Mathematical Research on Deep-Strong Coupling Regime of Interaction between Artificial Atom and Photon in Circuit QED

2022 Fiscal Year Final Research Report

• Project/Area Number: 20K03768
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 13010:Mathematical physics and fundamental theory of condensed matter physics-related
• Research Institution: Kyushu University
• Principal Investigator: Hirokawa Masao 九州大学, システム情報科学研究院, 教授 (70282788)
• Project Period (FY): 2020-04-01 – 2023-03-31
• Keywords: 量子ラビ模型 / 深強結合領域 / シュレディンガーの猫状態 / 強結合極限 / 超対称性 / 自発的超対称性の破れ / ヒッグスポテンシャル / 質量生成

Outline of Final Research Achievements

I have made the mathematical research on the deep-strong coupling regime of the interaction between an artificial atom and a 1-mode photon in circuit QED. I have studied the quantum Rabi model and that model with the quadratic interaction as the mathematical models describing that physical system. I have considered the strong coupling limit for both the models, and then, I have shown that the quantum Rabi model reveals different aspects of its bound states depending on whether it has the quadratic interaction or not, which is caused by the effect coming from the virtual Bose particles. Based on the results, I have developed the mathematical theory with those models of the virtual Bose particle coupled with a qubit so that it illustrates the phase transition from supersymmetry (SUSY) to its spontaneous breaking. In particular, I have proved that the spontaneous SUSY breaking works for the mass enhancement in the fermionic states as well as the bosonic states.

Free Research Field

数理物理学

Academic Significance and Societal Importance of the Research Achievements

本研究課題で，量子ビットと相互作用する仮想ボーズ粒子の数理モデルを超対称性からその自発的破れへ向かう相転移を示す数理模型へと発展させた．ボーズ粒子に関する２次の相互作用が無い場合に，清華大学の実験チームがこの数理模型による理論予想の幾つかを実験検証したと報告したが，本研究課題の結果に基づけば，そこで扱った２次の項を実験的に実現すれば，自発的超対称性の破れによる質量生成をも観ることができるかもしれない．この実験結果が報告される迄は，超対称性とその自発的破れが物理的実在なのかは未解決であったが，超対称性粒子を探す巨大施設ではなく，超対称性量子力学を実験室で検証する可能性を示唆できたように思う．