Phase relations between quantum states represent a resource for storing and processing quantum information. Although quantum phases are commonly controlled dynamically by tuning energetic interactions, the use of geometric phases that accumulate during cyclic evolution may offer superior robustness to noise. To date, demonstrations of geometric phase in solid-state systems employ microwave fields that have limited spatial resolution. Here, we demonstrate an all-optical method to accumulate a geometric phase, the Berry phase, in an individual nitrogen–vacancy centre in diamond. Using stimulated Raman adiabatic passage controlled by diffraction-limited laser light, we loop the nitrogen–vacancy centre's spin around the Bloch sphere to enclose an arbitrary Berry phase. We investigate the limits of this control due to the loss of adiabaticity and decoherence, as well as its robustness to noise introduced into the experimental control parameters. These techniques set the foundation for optical geometric manipulation in photonic networks of solid-state qubits linked and controlled by light.
This is a preview of subscription content, access via your institution
Open Access articles citing this article.
Experimental observation of Berry phases in optical Möbius-strip microcavities
Nature Photonics Open Access 22 December 2022
Generalized Ramsey interferometry explored with a single nuclear spin qudit
npj Quantum Information Open Access 24 October 2018
Universal holonomic quantum gates over geometric spin qubits with polarised microwaves
Nature Communications Open Access 13 August 2018
Subscribe to this journal
Receive 12 print issues and online access
$209.00 per year
only $17.42 per issue
Rent or buy this article
Get just this article for as long as you need it
Prices may be subject to local taxes which are calculated during checkout
Pancharatnam, S. Generalized theory of interference, and its applications. Proc. Indian Acad. Sci. A 44, 247–262 (1956).
Berry, M. V. Quantal phase factors accompanying adiabatic changes. Proc. R. Soc. Lond. A 392, 45–57 (1984).
De Chiara, G. & Palma, G. M. Berry phase for a spin 1/2 particle in a classical fluctuating field. Phys. Rev. Lett. 91, 090404 (2003).
Berger, S. et al. Exploring the effect of noise on the Berry phase. Phys. Rev. A 87, 060303 (2013).
Zanardi, P. & Rasetti, M. Holonomic quantum computation. Phys. Lett. A 264, 94–99 (1999).
Duan, L. M., Cirac, J. I. & Zoller, P. Geometric manipulation of trapped ions for quantum computation. Science 292, 1695–1697 (2001).
Anandan, J. Non-adiabatic non-Abelian geometric phase. Phys. Lett. A 133, 171–175 (1988).
Jones, J., Vedral, V., Ekert, A. & Castagnoli, G. Geometric quantum computation using nuclear magnetic resonance. Nature 403, 869–871 (2000).
Leibfried, D. et al. Experimental demonstration of a robust, high-fidelity geometric two ion-qubit phase gate. Nature 422, 412–415 (2003).
Leek, P. J. et al. Observation of Berry's phase in a solid-state qubit. Science 318, 1889–1892 (2007).
Abdumalikov, A. A. Jr et al. Experimental realization of non-Abelian non-adiabatic geometric gates. Nature 496, 482–485 (2013).
Zu, C. et al. Experimental realization of universal geometric quantum gates with solid-state spins. Nature 514, 72–75 (2014).
Arroyo-Camejo, S., Lazariev, A., Hell, S. W. & Balasubramanian, G. Room temperature high-fidelity holonomic single-qubit gate on a solid-state spin. Nature Commun. 5, 4870 (2014).
Zhang, K., Nusran, N. M., Slezak, B. R. & Dutt, M. V. G. Measurement of the Berry phase in a single solid-state spin qubit. Preprint at http://arxiv.org/abs/1410.2791 (2014).
Lončar, M. & Faraon, A. Quantum photonic networks in diamond. MRS Bull. 38, 144–148 (2013).
Toyli, D. M., Weis, C. D., Fuchs, G. D., Schenkel, T. & Awschalom, D. D. Chip-scale nanofabrication of single spins and spin arrays in diamond. Nano Lett. 10, 3168–3172 (2010).
Toyoda, K., Uchida, K., Noguchi, A., Haze, S. & Urabe, S. Realization of holonomic single-qubit operations. Phys. Rev. A 87, 052307 (2013).
Kis, Z. & Renzoni, F. Qubit rotation by stimulated Raman adiabatic passage. Phys. Rev. A 65, 032318 (2002).
Møller, D., Madsen, L. B. & Mølmer, K. Geometric phase gates based on stimulated Raman adiabatic passage in tripod systems. Phys. Rev. A 75, 062302 (2007).
Gaubatz, U., Rudecki, P., Schiemann, S. & Bergmann, K. Population transfer between molecular vibrational levels by stimulated Raman scattering with partially overlapping laser fields. A new concept and experimental results. J. Chem. Phys. 92, 5363–5376 (1990).
Bergmann, K., Theuer, H. & Shore, B. W. Coherent population transfer among quantum states of atoms and molecules. Rev. Mod. Phys. 70, 1003–1025 (1998).
