Optical geometric manipulation of an electron spinin diamond
Yuhei Sekiguchi, Naeko Niikura, Ryota Kuroiwa, Hiroki Kano and Hideo Kosaka*
Yokohama National University, 79-5 Tokiwadai, Hodogaya, Yokohama 240-8501, Japan*Corresponding author: kosaka-hideo-yp@ynu.ac.jp

Abstract: We report single electron spin quantum gates using spin-state-dependent
geometric phase induced by a cyclic rotation in the orbital space with a polarized light. By
performing quantum process tomography, we achieved manipulation fidelity over 90% inaverage.
1. Introduction
Solid-state spin is a stable and scalable quantum medium, promised as a quantum engineering platform, suchas quantum information and quantum sensing. As a method of spin manipulation to maintain this scalability,
light gives a local field to access individual spins. However, while a spin-orbit interaction mediates between
the optical field and the spin, which never interact with each other directly, the orbital instability prevents apractical spin manipulation, in contrast to direct spin manipulation with microwave. Although previous works
adiabatically eliminate the orbital exited state by using far-detuned light to reduce the effect of the exitedstate relaxation [1, 2], the long operation time increases the total effect of the relaxation or other incoherent
processes. In contrast, non-adiabatic rotation the orbit state to obtain a spin-state-dependent geometric phase
can also rotate the spin state [3].
A nitrogen-vacancy (NV) center in diamond has stable electron spin and spin-orbit interaction for a spinphoton interface, which was demonstrated as spin-photon entanglement generation [4] and measurement [5].
Although this electron spin can be reliably operated with microwaves, it is still a challenging task to faithfully
manipulate it arbitrarily with light defined by polarization under a zero field [6].

2. Scheme for non-adiabatic geometric spin rotation
Electron spin states |𝑚𝑆 = ±1⟩ of an orbital ground state in a NV center degenerate under a zero magnetic
field. Spin-orbit interaction and spin-spin interaction couple the electron spin and orbit exited states|𝑚𝐿 = ±1⟩ to make an excited state |𝐴2 ⟩ = |+1⟩𝐿 |−1⟩𝑆 + |−1⟩𝐿 |+1⟩𝑆 under a low temperature. By
selecting the driven orbital state depending on the polarization of light, spin-dependent orbital rotation canbe achieved. Spin-dependent cyclic evolution of the orbital state obtains a geometric phase, which depends
on the state evolution trajectory, to rotate the degenerate spin. Here, we control the trajectory by changing thedetuning of light. Hence, an arbitrary single-spin rotation can be achieved by properly choosing thepolarization and detuning of light for the rotation axis and angle, respectively. Since the spin coherence
prolongs [7] and the spin basis are spatially defined as a polarization of light under a zero magnetic field, therotation can be practically performed.

3. Experimental results
We performed Pauli-X, Y and Z gate, which consist of 4 ns pulse using horizontal, diagonal and right circularpolarized light. Figure 1 shows quantum process tomography using a geometric spin state preparation andreadout technique [2]. The achieved fidelity is over 90% in average, which is limited by the exited state
relaxation.
4. Conclusion
We demonstrate universal optical geometric manipulation of an electron spin in diamond with practical
fidelity. The optical geometric spin rotation under zero field is not only allow quick and local access but also
immune to driving and environmental error, thus opening the way to fast quantum random access memories
and quantum processors.

5. Acknowledgement

We thank Yuichiro Matsuzaki, Burkhard Scharfenberger, Kae Nemoto, William Munro, Norikazu Mizuochi,
Nobuhiko Yokoshi, Fedor Jelezko, and Joerg Wrachtrup for their discussions and experimental help. This
work was supported by National Institute of Information and Communications Technology (NICT) Quantum
Repeater Project, and by Japan Society for the Promotion of Science (JSPS) Grant-in-Aid for Scientific
Research (24244044, 16H06326, 16H01052) and Ministry of Education, Culture, Sports, Science andTechnology (MEXT) as “Exploratory Challenge on Post-K computer” (Frontiers of Basic Science:
Challenging the Limits).

6. References[1] D. Press, T. D. Ladd, B. Zhang and Y. Yamamoto, Complete quantum control of a single quantum dot spin using ultrafast opticalpulses. Nature 456, 218–221 (2008).
[2] B. B. Buckley, G. D. Fuchs, L. C. Bassett and D. D. Awschalom, Spin-Light Coherence for Single-Spin Measurement and Controlin Diamond. Science 330, 1212–1215 (2010).
[3] E. Sjöqvist et al., Non-adiabatic holonomic quantum computation. New J. Phys. 14, 103035 (2012).
[4] E. Togan et al., Quantum entanglement between an optical photon and a solid-state spin qubit. Nature 466, 730–734 (2010).
[5] H. Kosaka and N. Niikura, Entangled Absorption of a Single Photon with a Single Spin in Diamond. Phys. Rev. Lett. 114, 053603(2015).
[6] Y. Sekiguchi, N. Niikura, R. Kuroiwa, H. Kano, and H. Kosaka, Nat. Photon. in press (2017).
[7] Y. Sekiguchi et al., Geometric spin echo under zero field. Nat. Commun. 7, 11668 (2016).

Fig.1. Quantum process tomography for Pauli-X, Y and Z gates.