Formulation of phase reduction theory for nonlinear oscillations in quantum dissipative systems

2019 Fiscal Year Final Research Report

• Project/Area Number: 16K13847
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Mathematical physics/Fundamental condensed matter physics
• Research Institution: Tokyo Institute of Technology
• Principal Investigator: Nakao Hiroya 東京工業大学, 工学院, 教授 (40344048)
• Project Period (FY): 2016-04-01 – 2020-03-31
• Keywords: 量子散逸系 / 非線形振動 / 位相縮約理論 / 同期現象 / 最適化

Outline of Final Research Achievements

Phase reduction theory for nonlinear oscillations in quantum dissipative systems was developed. Recent advances in nanotechnology arose interest in nonlinear oscillations in microscale physical systems like optomechanical and laser systems, in which quantum effects play important roles, and their application to quantum information processing. For nonlinear oscillators in classical physical systems, phase reduction theory, which allows us to represent the system dynamics by a simple phase equation, had been developed and used to analyze their synchronization dynamics. However, this method had not been applicable to quantum nonlinear oscillators. In this study, we formulated a phase reduction theory for quantum nonlinear oscillators by focusing on the semi-classical regime where the quantum effect is not too strong. We then used the theory to analyze synchronization dynamics of the system.

Free Research Field

非線形物理学

Academic Significance and Societal Importance of the Research Achievements

本研究では、量子散逸系の非線形振動現象に対して適用可能な位相縮約理論を定式化して、これを用いて量子的な非線形振動子の同期現象を解析した。さらに、この理論に基づいて、量子非線形振動子の同期の安定性を最適化する周期外力の形状を求め、実際に数値シミュレーションにより最適化した周期外力が単なる調和外力に比べより高い安定性を実現し、より速い同期状態への収束に導くことを示した。近年、ミクロな物理系に関する実験技術の発展が著しく、本研究で定式化した量子非線形振動子の同期現象の解析と制御に関する基礎理論は、将来的に量子センサーや量子情報処理などに応用できる可能性がある。