The geometric phase is a common phenomenon in a variety of physical systems, with significant applications in optics. We report the first experimental demonstration of the adiabatic geometric phase in nonlinear frequency conversion, wherein the coupling between the signal and idler frequencies constitutes the intrinsic two-level dynamics of the system. We observe a variety of effects associated with the geometric phase, including the adiabatic broadening of bandwidth, asymmetric transmission for opposite propagation directions, conjugation of the phase for orthogonal eigenstates, and the nonreciprocity associated with the pump field bias. Our work paves the way towards all-optically controlled geometric phase elements for wavefront shaping, isolation, guiding, and quantum optical applications, harnessing spectral and spatial correlations.

中文翻译：

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非线性变频中几何相位的实验观察

几何相位是各种物理系统中的常见现象，在光学中有重要的应用。我们报告了非线性变频中绝热几何相位的第一个实验演示，其中信号和惰轮频率之间的耦合构成了系统的固有两级动力学。我们观察到了与几何相位相关的各种影响，包括绝热扩宽，相反传播方向的不对称传输，正交本征态的相位共轭以及与泵浦场偏置相关的不可逆性。我们的工作为通向波阵面成形，隔离，导引和量子光学应用的全光控几何相位元素铺平了道路，并利用了光谱和空间相关性。