Research Group for Spin-Energy Transformation ScienceGroup Leader : SAITOH Eiji
Members: MORI Michiyasu, ONISHI Hiroaki, IEDA Jun’ichi, NAKATA Koki, YAMAMOTOKei, ARAKI Yasufumi, OKAYASU Satoru, CHUDO Hiroyuki, SATO Nana, IMAI Masaki,
UMEDA Maki

Research on mutual energy conversion among various forms
in condensed matters is a key to improving energy efficiency
and furthering energy sustainability. We study the energy
conversion using electron spins and their couplings to varioustypes of angular momentum, including mechanical rotation.
Barnett field, rotational Doppler effect, and Berry phasestudied by nuclear quadrupole resonance with rotation
We study the phenomena, which appear when a spin is
exposed to classical rotational motions. The Barnett field,
rotational Doppler effect (RDE), and Berry phase are known forthese phenomena, but they have been proposed and studied
individually, and there has been no study to clarify the relation
among them. Here, applying the coil-spinning technique fornuclear quadrupole resonance (NQR) measurements, we
succeeded in clarifying the associations among them in terms of
the rotational degrees of freedom such as the relative rotation
between a sample and a coil as a signal detector, and theabsolute rotation of the sample.
The Barnett field is an inertial magnetic field, which appears
when a spin is in a rotating frame of reference. To observe suchan inertial field, we need to simultaneously rotate the sampleand coil. We observe the NQR line splitting corresponding to
the emergence of the magnetic field as shown in Fig. 1(a). On
the other hand, when we rotate solely the coil, we observe theRDE caused by the relative rotational motion. As shown in Fig.
1(b), the NQR line splits into two. Note that the NQR spectra
shown in Figs. 1(a) and (b) are clearly different from each other,indicating the difference between the Barnett field and RDE.
Furthermore, when we rotate solely the sample, we cannot
observe the inertial field but observe the periodically driven
quantum system, which causes the accumulation of the Berryphase within the adiabatic (Born-Oppenheimer) approximation.
In addition, the relative rotation must be taken into account. Asa result, the NQR line splits into two as indicated by the green
triangles in Fig. 1 (c) and each of the resulting lines has ashoulder (the blue triangles). The NQR spectrum can becompletely described by the RDE and Berry phase, offering afull understanding of the rotational effect on spins.

Half-integer Shapiro-steps in superconducting qubit with a
π-Josephson junction
A superconducting quantum interference device (SQUID)
shows steps in the current-voltage (I-V) curve under microwave
irradiation (Fig. 2). This feature called Shapiro-steps (SS)appears at the voltages V = n(h/2e)f with integer n, microwave
frequency f, the Planck constant h, and the elementary charge ofelectron e. Because the microwave frequency and thefundamental constants are precisely determined the voltage canbe defined in the order of 10-9 accuracy. Thus, the SS is utilized
to the voltage standard.
A set of two superconductors separated by a thin insulator or
metal is called a Josephson junction (JJ). The maximum current
through a JJ sinusoidally changes with an applied magnetic flux.
In a JJ separated by a ferromagnet, the sinusoidal current-flux
relation is shifted by π compared with the conventional JJ (0-JJ).
The former is called π-JJ and is studied for a solid-state qubit(π-qubit) as a key to realizing quantum computers. The qubit
using superconductors usually needs an external magnetic field,
whereas the π-qubit does not. This is a big advantage todecoupling the qubit from environmental noises.
We studied the SS in a π-SQUID comprising a 0-JJ and a π-JJ
as shown in the inset of Fig. 2. The I-V curve can be calculated
as shown in Fig. 2 using the resistively shunted junction (RSJ)model with two parallel circuits of JJs. In the π-SQUID, the SS
appears at voltages with half-integer multiples of microwave
frequency in addition to the integer multiples. This phenomenon
originates from the coupling between a 0-JJ and a π-JJ. We
found that the half-integer SS and the π-qubit are two sides ofthe same coin. The appearance of half-integer SS means that theπ-SQUID can work as π-qubit. The key parameter is Jπ/J0
meaning the asymmetry of two JJs. The half-integer SS is
optimized by making the 0- and π-JJs equivalent. Making twoJJs in π-SQUID equivalent yields a π-qubit.

Fig. 2 I-V curves in a SQUID (black) and in a π-SQUID (red). The inset
shows schematic of the π-SQUID with superconductor channels(blue) separated by a 0-JJ (green) and a π-JJ (orange).

Fig. 1 NQR spectra obtained by using the setup of (a) simultaneous coiland sample rotation, (b) only coil rotation, and (c) only samplerotation.

References[1] H. Chudo, M. Matsuo, S. Maekawa, and E. Saitoh,Phys. Rev. B 103, 174308 (2021).
[2] M. Mori and S. Maekawa, Appl. Phys. Express 14, 103001(2021).