Joint Research into Mathematical Science for Qunatum Information Devices

• Project/Area Number: 26310210
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Partial Multi-year Fund
• Section: 特設分野
• Research Field: Mathematical Sciences in Search of New Cooperation
• Research Institution: Hiroshima University
• Principal Investigator: Hirokawa Masao 広島大学, 工学研究科, 教授 (70282788)
• Research Collaborator: KOSAKA Hideo ; NAKAMURA Yasunobu ; NEMOTO Kae ; OSHITA Yoshihito ; SEMBA Kouichi ; HASHIZUME Tomihiro ; HIGUCHI Yusuke ; ICHIMURA Kouichi ; MINE Takuya ; MUNRO Bill ; NEIDHARDT Hagen ; NOMURA Yuji ; OGURISU Osamu
• Project Period (FY): 2014-07-18 – 2019-03-31
• Project Status: Completed (Fiscal Year 2018)
• Budget Amount: ¥15,990,000 (Direct Cost: ¥12,300,000、Indirect Cost: ¥3,690,000); Fiscal Year 2018: ¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000); Fiscal Year 2017: ¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000); Fiscal Year 2016: ¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000); Fiscal Year 2015: ¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000); Fiscal Year 2014: ¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
• Keywords: 一般化された量子ラビ模型 / 超強結合領域 / 深強結合領域 / スピントロニック量子ビット / 量子細線 / トンネル効果 / 位相因子 / 量子情報デバイス / 量子ラビ模型 / 応用数理物理学 / 一般化された量子Rabi模型 / 仮想光子 / 実光子 / 物理的状態 / 裸の状態 / メゾン・ペア理論 / 量子ラビ・モデル / コヒーレント状態 / シュレディンガーの猫状態 / dark state / quasi-dark state / duality / Rabi モデル / 非可換調和振動子 / N=2超対称量子力学 / 超対称性の自発的破れ / Rabi model / Jaynes-Cumming model / 超対称性量子力学 / カイラル性 / カイラル対称性

Outline of Final Research Achievements

In this project, I mainly studied the following two subjects in the light of mathematical science:(1) a mathematical analysis of the energy spectrum for a mathematical model describing the interaction between a qubit and the light in the ultra strong coupling regime and in the deep strong coupling regime; (2) an operator analysis of a mathematical model describing the spintronic qubit passing through the junction between two quantum wires.

Academic Significance and Societal Importance of the Research Achievements

量子デバイスの機能，制御部，記憶部，輸送部のうち，(1) 制御部に関しては，(人工)原子が作る２準位量子系をフォトンの量子場で制御する数理模型に対し，そのエネルギー・スペクトルに焦点を当てた数理解析；(2) 輸送部に関しては，量子細線に接合を咬ませ，その接合を電子スピンで実装するスピントロニック量子ビットがトンネルする物理的様子の作用素解析；という学術的知見を得，さらに，本研究課題を土台に，数理科学と理論・実験物理学の連携研究の次のテーマを探し，さらに連携を量子工学へと発展させることができた．

