Phonon-assisted relaxation and decoherence of singlet-triplet qubits in Si/SiGe quantum dots

Viktoriia Kornich; Christoph Kloeffel; Daniel Loss

doi:10.22331/q-2018-05-28-70

Phonon-assisted relaxation and decoherence of singlet-triplet qubits in Si/SiGe quantum dots

Viktoriia Kornich^1,2, Christoph Kloeffel¹, and Daniel Loss^1,3

¹Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland
²Department of Physics, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA
³CEMS, RIKEN, Wako, Saitama 351-0198, Japan

Published:	2018-05-28, volume 2, page 70
Eprint:	arXiv:1511.07369v5
Doi:	https://doi.org/10.22331/q-2018-05-28-70
Citation:	Quantum 2, 70 (2018).

Find this paper interesting or want to discuss? Scite or leave a comment on SciRate.

Abstract

We study theoretically the phonon-induced relaxation and decoherence of spin states of two electrons in a lateral double quantum dot in a SiGe/Si/SiGe heterostructure. We consider two types of singlet-triplet spin qubits and calculate their relaxation and decoherence times, in particular as a function of level hybridization, temperature, magnetic field, spin orbit interaction, and detuning between the quantum dots, using Bloch-Redfield theory. We show that the magnetic field gradient, which is usually applied to operate the spin qubit, may reduce the relaxation time by more than an order of magnitude. Using this insight, we identify an optimal regime where the magnetic field gradient does not affect the relaxation time significantly, and we propose regimes of longest decay times. We take into account the effects of one-phonon and two-phonon processes and suggest how our theory can be tested experimentally. The spin lifetimes we find here for Si-based quantum dots are significantly longer than the ones reported for their GaAs counterparts.

► BibTeX data

@article{Kornich2018phononassisted,
  doi = {10.22331/q-2018-05-28-70},
  url = {https://doi.org/10.22331/q-2018-05-28-70},
  title = {Phonon-assisted relaxation and decoherence of singlet-triplet qubits in {S}i/{S}i{G}e quantum dots},
  author = {Kornich, Viktoriia and Kloeffel, Christoph and Loss, Daniel},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {2},
  pages = {70},
  month = may,
  year = {2018}
}

► References

[1] D. Loss and D. P. DiVincenzo, Phys. Rev. A 57, 120 (1998).
https://doi.org/10.1103/physreva.57.120

[2] R. Hanson, L. P. Kouwenhoven, J. R. Petta, S. Tarucha, and L. M. K. Vandersypen, Rev. Mod. Phys. 79, 1217 (2007).
https://doi.org/10.1103/revmodphys.79.1217

[3] C. Kloeffel and D. Loss, Annu. Rev. Condens. Matter Phys. 4, 51 (2013).
https://doi.org/10.1146/annurev-conmatphys-030212-184248

[4] G. Burkard, D. Loss, and D. P. DiVincenzo, Phys. Rev. B 59, 2070 (1999).
https://doi.org/10.1103/physrevb.59.2070

[5] J. Levy, Phys. Rev. Lett. 89, 147902 (2002).
https://doi.org/10.1103/physrevlett.89.147902

[6] A. V. Khaetskii, D. Loss, and L. Glazman, Phys. Rev. Lett. 88, 186802 (2002).
https://doi.org/10.1103/physrevlett.88.186802

[7] I. A. Merkulov, Al. L. Efros, and M. Rosen, Phys. Rev. B 65, 205309 (2002).
https://doi.org/10.1103/physrevb.65.205309

[8] W. A. Coish and D. Loss, Phys. Rev. B 70, 195340 (2004).
https://doi.org/10.1103/physrevb.70.195340

[9] A. C. Johnson, J. R. Petta, J. M. Taylor, A. Yacoby, M. D. Lukin, C. M. Marcus, M. P. Hanson, and A. C. Gossard, Nature (London) 435, 925 (2005).
https://doi.org/10.1038/nature03815

[10] J. M. Taylor, H.-A. Engel, W. Dür, A. Yacoby, C. M. Marcus, P. Zoller, and M. D. Lukin, Nat. Phys. 1, 177 (2005).
https://doi.org/10.1038/nphys174

