トポロジカル相を活用した光ダイナミクスの時空間制御

• Project Area: Frontiers of materials science spun from topology
• Project/Area Number: 16H00975
• Research Category: Grant-in-Aid for Scientific Research on Innovative Areas (Research in a proposed research area)
• Allocation Type: Single-year Grants
• Review Section: Science and Engineering
• Research Institution: Hokkaido University
• Principal Investigator: 小布施 秀明 北海道大学, 工学研究院, 助教 (50415121)
• Project Period (FY): 2016-04-01 – 2018-03-31
• Project Status: Completed (Fiscal Year 2017)
• Budget Amount: ¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000); Fiscal Year 2017: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000); Fiscal Year 2016: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
• Keywords: PT対称性 / トポロジカル相 / エッジ状態 / 量子ウォーク / ローレンツ収縮 / 光ダイナミクス / 量子探索問題 / ローレンツ変換 / フォトニックトポロジカル相

Outline of Annual Research Achievements

本研究の目的は、光学系におけるトポロジカル相を活用することにより、光ダイナミクスの制御を行うための理論手法を確立することである。
減衰効果の強い光学系において，減衰効果を制御することは重要である．この観点から，開放系に対し空間-時間反転対称性(PT対称性)を要請し，さらにトポロジカル相に由来するエッジ状態を活用することにより，光の振幅制御を目指した．前年度の研究で得られた理論結果を検証するために，実験グループと国際共同研究を行った．実験では，減衰の効果を高精度に制御することが可能な光学系を構築し，さらにもつれ合った光子対を用いた．実験の結果、エッジ状態の成分のみを選択的に系に残すことなど上記理論予測と非常に良く一致する結果を得た。この研究をまとめた論文は，本年度Nature Physics誌に掲載された．
また,トポロジカル相を活用した光の位置の動的制御という観点から,トポロジカル数の相境界を等速度で変化させることにより,エッジ状態に局在した光の動的安定性についての研究を行った.その結果,トポロジカル相に由来するエッジ状態の運動方程式はDirac方程式であるため、トポロジカル数の相境界が有効光速に近い速度で等速直線運動する系においては,特殊相対論的効果が現れることが分かった.このことを反映し,エッジ状態の移動速度が系の有効的な光速に近づくにつれ,エッジ状態の局在幅はローレンツ収縮により短くなり,移動速度が有効的な光速になると,エッジ状態が消失することが分かった.これは,エッジ状態を移動させる速度の上限はその系における有効光速となることを意味し,応用利用に向け重要な結論が得られた.