Research Products

• [Int'l Joint Research] Aarhus University(デンマーク)
• [Journal Article] Quantum Simulation of Interaction between Atom and Light (2018)
  • Author(s): Masao Hirokawa
  • Journal Title: 京都大学数理解析研究所講究録 Volume: 2089
  • Open Access
• [Journal Article] A mathematical analysis of dressed photon in ground state of generalized quantum Rabi model using pair theory (2017)
  • Author(s): Hirokawa Masao, Moeller Jacob S, Sasaki Itaru
  • Journal Title: Journal of Physics A: Mathematical and Theoretical Volume: 50 Issue: 18 Pages: 184003-184003
  • DOI: 10.1088/1751-8121/aa677c
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] A mathematical modeling of electron-phonon interaction for small wave numbers close to zero (2017)
  • Author(s): M. Hirokawa
  • Journal Title: EMS Series of Congress Reports, Functional Analysis and Operator Theory for Quantum Physics Volume: The P. Exner Anniversary Vol. Pages: 373-400
  • DOI: 10.4171/175-1/18
  • ISBN: 9783037191750, 9783037196755
  • Peer Reviewed
• [Journal Article] Duality between A Dark State And A Quasi-Dark State (2017)
  • Author(s): Masao Hirokawa
  • Journal Title: Annals of Physics (N.Y.) Volume: 377 Pages: 229-242
  • DOI: 10.1016/j.aop.2016.12.032
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] The Rabi model gives off a flavor of spontaneous SUSY breaking (2015)
  • Author(s): Masao Hirokawa
  • Journal Title: Quantum Studies: Mathematics and Foundations Volume: 2 Issue: 4 Pages: 379-388
  • DOI: 10.1007/s40509-015-0041-y
  • Peer Reviewed / Acknowledgement Compliant
• [Presentation] Topological Superconductors in Ferromagnetic Nanowires with Domain Wall (2019)
  • Author(s): Masahiko Ichimura, Masao Hirokawa
  • Organizer: 2019 Joint MMM-Intermag Conference
• [Presentation] Approximated Eigenstates of Generalized Quantum Rabi Model with A^2-Term in Deep-Strong Coupling Regime (2018)
  • Author(s): Masao Hirokawa
  • Organizer: Strongly Coupled Light-Matter Interactions: Models and Applications, Lanzhou University, Lanzhou, China
  • Int'l Joint Research / Invited
• [Presentation] 磁壁を有する強磁性ナノワイヤにおけるトポロジカル超伝導体 (2018)
  • Author(s): 市村雅彦, 廣川真男
  • Organizer: 2018年第79回応用物理学会秋季学術講演会
• [Presentation] Virtual and real photons in ground state of generalized quantum Rabi model in ultra-strong coupling regime (2017)
  • Author(s): Masao Hirokawa
  • Organizer: Virtual Photons in Ultra-Strongly Coupled Systems
  • Place of Presentation: 理化学研究所
  • Year and Date: 2017-01-26
  • Int'l Joint Research / Invited
• [Presentation] Possibility of Spintronic-Qubit Control Through Tunnel-Junction on Quantum Wire (2017)
  • Author(s): M. Hirokawa
  • Organizer: BIT's 7th Annual World Congress of Nano Science & Technology 2017
  • Int'l Joint Research
• [Presentation] Quantum simulation of the atom-light interaction (2017)
  • Author(s): M. Hirokawa
  • Organizer: Quantum Circle at the Doppler Institute, Czech
• [Presentation] A Quantum Simulation of Cavity Optomechanics (2017)
  • Author(s): M. Hirokawa
  • Organizer: Math/Phys Seminar at Aarhus University, Denmark
• [Presentation] A Mathematical Analysis of Photon in Ground State of Generalized Quantum Rabi Model with the A^2-Term (2016)
  • Author(s): Masao Hirokawa
  • Organizer: International Workshop on Ultra-Strong Light-Matter: Theory and Applications to Quantum Information
  • Place of Presentation: Quantum Technologies for Information Science, University of the Basque Country, Spain
  • Year and Date: 2016-09-19
  • Int'l Joint Research / Invited
• [Presentation] On the Hepp-Lieb-Preparata quantum phase transition for the quantum Rabi model (2016)
  • Author(s): Masao Hirokawa
  • Organizer: Technical Committee on Quantum Information Technology(量子情報技術研究会)
  • Place of Presentation: 高知工科大学
  • Year and Date: 2016-05-31
  • Invited
• [Presentation] Mathematical Modeling for Quantum Devices (2016)
  • Author(s): M. Hirokawa
  • Organizer: Joint Mathematics and Physics Seminar
  • Place of Presentation: Aarhus University (Denmark)
  • Year and Date: 2016-03-17
  • Int'l Joint Research / Invited
• [Presentation] A Mathematical Aspect of A Tunnelling Phase for Spintronic Qubit (2014)
  • Author(s): M. Hirokawa
  • Organizer: The Asia-Pacific Workshops and Conferences on Quantum Information Science 2014
  • Place of Presentation: Conference Center, National Cheng Kung Kung University, 台南，台湾
  • Year and Date: 2014-12-12
  • Invited
• [Presentation] Two Mathematical Aspects of The Interaction between A Two-Level Atom and A One-Mode Light (2014)
  • Author(s): M. Hirokawa
  • Organizer: Mathematics and Physics of Interacting Quantum Systems
  • Place of Presentation: Institute of Mathematics for Industry, Kyushu University, 福岡，日本
  • Year and Date: 2014-10-23
  • Invited
• [Book] 数物系に向けた フーリエ解析とヒルベルト空間論 (2017)
  • Author(s): 廣川真男
  • Total Pages: 192
  • Publisher: サイエンス社
• [Funded Workshop] Interdisciplinary Workshop on Quantum Device (IWQD) 2017 (2017)
  • Place of Presentation: 国立情報学研究所
  • Year and Date: 2017-03-06
• [Funded Workshop] Interdisciplinary Workshop on Quantum Device (2015)
  • Place of Presentation: 国立情報学研究所
  • Year and Date: 2015-10-13
• [Funded Workshop] Satellite Seminar of IWQD 2015 (2015)
  • Place of Presentation: 広島大学
  • Year and Date: 2015-10-07