Geometric manipulation with polarized microwaves
over an electron and a nuclear spin in diamond
Kodai Nagata, Naoki Ishida, Koyo Kuramitani, Koji Sato, Yuhei Sekiguchi, and Hideo Kosaka*
Yokohama National University, 79-5 Tokiwadai, Hodogaya, Yokohama 240-8501, Japan*Corresponding author: kosaka-hideo-yp@ynu.ac.jp

Abstract: We succeeded to generate and manipulate any arbitrary quantum state withpolarized microwaves across a crossed wire over an electron spin and a nuclear spin innitrogen-vacancy center in diamond. We achieved manipulation fidelity over 80% for both.
1. Introduction
We have recently demonstrated teleportation-based quantum media conversion from a photon to a nuclear
spin [1], geometric spin echo [2], and optical single electron quantum gates [3] in a nitrogen vacancy centerin diamond. Although these demonstrations use a degenerate ±1 subspace of a spin-1 system of an electron
and a nuclear spin as qubits under a zero magnetic field, arbitrary manipulation of these degenerate qubits
cannot be performed by using linearly polarized microwaves or radiowaves, which are generated by theconventional a single wire or a strip line. Here we show that we can manipulate the degenerate qubits withpolarized microwaves or radiowaves, respectively, instead of energy gaps of two spin sublevels with utilizing
the geometric nature of those spins.

2. Experimental setups
We used a native NV center in a high-purity type-IIa chemical-vapor-deposition grown bulk diamond with a<001> crystal orientation (electronic grade from Element Six) without any electron-beam dose or annealing.
A negatively charged NV center located at about 30 m below the surface was found using a confocal laser
microscope. Two nearly perpendicularly crossed copper wires of 25-m in diameter mechanically attached tothe surface of the diamond were used to apply microwaves and radiowaves for the optically detected magnetic
resonance (ODMR) measurement (Fig. 1). An external magnetic field to the NV axis was applied tocompensate the geomagnetic field of about 0.045 mT using a permanent magnet. Careful orientation of themagnet was conducted with monitoring of the ODMR spectrum within 0.1 MHz. All experiments wereperformed at room temperature.
The spin sublevels ±1 of spin-1 electron and 14N nuclear spins in an NV center completely degenerate
under a zero magnetic field. We first initialize those spin states into ms=0 and mI=0 states. We then apply apolarized microwave for the electron spin or a polarized radiowave for the nuclear spin, respectively, withusing the crossed wires to prepare the corresponding logical qubit state in the ±1 subspace. We then apply
another microwave or radiowave to add a geometric phase induced by a cyclic rotation of the bight statecorresponding to the polarization via the ms=0 or mI=0 states as ancillary states. This allows any arbitrary axis
rotation of the degenerate logical qubits with properly selected polarization. We finally perform quantum state
tomography and quantum process tomography using the bright state projection technique [4].

3. Experimental results
We succeeded to generate arbitrary quantum states of an electron and a nuclear spin and manipulate themgeometrically with a polarized microwave and radiowave, respectively, using crossed wires. We achieved
manipulation fidelities of as high as 86% for an electron spin and 93% for a nuclear spin in average based on
the quantum state tomography (not shown). Further detailed analysis using the process tomography indicatesthat the X-axis rotation has the fidelity of 82% and 97% for respectively the electron and nuclear spins (Fig.
2).

4. Acknowledgements
We thank Yuichiro Matsuzaki, Nobuhiko Yokoshi, Kae Nemoto, William Munro, Norikazu Mizuochi, FedorJelezko, and Joerg Wrachtrup for their discussions and experimental help. This work has been supported by
National Institute of Information and Communications Technology (NICT) Quantum Repeater Project andby Japan Society for the Promotion of Science (JSPS) Grant-in-Aid for Scientific Research (24244044

16H06326 16H01052) and Ministry of Education Culture Sports Science and Technology (MEXT) as“Exploratory Challenge on Post-K computer” (Frontiers of Basic Science: Challenging the Limits).
5. References[1] S. Yang et al., Nat. Photon. 10 507-511 (2016).
[2] Y. Sekiguchi, Y. Komura, S. Mishima, T. Tanaka, N. Niikura and H. Kosaka, Geometric spin echo under zero field. Nat. Commun.
7, 11668 (2016).
[3] Y. Sekiguchi, N. Niikura, R. Kuroiwa, H. Kano, and H. Kosaka, Nat. Photon. in press (2017).
[4] H. Kosaka and N. Niikura, Entangled Absorption of a Single Photon with a Single Spin in Diamond. Phys. Rev. Lett. 114, 053603(2015).

Fig.1. Experimental configuration showing the crossed wire and nitrogen-vacancy center in diamondFig.2. Experimental results showing the fidelity of the electron spin and nuclear spin rotation.