Yoshihara F, Ashhab S, Fuse T, Bamba M, Semba K
Advanced ICT Research Institute, National Institute of Information and Communications Technology, 4-2-1, Nukuikitamachi, Koganei, Tokyo, 184-8795, Japan.
Qatar Environment and Energy Research Institute, Hamad Bin Khalifa University, Qatar Foundation, Doha, Qatar.
Sci Rep. 2022 Apr 26;12(1):6764. doi: 10.1038/s41598-022-10203-1.
We derive the Hamiltonian of a superconducting circuit that comprises a single-Josephson-junction flux qubit inductively coupled to an LC oscillator, and we compare the derived circuit Hamiltonian with the quantum Rabi Hamiltonian, which describes a two-level system coupled to a harmonic oscillator. We show that there is a simple, intuitive correspondence between the circuit Hamiltonian and the quantum Rabi Hamiltonian. While there is an overall shift of the entire spectrum, the energy level structure of the circuit Hamiltonian up to the seventh excited states can still be fitted well by the quantum Rabi Hamiltonian even in the case where the coupling strength is larger than the frequencies of the qubit and the oscillator, i.e., when the qubit-oscillator circuit is in the deep-strong-coupling regime. We also show that although the circuit Hamiltonian can be transformed via a unitary transformation to a Hamiltonian containing a capacitive coupling term, the resulting circuit Hamiltonian cannot be approximated by the variant of the quantum Rabi Hamiltonian that is obtained using an analogous procedure for mapping the circuit variables onto Pauli and harmonic oscillator operators, even for relatively weak coupling. This difference between the flux and charge gauges follows from the properties of the qubit Hamiltonian eigenstates.
我们推导了一个超导电路的哈密顿量，该电路由一个通过电感耦合到一个LC振荡器的单约瑟夫森结磁通量子比特组成，并且我们将推导得到的电路哈密顿量与量子拉比哈密顿量进行了比较，后者描述了一个与简谐振子耦合的二能级系统。我们表明，电路哈密顿量与量子拉比哈密顿量之间存在一种简单、直观的对应关系。虽然整个能谱存在整体偏移，但即使在耦合强度大于量子比特和振荡器频率的情况下，即当量子比特 - 振荡器电路处于深度强耦合 regime 时，电路哈密顿量直至第七个激发态的能级结构仍能被量子拉比哈密顿量很好地拟合。我们还表明，尽管电路哈密顿量可以通过一个酉变换变换为一个包含电容耦合项的哈密顿量，但即使对于相对较弱的耦合，所得的电路哈密顿量也不能由通过将电路变量映射到泡利算符和谐振子算符的类似过程得到的量子拉比哈密顿量的变体来近似。磁通规范和电荷规范之间的这种差异源于量子比特哈密顿量本征态的性质。