Research Progress Status

29年度が最終年度であるため、記入しない。

Strategy for Future Research Activity

29年度が最終年度であるため、記入しない。

Research Products

• [Int'l Joint Research] 東南大学/中国科学技術大学(中国)
• [Int'l Joint Research] カルガリー大学(カナダ)
• [Int'l Joint Research] 東南大学/中国科学技術大学(中国)
• [Journal Article] Observation of topological edge states in parity-time-symmetric quantum walks (2017)
  • Author(s): L. Xiao, X. Zhan, Z. H. Bian, K. K. Wang, X. Zhang, X. P. Wang, J. Li, K. Mochizuki, D. Kim, N. Kawakami, W. Yi, H. Obuse, B. C. Sanders, P. Xue
  • Journal Title: Nature Physics Volume: 13 Issue: 11 Pages: 1117-1123
  • DOI: 10.1038/nphys4204
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Sensitivity of quantum walks to a boundary of two-dimensional lattices: approaches based on the CGMV method and topological phases (2017)
  • Author(s): Takako Endo, Norio Konno, Hideaki Obuse, Etsuo Segawa
  • Journal Title: Journal of Physics A -Mathematical and Theoretical Volume: 50 Issue: 45 Pages: 455302-455302
  • DOI: 10.1088/1751-8121/aa8c5e
  • Peer Reviewed
• [Journal Article] Effects of Disorder on Non-unitary <i>PT</i> Symmetric Quantum Walks (2017)
  • Author(s): Ken Mochizuki and Hideaki Obuse
  • Journal Title: Interdisciplinary Information Sciences Volume: 23 Issue: 1 Pages: 95-103
  • DOI: 10.4036/iis.2017.A.12
  • NAID: 130005519659
  • ISSN: 1340-9050, 1347-6157
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] Explicit definition of PT symmetry for nonunitary quantum walks with gain and loss (2016)
  • Author(s): Ken Mochizuki, Dakyeong Kim, and Hideaki Obuse
  • Journal Title: Physical Review A Volume: 93 Issue: 6
  • DOI: 10.1103/physreva.93.062116
  • NAID: 120005820741
  • Peer Reviewed / Acknowledgement Compliant
• [Presentation] Topological phases on quantum walks (2018)
  • Author(s): Hideaki Obuse
  • Organizer: Workshop: Mathematical approach for topological physics (I)
  • Int'l Joint Research / Invited
• [Presentation] Edge states in PT symmetric quantum walks with higher topological numbers (2018)
  • Author(s): Hideaki Obuse
  • Organizer: Non-Hermitian Physics - PHHQP XVIII
  • Int'l Joint Research
• [Presentation] トポロジカル相を利用したエッジ状態の動的制御：等速運動する1次元エッジ状態に対するスペクトル解析と三準位モデルとの比較 (2018)
  • Author(s): 藤澤有祐, 矢久保考介, 川上則雄, 小布施秀明
  • Organizer: 2018年日本物理学会年次大会
• [Presentation] PT対称な3ステップ量子ウォークにおけるトポロジカル相 (2018)
  • Author(s): 河崎真樹男, 望月健, 川上則雄, 小布施秀明
  • Organizer: 2018年日本物理学会年次大会
• [Presentation] Floqeut Topological Phases in PT Symmetric Passive Hadamard Quantum Walks (2017)
  • Author(s): Hideaki Obuse, Ken Mochizuki, Dakyeong Kim, and Norio Kawakami
  • Organizer: META 2017
  • Place of Presentation: Incheon-Seoul, Korea
  • Year and Date: 2017-07-25
  • Int'l Joint Research
• [Presentation] PT symmetry and pseudo-unitarity of nonunitrary quantum walks (2017)
  • Author(s): Ken Mochizuki and Hideaki Obuse
  • Organizer: META 2017
  • Place of Presentation: Incheon-Seoul, Korea
  • Year and Date: 2017-07-25
  • Int'l Joint Research
• [Presentation] Floqeut Topological Phases in PT Symmetric Quantum Walks with Gain and Loss (2017)
  • Author(s): Hideaki Obuse, Ken Mochizuki, Dakyeong Kim, and Norio Kawakami
  • Organizer: CLEO/Europe-EQEC 2017
  • Place of Presentation: Munich, Germany
  • Year and Date: 2017-06-25
  • Int'l Joint Research
• [Presentation] Floquet topological phases in PT symmetric non-unitary quantum walks: theory and experiment (2017)
  • Author(s): Hideaki Obuse, Ken Mochizuki, Dakyeong Kim, and Norio Kawakami
  • Organizer: PHHQP17: Non-Hermitian Hamiltonians in Physics: Theory and Experiment
  • Place of Presentation: Bad Honnef, Germany
  • Year and Date: 2017-05-15
  • Int'l Joint Research
• [Presentation] Observation of edge states of Floquet topological phases in PT symmetric quantum walks (2017)
