УДК: 538.9, 53.098

On the possibility of creating single-electron states in quantum dots in a magnetic field for problems of optical quantum computations

Grigoriev, S.N., Mandel, A.M., Oshurko, V.B., Solomakho, G.I.

Publication in Journal of Optical Technology

For Russian citation (Opticheskii Zhurnal):

Григорьев С.Н., Мандель А.М., Ошурко В.Б., Соломахо Г.И. О возможности создания одноэлектронных состояний в квантовых точках в магнитном поле для задач оптических квантовых вычислений // Оптический журнал. 2015. Т. 82. № 5. С. 3–10.

Grigoriev S.N., Mandel A.M., Oshurko V.B., Solomakho G.I. On the possibility of creating single-electron states in quantum dots in a magnetic field for problems of optical quantum computations [in Russian] // Opticheskii Zhurnal. 2015. V. 82. № 5. P. 3–10.

For citation (Journal of Optical Technology):

S. N. Grigor’ev, A. M. Mandel’, V. B. Oshurko, and G. I. Solomakho, "On the possibility of creating single-electron states in quantum dots in a magnetic field for problems of optical quantum computations," Journal of Optical Technology. 82(5), 268-273 (2015). https://doi.org/10.1364/JOT.82.000268

Abstract:

The problem of creating pure and entangled states for the optical implementation of quantum computations, as well as a number of tasks involving the formation of active media on quantum dots, requires the formulation of conditions under which they contain exactly one bound energy level. The critical conditions are studied for the appearance of the first bound single-electron state, localized on a spherical quantum dot of small size in an external magnetic field. A simple analytical representation is obtained for the wave function of such a state, and the equation for determining its binding energy is formulated and solved. The results are compared with the well-known delta-potential approximation. It is shown that a bound level appears in an empty quantum dot only when the magnetic field exceeds a definite threshold value.

Keywords:

quantum dots, localized single-electron state, magnetic field

Acknowledgements:

This work was carried out with the support of the Ministry of Education and Science of the Russian Federation as part of State Contract No. 1678 and with the support of the Russian Foundation for Basic Research, Grant No. 13-07-00663.

OCIS codes: 020.2649, 140.5960, 020.7490, 350.3390

References:

1. A. Ya. Shik, L. G. Bakueva, S. F. Musikhin, and S. A. Rykov, The Physics of Small Systems (Nauka, St. Petersburg, 2001).
2. S. I. Borisenko, The Physics of Semiconductor Structures (Izd. Tomsk. Politekh. Univ., Tomsk, 2010).
3. V. M. Ledentsov, V. M. Ustinov, V. A. Shchukin, P. S. Kop’ev, Zh. I. Alferov, and D. Bimberg, “Quantum dot heterostructures: fabrication, properties, lasers (Review),” Fiz. Tekh. Poluprovodn. 32, 385 (1998) [Semiconductors 32, 343 (1998)].
4. G. G. Zegrya, O. V. Konstantinov, and A. V. Matveentsev, “Structure of energy quantum levels in a quantum dot shaped as an oblate body of revolution,” Fiz. Tekh. Poluprovodn. 37, 334 (2003) [Semiconductors 37, 317 (2003)].
5. D. Bowmeester, A. Ekert, and A. Zeilinger, The Physics of Quantum Information (Springer-Verlag, New York, 2000).
6. V. N. Rodionov, G. A. Kravtsova, and A. M. Mandel, “Equation for the complex energy of a bound particle in a laser radiation field in the presence of strong constant electromagnetic fields,” Theor. Math. Phys. 145, 1539 (2005).
7. V. N. Rodionov, G. A. Kravtsova, and A. M. Mandel, “On the influence of strong electric and magnetic fields on spatial dispersion and anisotropy of the optical properties of a semiconductor,” Pis’ma Zh. Eksp. Teor. Fiz. 78, 253 (2003) [JETP Lett. 78, 218 (2003)].
8. V. N. Rodionov, G. A. Kravtsova, and A. M. Mandel, “Wave function and the probability current distribution for a bound electron moving in a uniform magnetic field,” Theor. Math. Phys. 164, 960 (2010).
9. S. N. Grigoriev, A. M. Mandel, V. B. Oshurko, and G. I. Solomakho, “Determining the effective fractal dimension of nanodimensional coatings with the aid of magnetic field,” Pis’ma Zh. Tekh. Fiz. 37, No. 24, 74 (2011) [Tech. Phys. Lett. 37, 1176 (2011)].
10. A. M. Mandel’, V. B. Oshurko, and G. I. Solomakho, “On the localization by a magnetic field of single-electron states in the neighborhood of fractional-dimension quantum dots,” Élektromag. Volny Élektron. Sis. No. 6, 67 (2014).
11. Yu. N. Demkov and V. N. Ostrovskiı˘, Method of Zero-Radius Potential in Atomic Physics (Izdatel’stvo LGU, Leningrad, 1975).
12. A. I. Baz’, Ya. B. Zel’dovich, and A. M. Perelomov, Scattering, Reactions, and Decays in Nonrelativistic Quantum Mechanics (Nauka, Moscow, 1966).
13. N. E. Kaputkina and Yu. E. Lozovik, “Magnetic field influence on spectrum rearrangement and spin transformation of coupled quantum dots,” J. Phys. Condens. Matter 18, 2169 (2006).
14. A. O. Govorov and A. V. Chaplic, “Magnetoabsorption in quantum dots,” Pis’ma Zh. Eksp. Teor. Fiz. 52, 681 (1990) [JETP Lett. 52, 31 (1990)].
15. A. Puente, M. Pons, and R. G. Nazmitdinov, “Interaction effects in quantum dots in a vertical magnetic field,” J. Phys. Conf. Ser. 248, 012017, (2010).
16. W. Kohn, “Cyclotron resonance and de Haas–van Alphen oscillations of an interacting electron gas,” Phys. Rev. 123, 1242 (1961).
17. W. Que, “Excitons in quantum dots with parabolic confinement,” Phys. Rev. B 45, 11036 (1992).
18. V. E. Adrianov, V. G. Maslov, A. V. Baranov, A. V. Fedorov, and M. V. Artem’ev, “Spectral study of the self-organization of quantum dots during the evaporation of colloidal solutions,” Opt. Zh. 78, No. 11, 11 (2011) [J. Opt. Technol. 78, 699 (2011)].
19. Yu. N. Demkov and G. N. Drukarev, “A particle with low binding energy in a magnetic field,” Zh. Eksp. Teor. Fiz. 49, 257 (1965) [JETP 22, 182 (1966)].
20. K. Zeeger, Semiconductor Physics (Springer-Verlag, New York, 1973).
21. G. Beı˘tmen and A. Érdeı˘i, Higher Transcendental Functions, Vol. 1 (Nauka, Moscow, 1973).
22. V. N. Rodionov, G. A. Kravtsova, and A. M. Mandel’, “The lack of the stabilization of quasi-stationary electron states in a strong magnetic field,” Dok. Ross. Akad. Nauk 386, 753 (2002) [Phys.–Dokl. 47, 725 (2002)].
23. V. N. Rodionov, A. M. Mandel’, and G. A. Kravtsova, “Ionization from a short-range potential under the action of a complex configuration,” Pis’ma Zh. Eksp. Teor. Fiz. 75, 435 (2002) [JETP Lett. 75, 363 (2002)].
24. S. N. Grigor’ev, V. B. Oshurko, A. E. Shtan’ko, and M. A. Volosova, “Speckle interferometer for measuring radial displacements,” Meas. Tech. 55, 546 (2012).
25. O. O. Dan’kiv and R. M. Peleshchak, “Strain-renormalized energy spectra of electrons and holes in InAs quantum dots in the InAs/GaAs heterosystem,” Pis’ma Zh. Tekh. Fiz. 31, No. 16, 33 (2005) [Tech. Phys. Lett. 31, 691 (2005)].