[11] J. R. Petta, A. C. Johnson, J. M. Taylor, E. A. Laird, A. Yacoby, M. D. Lukin, C. M. Marcus, M. P. Hanson, and A. C. Gossard, Science 309, 2180 (2005).
https://doi.org/10.1126/science.1116955

[12] S. Foletti, H. Bluhm, D. Mahalu, V. Umansky, and A. Yacoby, Nat. Phys. 5, 903 (2009).
https://doi.org/10.1038/nphys1424

[13] H. Bluhm, S. Foletti, I. Neder, M. Rudner, D. Mahalu, V. Umansky, and A. Yacoby, Nat. Phys. 7, 109 (2011).
https://doi.org/10.1038/nphys1856

[14] M. D. Shulman, O. E. Dial, S. P. Harvey, H. Bluhm, V. Umansky, and A. Yacoby, Science 336, 202 (2012).
https://doi.org/10.1126/science.1217692

[15] J. Klinovaja, D. Stepanenko, B. I. Halperin, and D. Loss, Phys. Rev. B 86, 085423 (2012).
https://doi.org/10.1103/physrevb.86.085423

[16] J. Yoneda, T. Otsuka, T. Nakajima, T. Takakura, T. Obata, M. Pioro-Ladrière, H. Lu, C. J. Palmstrøm, A. C. Gossard, and S. Tarucha, Phys. Rev. Lett. 113, 267601 (2014).
https://doi.org/10.1103/physrevlett.113.267601

[17] P. Scarlino, E. Kawakami, P. Stano, M. Shafiei, C. Reichl, W. Wegscheider, and L. M. K. Vandersypen, Phys. Rev. Lett 113, 256802 (2014).
https://doi.org/10.1103/physrevlett.113.256802

[18] S. Chesi, Y.-D. Wang, J. Yoneda, T. Otsuka, S. Tarucha, and D. Loss, Phys. Rev. B 90, 235311 (2014).
https://doi.org/10.1103/physrevb.90.235311

[19] P. Cerfontaine, T. Botzem, D. P. DiVincenzo, and H. Bluhm, Phys. Rev. Lett. 113, 150501 (2014).
https://doi.org/10.1103/physrevlett.113.150501

[20] D. E. F. Biesinger, C. P. Scheller, B. Braunecker, J. Zimmerman, A. C. Gossard, and D. M. Zumbühl, Phys. Rev. Lett. 115, 106804 (2015).
https://doi.org/10.1103/physrevlett.115.106804

[21] M. P. Wardrop and A. C. Doherty, Phys. Rev. B 93, 075436 (2016).
https://doi.org/10.1103/physrevb.93.075436

[22] F. Martins, F. K. Malinowski, P. D. Nissen, E. Barnes, S. Fallahi, G. C. Gardner, M. J. Manfra, C. M. Marcus, and F. Kuemmeth, Phys. Rev. Lett. 116, 116801 (2016).
https://doi.org/10.1103/physrevlett.116.116801

[23] R. Maurand, X. Jehl, D. Kotekar-Patil, A. Corna, H. Bohuslavskyi, R. Laviéville, L. Hutin, S. Barraud, M. Vinet, M. Sanquer, and S. De Franceschi, Nat. Commun. 7, 13575 (2016).
https://doi.org/10.1038/ncomms13575

[24] H. Watzinger, C. Kloeffel, L. Vukusic, M. D. Rossell, V. Sessi, J. Kukucka, R. Kirchschlager, E. Lausecker, A. Truhlar, M. Glaser, A. Rastelli, A. Fuhrer, D. Loss, and G. Katsaros, Nano Lett. 16, 6879 (2016).
https://doi.org/10.1021/acs.nanolett.6b02715

[25] C. Kloeffel, M. Trif, and D. Loss, Phys. Rev. B 84, 195314 (2011).
https://doi.org/10.1103/physrevb.84.195314

[26] Y. Hu, F. Kuemmeth, C. M. Lieber, and C. M. Marcus, Nat. Nanotechnol. 7, 47 (2012).
https://doi.org/10.1038/nnano.2011.234

[27] F. Maier, C. Kloeffel, and D. Loss, Phys. Rev. B 87, 161305(R) (2013).
https://doi.org/10.1103/physrevb.87.161305

[28] C. Kloeffel, M. Trif, P. Stano, and D. Loss, Phys. Rev. B 88, 241405(R) (2013).
https://doi.org/10.1103/physrevb.88.241405

