Quantum information processing requires accurate coherent control of quantum-mechanical two-level systems, but is hampered in practice by their coupling to an uncontrolled environment. For electron spins in III–V quantum dots, the random environment is mostly given by the nuclear spins in the quantum-dot host material; they collectively act on the electron spin through the hyperfine interaction, much like a random magnetic field. Here we show that the same hyperfine interaction can be harnessed such that partial control of the normally uncontrolled environment becomes possible. In particular, we observe that the electron-spin-resonance frequency remains locked to the frequency of an applied microwave magnetic field, even when the external magnetic field or the excitation frequency are changed. The nuclear field thereby adjusts itself such that the electron-spin-resonance condition remains satisfied. General theoretical arguments indicate that this spin-resonance locking might be accompanied by a significant reduction of the randomness in the nuclear field.
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Hanson, R., Kouwenhoven, L. P., Petta, J. R., Tarucha, S. & Vandersypen, L. M. K. Spins in few-electron quantum dots. Rev. Mod. Phys. 79, 1217–1265 (2007).
Khaetskii, A. V., Loss, D. & Glazman, L. Electron spin decoherence in quantum dots due to interaction with nuclei. Phys. Rev. Lett. 88, 186802 (2002).
Merkulov, I. A., Efros, Al. L. & Rosen, M. Electron spin relaxation by nuclei in semiconductor quantum dots. Phys. Rev. B 65, 205309 (2002).
Petta, J. R. et al. Coherent manipulation of coupled electron spins in semiconductor quantum dots. Science 309, 2180–2184 (2005).
Koppens, F. H. L., Nowack, K. C. & Vandersypen, L. M. K. Spin echo of a single electron spin in a quantum dot. Phys. Rev. Lett. 100, 236802 (2008).
Greilich, A. et al. Mode locking of electron spin coherences in singly charged quantum dots. Science 313, 341–345 (2006).
Koppens, F. H. L. et al. Driven coherent oscillations of a single electron spin in a quantum dot. Nature 442, 766–771 (2006).
Burkard, G., Loss, D. & DiVincenzo, D. P. Coupled quantum dots as quantum gates. Phys. Rev. B 59, 2070–2078 (1999).
Klauser, D., Coish, W. A. & Loss, D. Nuclear spin state narrowing via gate-controlled Rabi oscillations in a double quantum dot. Phys. Rev. B 73, 205302 (2006).
Giedke, G., Taylor, J. M., D’Alessandro, D., Lukin, M. D. & Imamoğlu, A. Quantum measurement of a mesoscopic spin ensemble. Phys. Rev. A 74, 032316 (2006).
Stepanenko, D., Burkard, G., Giedke, G. & Imamoğlu, A. Enhancement of electron spin coherence by optical preparation of nuclear spins. Phys. Rev. Lett. 96, 136401 (2006).
Coish, W. A. & Loss, D. Hyperfine interaction in a quantum dot: Non-Markovian electron spin dynamics. Phys. Rev. B 70, 195340 (2004).
Witzel, W. M. & Das Sarma, S. Quantum theory for electron spin decoherence induced by nuclear spin dynamics in semiconductor quantum computer architectures: Spectral diffusion of localized electron spins in the nuclear solid-state environment. Phys. Rev. B 74, 035322 (2006).
Greilich, A. et al. Collective single mode precession of electron spins in a quantum dot ensemble. Phys. Rev. B 79, 201305(R) (2009).
Reilly, D. J. et al. Suppressing spin qubit dephasing by nuclear state preparation. Science 321, 817–821 (2008).
Ono, K. & Tarucha, S. Nuclear-spin-induced oscillatory current in spin-blockaded quantum dots. Phys. Rev. Lett. 92, 256803 (2004).
Koppens, F. H. L. et al. Control and detection of singlet–triplet mixing in a random nuclear field. Science 309, 1346–1350 (2005).
Reilly, D. J. et al. Measurement of temporal correlations of the Overhauser field in a double quantum dot. Phys. Rev. Lett. 101, 236803 (2008).
Foletti, S. et al. Dynamic nuclear polarization using a single pair of electrons. Preprint at <http://arxiv.org/abs/0801.3613> (2008).
Baugh, J., Kitamura, Y., Ono, K. & Tarucha, S. Large nuclear Overhauser fields detected in vertically coupled double quantum dots. Phys. Rev. Lett. 99, 096804 (2007).
Tartakovskii, A. I. et al. Nuclear spin switch in semiconductor quantum dots. Phys. Rev. Lett. 98, 026806 (2007).
Braun, P.-F. et al. Bistability of the nuclear polarization created through optical pumping in In1−xGaxAs quantum dots. Phys. Rev. B 74, 245306 (2006).
Maletinsky, P., Lai, C. W., Badolato, A. & Imamoğlu, A. Nonlinear dynamics of quantum dot nuclear spins. Phys. Rev. B 75, 035409 (2007).
Ono, K., Austing, D. G., Tokura, Y. & Tarucha, S. Current rectification by Pauli exclusion in a weakly coupled double quantum dot system. Science 297, 1313–1317 (2002).
Koppens, F. H. L. et al. Detection of single electron spin resonance in a double quantum dot. J. Appl. Phys. 101, 081706 (2007).
Danon, J. et al. Multiple nuclear polarization states in a double quantum dot. Phys. Rev. Lett. 103, 046601 (2009).
Danon, J. & Nazarov, Yu. V. Nuclear tuning and detuning of the electron spin resonance in a quantum dot: Theoretical consideration. Phys. Rev. Lett. 100, 056603 (2008).
Rudner, M. S. & Levitov, L. S. Electrically driven reverse Overhauser pumping of nuclear spins in quantum dots. Phys. Rev. Lett. 99, 246602 (2007).
Laird, E. A. et al. Hyperfine-mediated gate-driven electron spin resonance. Phys. Rev. Lett. 99, 246601 (2007).
We thank F. R. Braakman, P. C. de Groot, R. Hanson, M. Laforest, L. R. Schreiber, G. A. Steele and S.-C. Wang for help and discussions, and R. Schouten, A. van der Enden, R. G. Roeleveld and P. van Oossanen for technical support. This work is supported by the ‘Stichting voor Fundamenteel Onderzoek der Materie (FOM)’ and the ‘Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO)’.
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Vink, I., Nowack, K., Koppens, F. et al. Locking electron spins into magnetic resonance by electron–nuclear feedback. Nature Phys 5, 764–768 (2009). https://doi.org/10.1038/nphys1366
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