rev. Lett. 115 020403 Google Scholar
[12]	李保民, 胡明亮, 范桁 2019 物理学报 68 030304 Google Scholar Li B M, Hu M L, Fan H 2019 Acta Phys. Sin. 68 030304 Google Scholar
[13]	Xu P, Wang D, Ye L 2013 Chin. Phys. B 22 100306 Google Scholar
[14]	Zhang Y H, Kang L S, Xu X L, Tang X, Li H B, Cai X J 2017 Mod. Phys. Lett. B 31 1730004 Google Scholar
[15]	Zheng S B, Guo G C 2000 Phys. Rev. Lett. 85 2392 Google Scholar
[16]	Gurvitz S A 1997 Phys. Rev. B 56 15215 Google Scholar
[17]	Cai X J, Zheng Y J 2016 Phys. Rev. A 94 042110 Google Scholar
[18]	Sun S N, Zheng Y J 2019 Phys. Rev. Lett. 123 180403 Google Scholar
[19]	Cai X J, Zheng Y J 2017 Phys. Rev. A 95 052104 Google Scholar
[20]	Cai X J, Meng R X, Zhang Y H, Wang L F 2019 Europhys. Lett. 125 30007 Google Scholar
[21]	尹永琦, 马佳宁, 李华, 王选章, 贺泽龙 2009 物理学报 58 4162 Google Scholar Yin Y Q, Ma J N, Li H, Wang X Z, He Z L 2009 Acta Phys. Sin. 58 4162 Google Scholar
[22]	Yang L W, Xia Y J 2016 Chin. Phys. B 25 110303 Google Scholar
[23]	杨军, 武文远, 龚艳春 2008 物理学报 57 448 Google Scholar Yang J, Wu W Y, Gong Y C 2008 Acta Phys. Sin. 57 448 Google Scholar
[24]	Li X Q, Cui P, Yan Y J 2005 Phys. Rev. Lett. 94 066803 Google Scholar
[25]	Ouyang S H, Lam C H, You J Q 2010 Phys. Rev. B 81 075301 Google Scholar
[26]	栗军, 刘玉, 平婧, 叶银, 李新奇 2012 物理学报 61 137202 Google Scholar Li J, Liu Y, Ping J, Ye Y, Li X Q 2012 Acta Phys. Sin. 61 137202 Google Scholar
[27]	Aguado R, Brandes T 2004 Phys. Rev. Lett. 92 206601 Google Scholar
[28]	Du L, Wu J H, Artoni M, Rocca G C 2019 Phys. Rev. A 100 052102 Google Scholar
[29]	Ford G W, Lewis J T, O'Connell R F 2001 Phys. Rev. A 64 032101 Google Scholar
[30]	Korotkov A N, Averin D V 2001 Phys. Rev. B 64 165310 Google Scholar
[31]	Korotkov A N 2001 Phys. Rev. B 63 085312 Google Scholar
[32]	Xu C R, Vavilov M G 2013 Phys. Rev. B 88 195307 Google Scholar
[33]	Gurvitz S A 2019 J. Phys. A: Math. Theor. 52 175301 Google Scholar
[34]	Levitov L S, Lesovik G B 1993 JETP Lett. 58 230
[35]	Levitov L S, Lee H, Lesovik G B 1996 J. Math. Phys. 37 4845 Google Scholar
[36]	Bagrets D A, Nazarov Yu V 2003 Phys. Rev. B 67 085316 Google Scholar
[37]	Flindt C, Novotný T, Braggio A, Jauho A 2010 Phys. Rev. B 82 155407 Google Scholar
[38]	Novotný T, Donarini A, Flindt C, Jauho A 2004 Phys. Rev. Lett. 92 248302 Google Scholar
[39]	Iannaccone G, Lombardi G, Macucci M, Pellegrini B 1998 Phys. Rev. Lett. 80 1054 Google Scholar
[40]	Kießlich G, Schöll E, Brandes T, Hohls F, Haug R J 2007 Phys. Rev. Lett. 99 206602 Google Scholar
[41]	Olsen M K, Corney J F 2013 Phys. Rev. A 87 033839 Google Scholar
[42]	鹿博, 韩成银, 庄敏, 柯勇贯, 黄嘉豪, 李朝红 2019 物理学报 68 040306 Google Scholar Lu B, Han C Y, Zhuang M, Ke Y G, Huang J H, Li C H 2019 Acta Phys. Sin. 68 040306 Google Scholar
[43]	Albert M, Haack G, Flindt C, Büttiker M 2012 Phys. Rev. Lett. 108 186806 Google Scholar
[44]	Tang G M, Xu F M, Wang J 2014 Phys. Rev. B 89 205310 Google Scholar
[45]	Gurvitz S A, Prager Y S 1996 Phys. Rev. B 53 15932 Google Scholar
[46]	Bagrets D A, Utsumi Y, Golubev D S, Schön G 2006 Fortschr. Phys. 54 917 Google Scholar
[47]	Emary C, Marcos D, Aguado R, Brandes T 2007 Phys. Rev. B 76 161404 Google Scholar
[48]	Zheng Y J, Brown F L H 2003 Phys. Rev. Lett. 90 238305 Google Scholar
[49]	Luo J Y, Jiao H J, Shen Y, Cen G, He X L, Wang C R 2011 J. Phys. Condens. Matter 23 145301 Google Scholar
[50]	Pfeifer P 1982 Phys. Rev. A 26 701 Google Scholar
[51]	Gurvitz S A 2003 Quantum. Inf. Process. 2 15 Google Scholar
[52]	Carmi A, Oreg Y 2012 Phys. Rev. B 85 045325 Google Scholar
[53]	Kok P, Munro W J, Nemoto K, Ralph T C, Dowling J P, Milburn G J 2007 Rev. Mod. Phys. 79 135 Google Scholar
[54]	Sukhorukov E V, Burkard G, Loss D 2001 Phys. Rev. B 63 125315 Google Scholar
[55]	Xue H B, Zhang Z X, Fei H M 2012 Eur. Phys. J. B 85 336 Google Scholar
[56]	Thielmann A, Hettler M H, König J, Schön G 2005 Phys. Rev. Lett. 95 146806 Google Scholar
[57]	Flindt C, Novotný T, Jauho A P 2004 Phys. Rev. B 70 205334 Google Scholar

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Vol. 69, Issue 4 - 2020-02-20

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