[29] M. Brauns, J. Ridderbos, A. Li, E. P. A. M. Bakkers, and F. A. Zwanenburg, Phys. Rev. B 93, 121408(R) (2016).
https://doi.org/10.1103/physrevb.93.121408

[30] A. Laucht, R. Kalra, J. T. Muhonen, J. P. Dehollain, F. A. Mohiyaddin, F. Hudson, J. C. McCallum, D. N. Jamieson, A. S. Dzurak, and A. Morello, Appl. Phys. Lett. 104, 092115 (2014).
https://doi.org/10.1063/1.4867905

[31] A. M. Tyryshkin, S. Tojo, J. J. L. Morton, H. Riemann, N. V. Abrosimov, P. Becker, H.-J. Pohl, T. Schenkel, M. L. W. Thewalt, K. M. Itoh, and S. A. Lyon, Nat. Mater. 11, 143 (2012).
https://doi.org/10.1038/nmat3182

[32] S. J. Hile, M. G. House, E. Peretz, J. Verduijn, D. Widmann, T. Kobayashi, S. Rogge, and M. Y. Simmons, Appl. Phys. Lett. 107, 93504 (2015).
https://doi.org/10.1063/1.4929827

[33] T. F. Watson, B. Weber, M. G. House, H. Büch, and M. Y. Simmons, Phys. Rev. Lett. 115, 166806 (2015).
https://doi.org/10.1103/physrevlett.115.166806

[34] Y. Wang, C.-Y. Chen, G. Klimeck, M. Y. Simmons, and R. Rahman, arXiv:1703.05370.
arXiv:1703.05370

[35] J. J. Pla, F. A. Mohiyaddin, K. Y. Tan, J. P. Dehollain, R. Rahman, G. Klimeck, D. N. Jamieson, A. S. Dzurak, and A. Morello, Phys. Rev. Lett. 113, 246801 (2014).
https://doi.org/10.1103/physrevlett.113.246801

[36] B. E. Kane, Nature 393, 133 (1998).
https://doi.org/10.1038/30156

[37] M. Steger, K. Saeedi, M. L. W. Thewalt, J. J. L. Morton, H. Riemann, N. V. Abrosimov, P. Becker, and H.-J. Pohl, Science 336, 1280 (2012).
https://doi.org/10.1126/science.1217635

[38] K. Saeedi, S. Simmons, J. Z. Salvail, P. Dluhy, H. Riemann, N. V. Abrosimov, P. Becker, H.-J. Pohl, J. J. Morton, and M. L. Thewalt, Science 342, 830 (2013).
https://doi.org/10.1126/science.1239584

[39] M. Usman, C. D. Hill, R. Rahman, G. Klimeck, M. Y. Simmons, S. Rogge, and L. C. L. Hollenberg, Phys. Rev. B 91, 245209 (2015).
https://doi.org/10.1103/physrevb.91.245209

[40] C. D. Hill, E. Peretz, S. J. Hile, M. G. House, M. Fuechsle, S. Rogge, M. Y. Simmons, and L. C. L. Hollenberg, Science Advances 1, e1500707 (2015).
https://doi.org/10.1126/sciadv.1500707

[41] J. T. Muhonen, J. P. Dehollain, A. Laucht, S. Simmons, R. Kalra, F. E. Hudson, D. N. Jamieson, J. C. McCallum, K. M. Itoh, A. S. Dzurak, and A. Morello, arXiv:1702.07991.
arXiv:1702.07991

[42] G. W. Morley, P. Lueders, M. H. Mohammady, S. J. Balian, G. Aeppli, C. W. M. Kay, W. M. Witzel, G. Jeschke, and T. S. Monteiro, Nat. Mater. 12, 103 (2013).
https://doi.org/10.1038/nmat3499

[43] J. T. Muhonen, A. Laucht, S. Simmons, J. P. Dehollain, R. Kalra, F. E. Hudson, S. Freer, K. M. Itoh, D. N. Jamieson, J. C. McCallum, A. S. Dzurak, and A. Morello, J. Phys. Condens. Matter 27, 154205 (2015).
https://doi.org/10.1088/0953-8984/27/15/154205