  • Author(s): Hideaki Obuse, Ken Mochizuki, Dakyeong Kim, Norio Kawakami L. Xiao, X. Zhan, Z.H. Bian, K.K. Wang, X. Zhang, X.P. Wang, J. Li, W. Yi, B. Sanders, P. Xue
  • Organizer: International Conference on Topological Materials Science 2017 (TopoMat2017)
  • Place of Presentation: Tokyo Institute of Technology, Tokyo
  • Year and Date: 2017-05-09
  • Int'l Joint Research
• [Presentation] 量子ウォークにおけるトポロジカル相 (2017)
  • Author(s): 小布施 秀明
  • Organizer: 日本物理学会第72回年次大会 領域11,1合同シンポジウム「量子ウォークの深化とその周辺」
  • Place of Presentation: 大阪大学, 大阪市
  • Year and Date: 2017-03-17
  • Invited
• [Presentation] 散逸を伴う PT 対称な量子ウォークにおけるフロッケトポロジカル相の理論とエッジ状態の実験による観測 (2017)
  • Author(s): 小布施 秀明, 望月 健, 金 多景, 川上 則雄, A.L. Xiao, B.X. Zhan, Z.H. Bian, K.K. Wang, X. Zhang, X.P. Wang, J.Li, W. Yi, P. Xue
  • Organizer: 日本物理学会 第72回年次大会
  • Place of Presentation: 大阪大学、大阪市
  • Year and Date: 2017-03-17
• [Presentation] 量子ウォークにおけるトポロジカル相、及びアンダーソン転移との接点 (2017)
  • Author(s): 小布施 秀明
  • Organizer: 数理解析研究所(RIMS)研究会「臨界関数不等式に関わる諸問題が持つ不変構造の探求」
  • Place of Presentation: 京都大学, 京都市
  • Year and Date: 2017-02-13
  • Invited
• [Presentation] Topological phases in PT symmetric nonunitary quantum walks (2017)
  • Author(s): Ken Mochizuki, Dakyeong Kim, Norio Kawakami, and Hideaki Obuse
  • Organizer: International School on Topological Science and Topological Matters
  • Place of Presentation: Kyoto University, Kyoto
  • Year and Date: 2017-02-13
  • Int'l Joint Research
• [Presentation] Observation of edge states of Floquet topological phases in PT symmetric quantum walks (2017)
  • Author(s): Hideaki Obuse
  • Organizer: International Conference on Topological Materials Science 2017 (TopoMat2017)
  • Int'l Joint Research
• [Presentation] Floquet topological phases in PT symmetric non-unitary quantum walks: theory and experiment (2017)
  • Author(s): Hideaki Obuse
  • Organizer: WE-Heraeus-Seminar Non-Hermitian Hamiltonians in Physics: Theory and Experiment
  • Int'l Joint Research
• [Presentation] Floqeut Topological Phases in PT Symmetric Quantum Walks with Gain and Loss (2017)
  • Author(s): Hideaki Obuse, Ken Mochizuki, Dakyeong Kim, Norio Kawakami
  • Organizer: CLEO/Europe-EQEC 2017
  • Int'l Joint Research
• [Presentation] Topological phases of quantum walks (2017)
  • Author(s): Hideaki Obuse
  • Organizer: Mini Workshop: Mathematical Aspects of Topological Phases of Matter and Quantum Computing
  • Int'l Joint Research / Invited
• [Presentation] Floquet Topological Phases in PT Symmetric Passive Hadamard Quantum Walks (2017)
  • Author(s): Hideaki Obuse, Ken Mochizuki, Dakyeong Kim, Norio Kawakami
  • Organizer: META’17
  • Int'l Joint Research
• [Presentation] PT symmetry and pseudo-unitarity of nonunitrary quantum walks (2017)
  • Author(s): Ken Mochizuki, Hideaki Obuse
  • Organizer: META’17
  • Int'l Joint Research
• [Presentation] PT対称性を有する非ユニタリ－量子ウォーク (2017)
  • Author(s): Hideaki Obuse
  • Organizer: 5th Yokohama workshop on quantum walks
• [Presentation] Controlling Quantum Optical Dynamics by Topological Phases and Parity-Time Symmetry (2017)
  • Author(s): Hideaki Obuse
  • Organizer: International Workshop on NanoScience and NanoOptics 2017
  • Int'l Joint Research
• [Presentation] Floqeut Topological Phases in PT Symmetric Quantum Walks with Gain and Loss (2017)
  • Author(s): Hideaki Obuse
  • Organizer: The 1st Asia-Pacific Workshop on Trapped Quantum Systems (APTQS 2017)
  • Int'l Joint Research / Invited
• [Presentation] 非線形1次元量子ウォークにおける エッジ状態の安定性とPT対称性 (2017)
  • Author(s): 望月健, 川上則雄, 小布施秀明
  • Organizer: 日本物理学会2017年秋季大会
• [Presentation] トポロジカル相の接合境界が動的に変化する1次元格子モデルにおけるエッジ状態 (2017)
  • Author(s): 藤澤有祐, 矢久保考介, 川上則雄, 小布施秀明
  • Organizer: 日本物理学会2017年秋季大会