Goto, H. & Ichimura, K. Population transfer via stimulated Raman adiabatic passage in a solid. Phys. Rev. A 74, 053410 (2006).
Golter, D. A. & Wang, H. Optically driven Rabi oscillations and adiabatic passage of single electron spins in diamond. Phys. Rev. Lett. 112, 116403 (2014).
Doherty, M. W. et al. The nitrogen-vacancy colour centre in diamond. Phys. Rep. 528, 1–45 (2013).
Batalov, A. et al. Low temperature studies of the excited-state structure of negatively charged nitrogen-vacancy color centers in diamond. Phys. Rev. Lett. 102, 195506 (2009).
Gao, W. B., Imamoglu, A., Bernien, H. & Hanson, R. Coherent manipulation, measurement and entanglement of individual solid-state spins using optical fields. Nature Photon. 9, 363–373 (2015).
Togan, E. et al. Quantum entanglement between an optical photon and a solid-state spin qubit. Nature 466, 730–734 (2010).
Kosaka, H. & Niikura, N. Entangled absorption of a single photon with a single spin in diamond. Phys. Rev. Lett. 114, 053603 (2015).
Buckley, B. B., Fuchs, G. D., Bassett, L. C. & Awschalom, D. D. Spin-light coherence for single-spin measurement and control in diamond. Science 330, 1212–1215 (2010).
Yale, C. G. et al. All-optical control of a solid-state spin using coherent dark states. Proc. Natl Acad. Sci. USA 110, 7595–7600 (2013).
Bassett, L. C. et al. Ultrafast optical control of orbital and spin dynamics in a solid-state defect. Science 345, 1333–1337 (2014).
Bernien, H. et al. Heralded entanglement between solid-state qubits separated by three metres. Nature 497, 86–90 (2013).
Pfaff, W. et al. Unconditional quantum teleportation between distant solid-state quantum bits. Science 345, 532–535 (2014).
Santori, C. et al. Coherent population trapping of single spins in diamond under optical excitation. Phys. Rev. Lett. 97, 247401 (2006).
Pingault, B. et al. All-optical formation of coherent dark states of silicon-vacancy spins in diamond. Phys. Rev. Lett. 113, 263601 (2014).
Rogers, L. J. et al. All-optical initialization, readout, and coherent preparation of single silicon-vacancy spins in diamond. Phys. Rev. Lett. 113, 263602 (2014).
Riedrich-Möller, J. et al. Deterministic coupling of a single silicon-vacancy color center to a photonic crystal cavity in diamond. Nano Lett. 14, 5281–5287 (2014).
Christle, D. J. et al. Isolated electron spins in silicon carbide with millisecond coherence times. Nature Mater. 14, 160–163 (2015).
Widmann, M. et al. Coherent control of single spins in silicon carbide at room temperature. Nature Mater. 14, 164–168 (2015).
Jungwirth, N. R. et al. A single-molecule approach to ZnO defect studies: single photons and single defects. J. Appl. Phys. 116, 043509 (2014).
Kolesov, R. Coherent population trapping in a crystalline solid at room temperature. Phys. Rev. A 72, 051801 (2005).
Xia, K. et al. All-optical preparation of coherent dark states of a single rare earth ion spin in a crystal. Phys. Rev. Lett. 115, 093602 (2015).
Hansom, J. et al. Environment-assisted quantum control of a solid-state spin via coherent dark states. Nature Phys. 10, 725–730 (2014).
López, C. Materials aspects of photonic crystals. Adv. Mater. 15, 1679–1704 (2003).
Robledo, L. et al. High-fidelity projective read-out of a solid-state spin quantum register. Nature 477, 574–578 (2011).
The authors thank C.P. Anderson, B.B. Buckley, D.J. Christle and C.F. de las Casas for discussions and H.L. Bretscher for experimental assistance. This work was supported by the Air Force Office of Scientific Research (FA9550-14-1-0231 and FA9550-15-1-0029), the National Science Foundation (NSF-DMR-1306300) and the German Research Foundation (SFB 767).
The authors declare no competing financial interests.
Rights and permissions
About this article
Cite this article
Yale, C., Heremans, F., Zhou, B. et al. Optical manipulation of the Berry phase in a solid-state spin qubit. Nature Photon 10, 184–189 (2016). https://doi.org/10.1038/nphoton.2015.278
This article is cited by
Experimental observation of Berry phases in optical Möbius-strip microcavities
Nature Photonics (2023)
Optically addressable universal holonomic quantum gates on diamond spins
Nature Photonics (2022)
Quantum guidelines for solid-state spin defects
Nature Reviews Materials (2021)
Room Temperature High-fidelity Non-adiabatic Holonomic Quantum Computation on Solid-state Spins in Nitrogen-vacancy Centers
International Journal of Theoretical Physics (2020)
Geometric phase from Aharonov–Bohm to Pancharatnam–Berry and beyond
Nature Reviews Physics (2019)