[44] M. Veldhorst, C. H. Yang, J. C. C. Hwang, W. Huang, J. P. Dehollain, J. T. Muhonen, S. Simmons, A. Laucht, F. E. Hudson, K. M. Itoh, A. Morello, and A. S. Dzurak, Nature 526, 410 (2015).
https://doi.org/10.1038/nature15263

[45] M. J. Calderón, B. Koiller, X. Hu, and S. Das Sarma, Phys. Rev. Lett. 96, 096802 (2006).
https://doi.org/10.1103/physrevlett.96.096802

[46] K. Takeda, T. Obata, Y. Fukuoka, W. M. Akhtar, J. Kamioka, T. Kodera, S. Oda, and S. Tarucha, Appl. Phys. Lett. 102, 123113 (2013).
https://doi.org/10.1063/1.4799287

[47] E. Kawakami, P. Scarlino, D. R. Ward, F. R. Braakman, D. E. Savage, M. G. Lagally, M. Friesen, S. N. Coppersmith, M. A. Eriksson, and L. M. K. Vandersypen, Nat. Nanotechnol. 9, 666 (2014).
https://doi.org/10.1038/nnano.2014.153

[48] D. M. Zajac, T. M. Hazard, X. Mi, K. Wang, and J. R. Petta, Appl. Phys. Lett. 106, 223507 (2015).
https://doi.org/10.1063/1.4922249

[49] K. Takeda, J. Kamioka, T. Otsuka, J. Yoneda, T. Nakajima, M. R. Delbecq, S. Amaha, G. Allison, T. Kodera, S. Oda, and S. Tarucha, Sci. Adv. 2, e1600694 (2016).
https://doi.org/10.1126/sciadv.1600694

[50] D. M. Zajac, A. J. Sigillito, M. Russ, F. Borjans, J. M. Taylor, G. Burkard, and J. R. Petta, Science 359, 439 (2018).
https://doi.org/10.1126/science.aao5965

[51] T. F. Watson, S. G. J. Philips, E. Kawakami, D. R. Ward, P. Scarlino, M. Veldhorst, D. E. Savage, M. G. Lagally, M. Friesen, S. N. Coppersmith, M. A. Eriksson, and L. M. K. Vandersypen, Nature 555, 633 (2018).
https://doi.org/10.1038/nature25766

[52] J. K. Gamble, M. Friesen, S. N. Coppersmith, and X. Hu, Phys. Rev. B 86, 035302 (2012).
https://doi.org/10.1103/physrevb.86.035302

[53] C. Tahan and R. Joynt, Phys. Rev. B 89, 075302 (2014).
https://doi.org/10.1103/physrevb.89.075302

[54] F. Schäffler, Semicond. Sci. Technol. 12, 1515 (1997).
https://doi.org/10.1088/0268-1242/12/12/001

[55] M. Friesen, S. Chutia, C. Tahan, and S. N. Coppersmith, Phys. Rev. B 75, 115318 (2007).
https://doi.org/10.1103/physrevb.75.115318

[56] F. A. Zwanenburg, A. S. Dzurak, A. Morello, M. Y. Simmons, L. C. L. Hollenberg, G. Klimeck, S. Rogge, S. N. Coppersmith, and M. A. Eriksson, Rev. Mod. Phys. 85, 961 (2013).
https://doi.org/10.1103/revmodphys.85.961

[57] S. Goswami, K. A. Slinker, M. Friesen, L. M. McGuire, J. L. Truitt, C. Tahan, L. J. Klein, J. O. Chu, P. M. Mooney, D. W. van der Weide, R. Joynt, S. N. Coppersmith, and M. A. Eriksson, Nat. Phys. 3, 41 (2007).
https://doi.org/10.1038/nphys475

[58] M. Xiao, M. G. House, and H. W. Jiang, Appl. Phys. Lett. 97, 032103 (2010).
https://doi.org/10.1063/1.3464324

[59] C. H. Yang, A. Rossi, R. Ruskov, N. S. Lai, F. A. Mohiyaddin, S. Lee, C. Tahan, G. Klimeck, A. Morello, and A. S. Dzurak, Nat. Commun. 4, 2069 (2013).
https://doi.org/10.1038/ncomms3069

[60] M. Prada, R. H. Blick, and R. Joynt, Phys. Rev. B 77, 115438 (2008).
https://doi.org/10.1103/physrevb.77.115438

