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Recently, the measurement scheme of quantum dot qubit decocoherence quantized by the longitudinal optical (LO) phonon spontaneous emission rate has attracted the attention and discussion of many researchers. However, it is not difficult to see that the above-mentioned measurement scheme still has some insufficient and imperfect aspects that are to be studied urgently. Considering from the physical mechanism, the essence of the above scheme is to quantify the decoherence time of qubit by using the excited state decay time or excited state lifetime of the polaron. However, so far, there is little research on how the ground state decay time and ground state lifetime of two-state polaron affect the coherence of qubit. There is no doubt that this is an equally important research topic. This is because, firstly, for the coherence of the quantum state of polaron, both the decay of the excited state and the decay of the ground state will destroy or attenuate the qubit coherence, secondly, the transition rate of the two-state polaron from the ground state to the excited state after absorbing an LO phonon is also a function quantifying the qubit decoherence time of two-state system of which the inverse is called the ground state decay time or the ground state lifetime. It may be called a measure of qubit decoherence time quantized by the ground state decay time or ground state lifetime of polaron. In this article, the ground-state and excited-state energy and wave function of the magnetopolaron in a donor-center quantum dot with asymmetric Gaussian potential are derived by Lee-Low-Pines transformation and Pekar-type variational methodd, and then the two-level structure for a qubit is constructed. The measure of qubit decoherence time of quantum dots quantified by ground state decay time of two-state polaron is established, which is compared with the well-known measure of qubit decoherence time of quantum dots quantified by polaron excited state decay time, and their physical mechanisms are revealed. By studying the influence of dielectric constant ratio, electro-phonons coupling constant, temperature and electromagnetic field on the ground state lifetime of magnetopolaron in the donor-center quantum dots with asymmetric Gaussian potential, the influences of material properties, temperature, electromagnetic field and other environmental factors on qubit decoherence of quantum dots are revealed, thereby revealing the mechanism of qubit decoherence caused by LO phonon effect.
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Keywords:
- donor-center quantum dots /
- asymmetric Gaussian potential /
- magnetopolaron /
- lifetime /
- decoherence
[1] Tiotsop M, Fotue A J, Talla P K, Kenfack S C, Fautso K G, Fotsin H, Fai L C 2018 Iran. J. Sci. Technol. A 42 933
Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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图 1 非对称高斯势曲线
Figure 1. Asymmetric Gaussian (AG) potential curve.
图 2 LO声子平均数
${N_0}$ 在不同电声耦合常数$\alpha $ 下随温度参数$\gamma $ 的变化Figure 2. Mean number
${N_0}$ of LO phonons as a function of the temperature parameter$\gamma $ at different electron-phonon coupling (EPC) constant$\alpha $ .
图 14 磁极化子基态寿命
${\tau _0}$ 在不同电场强度$F$ 下随抛物势范围${R_0}$ 的变化Figure 14. The ground-state lifetime
${\tau _0}$ as a function of the range${R_0}$ of the parabolic potential at different electric field$F$ .
图 3 磁极化子基态能量
${E_0}$ 及其各组成部分随高斯势阱宽$L$ 的变化Figure 3. Ground state energy
${E_0}$ of the magnetopolaron and its components versus the well width$L$ of the AG potential.
图 4 能隙
$\Delta E$ 在非对称高斯势不同阱深${V_0}$ 下随其阱宽$L$ 的变化Figure 4. Energy gap
$\Delta E$ as a function of the well width$L$ at different well depth${V_0}$ of the AG potential.
图 5 能隙
$\Delta E$ 在不同介电常数比$\eta $ 下随高斯势阱宽$L$ 的变化Figure 5. Energy gap
$\Delta E$ versus the well width$L$ of the AG potential under different dielectric constant (DC) ratio$\eta $ .
图 6 能隙
$\Delta E$ 在不同电声耦合常数$\alpha $ 下随高斯势阱深${V_0}$ 的变化Figure 6. Energy gap
$\Delta E$ as a function of the well depth${V_0}$ of the AG potential at different EPC constant$\alpha $ .
图 7 能隙
$\Delta E$ 在不同电场强度$F$ 下随高斯势阱深${V_0}$ 的变化Figure 7. Energy gap
$\Delta E$ versus the well depth${V_0}$ of the AG potential under different electric field$F$ .
图 8 能隙
$\Delta E$ 在不同磁场的回旋频率${\omega _{\rm{c}}}$ 下随抛物势范围${R_0}$ 的变化Figure 8. Energy gap
$\Delta E$ as a function of the range${R_0}$ of the parabolic potential at different magnetic-field cyclotron (MFC) frequency${\omega _{\rm{c}}}$ .
图 9 磁极化子基态寿命
${\tau _0}$ 在高斯势不同阱深${V_0}$ 下随其阱宽$L$ 的变化Figure 9. The ground-state lifetime
${\tau _0}$ of the magntopolaron as a function of the well width$L$ at different well depth${V_0}$ of the AG potential.
图 10 基态寿命
${\tau _0}$ 在不同电声耦合常数$\alpha $ 下随高斯势阱宽$L$ 的变化Figure 10. The ground-state lifetime
${\tau _0}$ as a function of the well width$L$ of the AG potential at different EPC constant$\alpha $ .
图 11 基态寿命
${\tau _0}$ 在不同温度参数$\gamma $ 下随高斯势阱宽$L$ 的变化Figure 11. The ground-state lifetime
${\tau _0}$ as a function of the well width$L$ of the AG potential at different temperature parameter$\gamma $ .
