Two-photon Rabi model: analytic solutions and spectral collapse
Two-photon Rabi model: analytic solutions and spectral collapse
复制标题
双光子拉比模型：解析解和光谱塌陷
DOI：
10.1088/1751-8113/49/46/464002
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发表时间：
2016-11-18
影响因子：
2.1
通讯作者：
Chen, Qing-Hu
中科院分区：
文献类型：
--
作者：
Duan, Liwei;Xie, You-Fei;Chen, Qing-Hu
利用Z4对称性和SU(1，1)代数分析了双光子量子Rabi模型。我们得到了G-函数，它的零点给出了哈密顿量的精确本征值。G函数的奇异性结构使得我们可以得出这些本征值在实轴上的分布的结论，并且我们得到了在临界耦合gc处的谱崩塌现象，这在以前的数值计算中已经发现。在gc处的光谱由离散的和连续的部分组成：基态总是被有限的激发间隙从连续谱中分离出来，排除了通常意义上的量子相变。对于大的量子比特分裂，其他低位能级也会从连续体中分裂出来。然而，微扰理论预言所有阶次的能隙都会消失，从而证明了它的非微扰性质。我们用基态的变分计算证实了这一结果。
The two-photon quantum Rabi model is analyzed using the Z 4 -symmetry and su ( 1 , 1 ) -algebra. We derive the G-function whose zeros give the exact eigenvalues of the Hamiltonian. The singularity structure of the G-function allows to draw conclusions about the distribution of these eigenvalues along the real axis and we derive the spectral collapse phenomenon at critical coupling g c , found numerically before. The spectrum at g c consists of a discrete and a continuous part: the ground state is always separated from the continuum by a finite excitation gap, ruling out a quantum phase transition in the usual sense. For large qubit splitting, also other low lying states split off from the continuum. However, perturbation theory predicts the vanishing of the gap to all orders, demonstrating its non-perturbative nature. We corroborate this result with a variational calculation for the ground state.