[61] M. Raith, P. Stano, and J. Fabian, Phys. Rev. B 86, 205321 (2012).
https://doi.org/10.1103/physrevb.86.205321

[62] B. M. Maune, M. G. Borselli, B. Huang, T. D. Ladd, P. W. Deelman, K. S. Holabird, A. A. Kiselev, I. Alvarado-Rodriguez, R. S. Ross, A. E. Scmitz, M. Sokolich, C. A. Watson, M. F. Gyure, and A. T. Hunter, Nature (London) 481, 344 (2012).
https://doi.org/10.1038/nature10707

[63] J. R. Prance, Z. Shi, C. B. Simmons, D. E. Savage, M. G. Lagally, L. R. Schreiber, L. M. K. Vandersypen, M. Friesen, R. Joynt, S. N. Coppersmith, and M. A. Eriksson, Phys. Rev. Lett. 108, 046808 (2012).
https://doi.org/10.1103/physrevlett.108.046808

[64] D. Culcer, L. Cywiński, Q. Li, X. Hu, and S. Das Sarma, Phys. Rev. B 80, 205302 (2009).
https://doi.org/10.1103/physrevb.80.205302

[65] J.-T. Hung, L. Cywiński, X. Hu, and S. Das Sarma, Phys. Rev. B 88, 085314 (2013).
https://doi.org/10.1103/physrevb.88.085314

[66] L. V. C. Assali, H. M. Petrilli, R. B. Capaz, B. Koiller, X. Hu, and S. Das Sarma, Phys. Rev. B 83, 165301 (2011).
https://doi.org/10.1103/physrevb.83.165301

[67] D. Culcer, A. L. Saraiva, B. Koiller, X. Hu, and S. Das Sarma, Phys. Rev. Lett. 108, 126804 (2012).
https://doi.org/10.1103/physrevlett.108.126804

[68] C. B. Simmons, J. R. Prance, B. J. Van Bael, T. S. Koh, Z. Shi, D. E. Savage, M. G. Lagally, R. Joynt, M. Friesen, S. N. Coppersmith, and M. A. Eriksson, Phys. Rev. Lett. 106, 156804 (2011).
https://doi.org/10.1103/physrevlett.106.156804

[69] A. M. Tyryshkin, S. A. Lyon, T. Schenkel, J. Bokor, J. Chu, W. Jantsch, F. Schäffler, J. L. Truitt, S. N. Coppersmith, and M. A. Eriksson, Physica E 35, 257 (2006).
https://doi.org/10.1016/j.physe.2006.08.021

[70] C. Tahan, M. Friesen, and R. Joynt, Phys. Rev. B 66, 035314 (2002).
https://doi.org/10.1103/physrevb.66.035314

[71] B. A. Glavin and K. W. Kim, Phys. Rev. B 68, 045308 (2003).
https://doi.org/10.1103/physrevb.68.045308

[72] L. Wang and M. W. Wu, J. Appl. Phys. 110, 043716 (2011).
https://doi.org/10.1063/1.3625240

[73] L. Wang, K. Shen, B. Y. Sun, and M. W. Wu, Phys. Rev. B 81, 235326 (2010).
https://doi.org/10.1103/physrevb.81.235326

[74] C. H. Wong, M. A. Eriksson, S. N. Coppersmith, and M. Friesen, Phys. Rev. B 92, 045403 (2015).
https://doi.org/10.1103/physrevb.92.045403

[75] X. Wu, D. R. Ward, J. R. Prance, D. Kim, J. K. Gamble, R. T. Mohr, Z. Shi, D. E. Savage, M. G. Lagally, M. Friesen, S. N. Coppersmith, and M. A. Eriksson, Proc. Natl. Acad. Sci. USA 111, 11938 (2014).
https://doi.org/10.1073/pnas.1412230111

[76] Y.-S. Shin, T. Obata, Y. Tokura, M. Pioro-Ladrière, R. Brunner, T. Kubo, K. Yoshida, and S. Tarucha, Phys. Rev. Lett. 104, 046802 (2010).
https://doi.org/10.1103/physrevlett.104.046802

[77] V. Kornich, C. Kloeffel, and D. Loss, Phys. Rev. B 89, 085410 (2014).
https://doi.org/10.1103/physrevb.89.085410