图 12 基态寿命
${\tau _0}$ 在不同介电常数比$\eta $ 下随抛物势范围${R_0}$ 的变化Figure 12. The ground-state lifetime
${\tau _0}$ as a function of the range${R_0}$ of the parabolic potential at different DC ratio$\eta $ 
图 13 基态寿命
${\tau _0}$ 在磁场的不同回旋频率${\omega _{\rm{c}}}$ 下随高斯势阱深${V_0}$ 的变化Figure 13. The ground-state lifetime
${\tau _0}$ versus the well depth${V_0}$ of the AG potential under different MFC frequencies${\omega _{\rm{c}}}$ -
[1] Tiotsop M, Fotue A J, Talla P K, Kenfack S C, Fautso K G, Fotsin H, Fai L C 2018 Iran. J. Sci. Technol. A 42 933
Google Scholar
[2] Lang Z H, Cai C U, Xiao J L 2019 Int. J. Theor. Phys. 58 2320
Google Scholar
[3] Jordan K, Stephen J P 2005 Phys. Rev. B 71 125332
Google Scholar
[4] Liang Z H, Xiao J L 2018 Indian J. Phys. 92 437
Google Scholar
[5] Chi F, Li S S 2006 J. Appl. Phys. 99 043705
Google Scholar
[6] Li S S, Xia J B, Yang F H, Niu Z C, Feng S L, Zheng H Z 2001 J. Appl. Phys. 90 6151
Google Scholar
[7] Petta J R, Johnson A C, Taylor J M, Laird E A, Yacoby A, Lukin M D, Marcus C M, Hanson M P, Gossard A C 2005 Science 309 2180
Google Scholar
[8] Varwig S, René A, Greilich A, Yakovlev D R, Reuter D, Wieck A D, Bayer B 2013 Phys. Rev. B 87 115307
Google Scholar
[9] Sun Y, Xiao J L 2019 Opt. Quantum Electron. 51 110
Google Scholar
[10] Xiao J L 2019 J. Low Temp. Phys. 195 442
Google Scholar
[11] Ma X J, Xiao J L 2018 Opt. Quantum Electron. 50 144
Google Scholar
[12] Xiao J L 2018 J. Low Temp. Phys. 192 41
Google Scholar
[13] Baumgratz T, Cramer M, Plenio M B 2014 Phys. Rev. Lett. 113 140401
Google Scholar
[14] Shao L H, Xi Z J, Fan H, Li Y M 2015 Phys. Rev. A 91 042120
Google Scholar
[15] Rana S, Parashar P, Lewenstein M 2016 Phys. Rev. A 93 012110
Google Scholar
[16] Streltsov A, Singh U, Dhar H S, Bera M N, Adesso G 2015 Phys. Rev. Lett. 115 020403
Google Scholar
[17] Ma J J, Yadin B, Girolami D, Vedral V, Gu M 2016 Phys. Rev. Lett. 116 160407
Google Scholar
[18] Davide G 2014 Phys. Rev. Lett. 113 170401
Google Scholar
[19] Pires D P, Céleri L C, Soares-Pinto D O 2015 Phys. Rev. A 91 042330
Google Scholar
[20] Fotue A J, Fobasso M F C, Kenfack S C, Tiotsop M, Djomou J R D, Ekosso C M, Nguimeya G P, Danga J E, Keumo Tsiaze R M, Fai L C 2016 Eur. Phys. J. Plus 131 205
Google Scholar
[21] Xiao W, Xiao J L 2016 Int. J. Theor. Phys. 55 2936
Google Scholar
[22] Sun Y, Ding Z H, Xiao J L 2014 J. Low Temp. Phys. 177 151
Google Scholar
[23] Sun Y, Ding Z H, Xiao J L 2017 J. Electron. Mater. 46 439
Google Scholar
[24] Bai X F, Xin W, Eerdunchaolu 2019 Int. J. Mod. Phys. B 33 1950322
Google Scholar
[25] 乌云其木格, 韩超, 额尔敦朝鲁 2019 68 247803
Google Scholar
Wuyunqimuge, Han C, Eerdunchaolu 2019 Acta Phys. Sin. 68 247803
Google Scholar
[26] Boucaud P, Sauvage S, Bras F, Fishman G, Ortéga J M, Gérard J M 2005 Physica E 26 59
Google Scholar
[27] AZibik E, Wilson L R, Green R P, Wells J P R, Phillips P J, Carder D A, Cockburn J W, Skolnick M S, Steer M J, Liu H Y, Hopkinson M 2004 Physica E 21 405
Google Scholar
[28] Verzelen O, Ferreira R, Bastard G 2002 Physica E 13 309
Google Scholar
[29] Yu Y F, Xiao J L, Yin J W, Wang Z W 2008 Chin. Phys. B 17 2236
Google Scholar
[30] Khordad R, Goudarzi S, Bahramiyan H 2016 Indian J. Phys. 90 659
Google Scholar
[31] Li Z X 2019 Indian J. Phys. 93 707
Google Scholar
[32] Lee T D 1953 Phys. Rev. 90 297
Google Scholar
[33] Landau L D, Pekar S I 1948 Zh. Eksp. Teor. Fiz. 18 419
[34] Brummell M A, Nicholas R J, Hopkins M A, Harris J J, Foxon C T 1987 Phys. Rev. Lett. 58 77
Google Scholar
[35] Bai X F, Xin W, Yin H W, Eerdunchaolu 2017 J. Korean Phys. Soc. 70 956
Google Scholar
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