• [Presentation] 2次元量子ウォークを用いた量子探索問題における不規則性の寄与 (2017)
  • Author(s): 清水洋祐, 小布施秀明
  • Organizer: 日本物理学会2017年秋季大会
• [Presentation] Floquet Topological Phases Driven by PT Symmetric Non-unitary Time Evolution (2016)
  • Author(s): Hideaki Obuse, Ken Mochizuki, Dakyeong Kim, and Norio Kawakami
  • Organizer: Topological Material Science 2nd Annual Meeting
  • Place of Presentation: Tohoku University, Sendai
  • Year and Date: 2016-12-16
  • Int'l Joint Research / Invited
• [Presentation] Effects of disorder in PT symmetric non-unitary quantum walks (2016)
  • Author(s): Ken Mochizuki, Dakyeong Kim, Norio Kawakami, and Hideaki Obuse
  • Organizer: Topological Material Science 2nd Annual Meeting
  • Place of Presentation: Tohoku University, Sendai
  • Year and Date: 2016-12-16
  • Int'l Joint Research
• [Presentation] Sensitivity of a quantum walk to boundary (2016)
  • Author(s): Etsuo Segawa and Hideaki Obuse
  • Organizer: Workshop of Quantum Simulation and Quantum Walks 2016
  • Place of Presentation: Prague, Czech
  • Year and Date: 2016-11-17
  • Int'l Joint Research / Invited
• [Presentation] PT symmetric non-unitary quantum walks (2016)
  • Author(s): Hideaki Obuse
  • Organizer: Workshop of Quantum Simulation and Quantum Walks 2016
  • Place of Presentation: Prague, Czech
  • Year and Date: 2016-11-17
  • Int'l Joint Research
• [Presentation] 量子ウォークにおけるトポロジカル相：物性物理的観点から (2016)
  • Author(s): 小布施 秀明
  • Organizer: 量子系の数理と物質制御への展開II：量子ウォークを架け橋に
  • Place of Presentation: 横浜国立大学, 横浜
  • Year and Date: 2016-10-20
  • Invited
• [Presentation] Quantum dynamics associated with topological phases in synthetic quantum systems (2016)
  • Author(s): Hideaki Obuse
  • Organizer: Okinawa school in physics : Coherent Quantum Dynamics
  • Place of Presentation: Okinawa Institute of Science and Technology(OIST), Okinawa
  • Year and Date: 2016-09-27
  • Int'l Joint Research / Invited
• [Presentation] 量子ウォークの縁に対する感受性 (2016)
  • Author(s): 小布施 秀明、瀬川 悦生
  • Organizer: 日本数学会 2016年度秋季総合分科会
  • Place of Presentation: 関西大学、大阪市
  • Year and Date: 2016-09-15
• [Presentation] 2次元2自由度量子ウォークにおける量子探索問題 (2016)
  • Author(s): 清水 洋祐, 小布施 秀明
  • Organizer: 日本物理学会2016年秋季大会
  • Place of Presentation: 金沢大学、金沢市
  • Year and Date: 2016-09-13
• [Presentation] 非ユニタリー量子ウォークにおける不規則性の効果と PT 対称性の一般化 (2016)
  • Author(s): 望月 健, 小布施 秀明
  • Organizer: 日本物理学会2016年秋季大会
  • Place of Presentation: 金沢大学、金沢市
  • Year and Date: 2016-09-13
• [Presentation] Floquet Topological phases of quantum walks and its connection to network models (2016)
  • Author(s): Hideaki Obuse
  • Organizer: International Workshop Anderson Localization in Topological Insulators
  • Place of Presentation: IBS Center for Theoretical Physics of Complex Systems, Daejeon, South Korea
  • Year and Date: 2016-09-05
  • Int'l Joint Research / Invited
• [Presentation] Floquet topological phases of non-unitary quantum walks with PT symmetry (2016)
  • Author(s): Hideaki Obuse, Ken Mochizuki, Dakyeong Kim, and Norio Kawakami
  • Organizer: PHHQP16: Progress in Quantum Physics with Non-Hermitian Operators
  • Place of Presentation: Kyoto University, Kyoto
  • Year and Date: 2016-08-08
  • Int'l Joint Research
• [Presentation] PT symmetry for nonunitary quantum walks and the extension to disordered systems (2016)
  • Author(s): Ken Mochizuki and Hideaki Obuse
  • Organizer: PHHQP16: Progress in Quantum Physics with Non-Hermitian Operators
  • Place of Presentation: Kyoto University, Kyoto
  • Year and Date: 2016-08-08
  • Int'l Joint Research
• [Remarks] 粒子が出入りする状況下における特殊な量子状態に関する理論を構築し，実験で裏付け
  • URL: https://www.hokudai.ac.jp/news/20170825_ko.pdf
• [Remarks] 粒子が出入りする状況下における特殊な量子状態に関する理論を構築し、実験で裏付け
  • URL: http://www.kyoto-u.ac.jp/ja/research/research_results/2017/170731_1.html