[78] A. V. Khaetskii and Y. V. Nazarov, Phys. Rev. B 61, 12639 (2000).
https://doi.org/10.1103/physrevb.61.12639

[79] I. L. Aleiner and V. I. Fal'ko, Phys. Rev. Lett. 87, 256801 (2001).
https://doi.org/10.1103/physrevlett.87.256801

[80] V. N. Golovach, A. V. Khaetskii, and D. Loss, Phys. Rev. Lett. 93, 016601 (2004).
https://doi.org/10.1103/physrevlett.93.016601

[81] P. Stano and J. Fabian, Phys. Rev. B 72, 155410 (2005).
https://doi.org/10.1103/physrevb.72.155410

[82] P. Stano and J. Fabian, Phys. Rev. Lett. 96, 186602 (2006).
https://doi.org/10.1103/physrevlett.96.186602

[83] C. Herring and E. Vogt, Phys. Rev. 101, 944 (1956).
https://doi.org/10.1103/physrev.101.944

[84] P. Y. Yu and M. Cardona, Fundamentals of Semiconductors: Physics and Material Properties, 4th ed. (Springer, Berlin, 2010).

[85] A. N. Cleland, Foundations of Nanomechanics: From Solid-State Theory to Device Applications (Springer, Berlin, 2003).

[86] S. Adachi, Properties of Group-IV, III-V and II-VI Semiconductors (John Wiley & Sons, Chichester, 2005).

[87] D. Stepanenko, M. Rudner, B. I. Halperin, and D. Loss, Phys. Rev. B 85, 075416 (2012).
https://doi.org/10.1103/physrevb.85.075416

[88] C. P. Slichter, Principles of Magnetic Resonance (Springer, Berlin, 1980).

[89] M. Borhani, V. N. Golovach, and D. Loss, Phys. Rev. B 73, 155311 (2006).
https://doi.org/10.1103/physrevb.73.155311

[90] R. Winkler, Spin-Orbit Coupling Effects in Two-Dimensional Electron and Hole Systems (Springer, Berlin, 2003).

[91] X. Hu, Phys. Rev. B 83, 165322 (2011).
https://doi.org/10.1103/physrevb.83.165322

[92] V. Srinivasa, J. M. Taylor, and C. Tahan, Phys. Rev. B 94, 205421 (2016).
https://doi.org/10.1103/physrevb.94.205421

[93] N. Rohling and G. Burkard, New J. Phys. 14, 083008 (2012).
https://doi.org/10.1088/1367-2630/14/8/083008

[94] H. Ribeiro, J. R. Petta, and G. Burkard, Phys. Rev. B 82, 115445 (2010).
https://doi.org/10.1103/physrevb.82.115445

[95] J. R. Petta, H. Lu, and A. C. Gossard, Science 327, 669 (2010).
https://doi.org/10.1126/science.1183628

[96] H. Ribeiro, G. Burkard, J. R. Petta, H. Lu, and A. C. Gossard, Phys. Rev. Lett. 110, 086804 (2013).
https://doi.org/10.1103/physrevlett.110.086804

[97] H. Ribeiro, J. R. Petta, and G. Burkard, Phys. Rev. B 87, 235318 (2013).
https://doi.org/10.1103/physrevb.87.235318

[98] Z. Wilamowski, W. Jantsch, H. Malissa, and U. Rössler, Phys. Rev. B 66, 195315 (2002).
https://doi.org/10.1103/physrevb.66.195315

[99] L. Vervoort, R. Ferreira, and P. Voisin, Phys. Rev. B 56, R12744 (1997).
https://doi.org/10.1103/physrevb.56.r12744

[100] L. Vervoort, R. Ferreira, and P. Voisin, Semicond. Sci. Technol. 14, 227 (1999).
https://doi.org/10.1088/0268-1242/14/3/004

[101] M. O. Nestoklon, E. L. Ivchenko, J.-M. Jancu, and P. Voisin, Phys. Rev. B 77, 155328 (2008).
https://doi.org/10.1103/physrevb.77.155328

[102] D. E. McCumber and M. D. Sturge, J. Appl. Phys. 34, 1682 (1963).
https://doi.org/10.1063/1.1702657

[103] W. M. Yen, W. C. Scott, and A. L. Schawlow, Phys. Rev. 136, A271 (1964).
https://doi.org/10.1103/physrev.136.a271

[104] S. B. Altner, G. Zumofen, U. P. Wild, and M. Mitsunaga, Phys. Rev. B 54, 17493 (1996).
https://doi.org/10.1103/physrevb.54.17493

[105] R. S. Meltzer, in Spectroscopic Properties of Rare Earths in Optical Materials, edited by G. Liu and B. Jacquier (Springer, Berlin, 2005), Chap. 4, pp. 191–265.

