#### Mikio NAKAHARA

Professor, Department of Physics, Kinki University- Field of Specialty：
- Theoretical and Mathematical Physics
- Topics of Research：
- (B01) Novel Edge Phenomena in Spin-Triplet Superfluids
- Specific Topics：
- Theory of topological condensed systems

##### ■ Laboratory Website

#### RESEARCH

I believe any beautiful mathematical theory has a physical system which is an embodiment of the theory. I particular, I have been seeking geometrical and topological beauties in physical systems in most of my research subjects. Even though I do research on rather mathematical subjects, I always have physical realizations of the theory in mind as mentioned above.

We have studied vortices and domain walls in superfluid ^{3}He, a *p*-wave BCS superfluid discovered in 1971. In my MSc work, I studied the texture of the superfluid under rotation. The vortex in the rotating superfluid with small angular frequency is not a usual singular vortex but a nonsingular vortex called the Mermin-Ho vortex. We proposed that a vortex lattice of such nonsingular Mermin-Ho vortices are formed in a rapidly rotating ^{3}He-A superfluid. The proposed texture was later found in a rotating superfluid ^{3}He-A by measuring the NMR satellite spectrum.

Currently I am working on the half-quantum vortices (HQV) in superfluid ^{3}He. This vortex is regarded as a superposition, so-to-speak, of a singular vortex and a uniform texture. We found a condition under which the HQV stably exists. We are also working on the HQV lattice interpolating the lattices of singular vortices.

We have proposed topological formation of vortices in BEC of alkali atoms. Here the vortex phase is imprinted by making use of the Berry phase associated with adiabatic change of the external magnetic field. As a result, the vortex has a large winding number of 2*F*, *F* being the hyperfine spin of the condensate. This vortex is successfully created in several laboratories worldwide.

I have been working on quantum information and quantum computing in the past 10 years. It has been found the physical realization of a working quantum computer is extremely challenging, though. It is believed that one of the final candidates of a practical quantum computer can be a topological quantum computer making use of braiding of Majorana fermions. We have explicitly proposed implementations of quantum gates using Majorana fermions trapped in vortices in *p*-wave superfluid of cold atoms. I am also interested in other candidates of a topological quantum computer, which is one of my current subjects of research.

#### EDUCATION

- 1976
- B.Sc. in Physics, Kyoto University (Advisors: Chushiro Hayashi & Kiyoshi Nakazawa)
- 1978
- M.S. in Physics, Kyoto University (Advisors: Toshihiko Tsuneto & Tetsuo Ohmi)
- 1982
- Ph.D. in Physics, Kyoto University (Advisors: Toshihiko Tsuneto & Kazumi Maki)
- 1983
- Diploma in Classical and Quantum Gravity , Department of Mathematics, King's College, University of London

#### PROFESSIONAL EXPERIENCE

- 1980-1981
- Research Fellow, Department of Physics, University of Southern California (Host: Kazumi Maki)
- 1981-1982
- Postdoctoral Fellow, Department of Physics, University of Southern California (Host: Kazumi Maki)
- 1983-1985
- Postdoctoral Fellow, Department of Physics, University of Alberta (Host: Hiroomi Umezawa)
- 1985-1986
- Postdoctoral Fellow, Physics Division, University of Sussex (Hosts: Norman Dombey and David Waxman)
- 1986-1993
- Associate Professor, Institute of Physics, Shizuoka University
- 1990-1993
- Visiting Professor, Physics Division, University of Sussex (Host: David Waxman)
- 1993-1999
- Associate Professor, Department of Physics, Kinki University
- 1999-present
- Professor, Department of Physics, Kinki University
- 2001-2002
- TEKES Visiting Professor, Helsinki University of Technology (Host: Martti Salomaa)
- 2002-
- Visiting Professor, Helsinki University of Technology (Hosts: Martti Salomaa and Mikko Paalanen)

#### SELECTION OF PUBLICATIONS

"Geometric Aspects of Composite Pulses",

T. Ichikawa, M. Bando, Y. Kondo, and **M. Nakahara**

*Phil. Trans. R. Soc. A, ***370**, 4671-4689 (2012).

"Dynamical invariants for quantum control of four-level systems",

U. G"ung"ord"u, Y. Wan, M. Ali. Fasihi, and **M. Nakahara**

*Phys. Rev. A* **86**, 062312 1-9 (2012).

"Half-Quantum Vortices in Thin Film of Superfluid 3He",

K. Kondo, T. Ohmi, **M. Nakahara**, T. Kawakami, Y. Tsutsumi, and K. Machida,

*J. Phys. Soc. Jpn., ***81**, 104603 1-5 (2012).

"Quantum Computing with *p*-Wave Superfluid Vortices",

T. Ohmi and **M. Nakahara**,

*J. Phys. Soc. Jpn. ***79**, 104602 1-5 (2010).

"Exact solutions of the isoholonomic problem and the optimal control problem in holonomic quantum computation",

S. Tanimura, **M. Nakahara** and D. Hayashi,

*J. Math. Phys. ***46**, 022101 1-15 (2005).

"Topological vortex formation in a Bose-Einstein condensate under gravitational field",

Y. Kawaguchi, **M. Nakahara** and T. Ohmi,

*Phys. Rev. A ***70**, 043605 1-6 (2004).

"Continuous creation of a vortex in a Bose-Einstein condensate with hyperfine spin *F* = 2",

M. M"ott"onen, N. Matsumoto, **M. Nakahara** and T. Ohmi,

*J. Phys.: Condens. Matter ***14**, 13481-13491 (2002).