We study the ground-state phase diagram of a nonlinear two-photon Rabi-Hubbard (RH) model in one dimension using quantum Monte Carlo simulations and density-matrix renormalization-group calculations. Our model includes a nonlinear photon-photon interaction term. Absent this term, the RH model has only one phase, the normal disordered phase, and suffers from spectral collapse at larger values of the photon-qubit interaction or intercavity photon hopping. The photon-photon interaction, no matter how small, stabilizes the system, which now exhibits two quantum phase transitions: Normal phase to photon-pair superfluid (PSF) transition and PSF to single-particle superfluid (SPSF). The discrete $Z_4$ symmetry of the Hamiltonian spontaneously breaks in two stages: First it breaks partially as the system enters the PSF and then it completely breaks when the system finally enters the SPSF phase. We show detailed numerical results supporting this, and map out the ground-state phase diagram.

中文翻译：

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非线性两光子Rabi-Hubbard模型：超辐射，光子和光子对Bose-Einstein凝聚

我们使用量子蒙特卡洛模拟和密度矩阵重归一化组计算，研究了一维非线性两光子拉比-哈伯德（RH）模型的基态相图。我们的模型包括非线性光子-光子相互作用项。没有这个术语，RH模型只有一个相，即正常的无序相，并且在较大的光子-量子位相互作用或腔内光子跳跃值下遭受光谱崩溃。无论多么小的光子-光子相互作用，都会稳定该系统，该系统现在表现出两个量子相变：正常相到光子对超流体（PSF）的转变和PSF到单颗粒超流体（SPSF）的转变。离散的${ž}_4$哈密​​顿量的对称性自发地破裂为两个阶段：首先，当系统进入PSF时，它部分破裂；然后，当系统最终进入SPSF阶段时，它完全破裂。我们显示了支持此的详细数值结果，并绘制了基态相图。