[106] K. Roszak and P. Machnikowski, Phys. Rev. B 80, 195315 (2009).
https://doi.org/10.1103/physrevb.80.195315

[107] V. Kornich, C. Kloeffel, and D. Loss, Phys. Rev. B 90, 079901(E) (2014).
https://doi.org/10.1103/physrevb.90.079901

[108] T. Meunier, I. T. Vink, L. H. Willems van Beveren, K-J. Tielrooij, R. Hanson, F. H. L. Koppens, H. P. Tranitz, W. Wegscheider, L. P. Kouwenhoven, and L. M. K. Vandersypen, Phys. Rev. Lett. 98, 126601 (2007).
https://doi.org/10.1103/physrevlett.98.126601

[109] V. N. Golovach, A. V. Khaetskii, and D. Loss, Phys. Rev. B 77, 045328 (2008).
https://doi.org/10.1103/physrevb.77.045328

[110] D. Culcer, L. Cywiński, Q. Li, X. Hu, and S. Das Sarma, Phys. Rev. B 82, 155312 (2010).
https://doi.org/10.1103/physrevb.82.155312

[111] A. V. Kuhlmann, J. Houel, A. Ludwig, L. Greuter, D. Reuter, A. D. Wieck, M. Poggio, and R. J. Warburton, Nat. Phys. 9, 570 (2013).
https://doi.org/10.1038/nphys2688

[112] O. E. Dial, M. D. Shulman, S. P. Harvey, H. Bluhm, V. Umansky, and A. Yacoby, Phys. Rev. Lett. 110, 146804 (2013).
https://doi.org/10.1103/physrevlett.110.146804

[113] D. Kim, D. R. Ward, C. B. Simmons, J. K. Gamble, R. Blume-Kohout, E. Nielsen, D. E. Savage, M. G. Lagally, M. Friesen, S. N. Coppersmith, and M. A. Eriksson, Nat. Nanotechnol. 10, 243 (2015).
https://doi.org/10.1038/nnano.2014.336

[114] X. Hu and S. Das Sarma, Phys. Rev. Lett. 96, 100501 (2006).
https://doi.org/10.1103/physrevlett.96.100501

[115] D. Culcer, X. Hu, and S. Das Sarma, Appl. Phys. Lett. 95, 073102 (2009).
https://doi.org/10.1063/1.3194778

[116] L. Cywiński, R. M. Lutchyn, C. P. Nave, and S. Das Sarma, Phys. Rev. B 77, 174509 (2008).
https://doi.org/10.1103/physrevb.77.174509

[117] L. Viola, S. Lloyd, and E. Knill, Phys. Rev. Lett. 83, 4888 (1999).
https://doi.org/10.1103/physrevlett.83.4888

[118] C. Barthel, J. Medford, C. M. Marcus, M. P. Hanson, and A. C. Gossard, Phys. Rev. Lett. 105, 266808 (2010).
https://doi.org/10.1103/physrevlett.105.266808

[119] D. Kim, D. R. Ward, C. B. Simmons, D. E. Savage, M. G. Lagally, M. Friesen, S. N. Coppersmith, and M. A. Eriksson, npj Quantum Inf. 1, 15004 (2015).
https://doi.org/10.1038/npjqi.2015.4

[120] M. D. Reed, B. M. Maune, R. W. Andrews, M. G. Borselli, K. Eng, M. P. Jura, A. A. Kiselev, T. D. Ladd, S. T. Merkel, I. Milosavljevic, E. J. Pritchett, M. T. Rakher, R. S. Ross, A. E. Schmitz, A. Smith, J. A. Wright, M. F. Gyure, and A. T. Hunter, Phys. Rev. Lett. 116, 110402 (2016).
https://doi.org/10.1103/physrevlett.116.110402

[121] A. L. Saraiva, M. J. Calderón, R. B. Capaz, X. Hu, S. Das Sarma, and B. Koiller, Phys. Rev. B 84, 155320 (2011).
https://doi.org/10.1103/physrevb.84.155320

[122] M. O. Nestoklon, L. E. Golub, and E. L. Ivchenko, Phys. Rev. B 73, 235334 (2006).
https://doi.org/10.1103/physrevb.73.235334

[123] S. Chutia, S. N. Coppersmith, and M. Friesen, Phys. Rev. B 77, 193311 (2008).
https://doi.org/10.1103/physrevb.77.193311

[124] J. K. Gamble, M. A. Eriksson, S. N. Coppersmith, and M. Friesen, Phys. Rev. B 88, 035310 (2013).
https://doi.org/10.1103/physrevb.88.035310

[125] T. B. Boykin, G. Klimeck, M. A. Eriksson, M. Friesen, S. N. Coppersmith, P. von Allmen, F. Oyafuso, and S. Lee, Appl. Phys. Lett. 84, 115 (2004).
https://doi.org/10.1063/1.1637718

Cited by

[1] Giordano Scappucci, Christoph Kloeffel, Floris A. Zwanenburg, Daniel Loss, Maksym Myronov, Jian-Jun Zhang, Silvano De Franceschi, Georgios Katsaros, and Menno Veldhorst, "The germanium quantum information route", Nature Reviews Materials 6 10, 926 (2020).

[2] Krzysztof Gawarecki and Paweł Machnikowski, "Phonon-assisted relaxation between triplet and singlet states in a self-assembled double quantum dot", Scientific Reports 11 1, 15256 (2021).

[3] Varsha, K. Lakaal, M. Kria, J. El Hamdaoui, V. Prasad, E. Feddi, D. Laroze, L. M. Pérez, and M. E. Mora Ramos, "Lattice deformation and potential effects on linear and nonlinear optical properties of doped SiGe quantum dot encapsulated in Si matrix", The European Physical Journal Plus 137 12, 1340 (2022).

[4] J. C. Abadillo-Uriel, M. A. Eriksson, S. N. Coppersmith, and Mark Friesen, "Enhancing the dipolar coupling of a S-T0 qubit with a transverse sweet spot", Nature Communications 10 1, 5641 (2019).

[5] Kailang Liu, Isabelle Berbezier, Luc Favre, Antoine Ronda, Marco Abbarchi, Patricia Donnadieu, Peter W. Voorhees, and Jean-Noël Aqua, "Capillary-driven elastic attraction between quantum dots", Nanoscale 11 16, 7798 (2019).

[6] Andrea Secchi, Laura Bellentani, Andrea Bertoni, and Filippo Troiani, "Inter- and intraband Coulomb interactions between holes in silicon nanostructures", Physical Review B 104 20, 205409 (2021).

[7] Guanjie He, Guo Xuan Chan, and Xin Wang, "Theory on Electron–Phonon Spin Dephasing in GaAs Multi‐Electron Double Quantum Dots", Advanced Quantum Technologies 6 3, 2200074 (2023).

[8] E. Ferraro, M. Fanciulli, and M. De Michielis, "Phonon-induced relaxation and decoherence times of the hybrid qubit in silicon quantum dots", Physical Review B 100 3, 035310 (2019).

[9] Viktoriia Kornich, Maxim G Vavilov, Mark Friesen, and S N Coppersmith, "Phonon-induced decoherence of a charge quadrupole qubit", New Journal of Physics 20 10, 103048 (2018).

[10] Yuan-Chi Yang, S. N. Coppersmith, and Mark Friesen, "Achieving high-fidelity single-qubit gates in a strongly driven charge qubit with 1/f charge noise", npj Quantum Information 5 1, 12 (2019).

[11] V. Srinivasa, J. M. Taylor, and Charles Tahan, "Entangling distant resonant exchange qubits via circuit quantum electrodynamics", Physical Review B 94 20, 205421 (2016).

The above citations are from Crossref's cited-by service (last updated successfully 2024-07-31 15:11:59) and SAO/NASA ADS (last updated successfully 2024-07-31 15:12:00). The list may be incomplete as not all publishers provide suitable and complete citation data.

This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.