Abstract：
Motivated by the recent developments in terahertz spectroscopy using pump-probe setups to study correlated electronic materials, we review the field theoretical formalism to compute finite frequency nonlinear electro-optical responses in centrosymmetric systems starting from basic time dependent perturbation theory. We express the nonlinear current kernel as a sum of several causal response functions. These causal functions cannot be evaluated using perturbative field theory methods, since they are not contour ordered. Consequently, we associate each response function with a corresponding imaginary time ordered current correlation function, since the latter can be factorized using Wick\'s theorem. The mapping between the response functions and the correlation functions, suitably analytically continued to real frequencies, is proven exactly. We derive constraints satisfied by the nonlinear current kernel and we prove a generalizedf-sum rule for the nonlinear conductivity, all of which are consequences of particle number conservation. The constraints guarantee that the nonlinear static responses are free from spurious divergences. We apply the theory to compute the gauge invariant nonlinear conductivity of a system of noninteracting electrons in the presence of weak disorder. As special cases of this generalized nonlinear response, we discuss its third harmonic and its instantaneous terahertz Kerr signals. The formalism can be used to compute the nonlinear conductivity in symmetry broken phases of electronic systems such as superconductors, density waves and nematic states.
摘要：
受使用泵浦探针设置研究相关电子材料的太赫兹光谱学的最新发展的启发，我们从基本的时间相关扰动理论出发，回顾了场理论形式主义，以计算中心对称系统中的有限频率非线性电光响应。我们将非线性当前内核表示为几个因果响应函数的总和。这些因果函数不能用摄动场论方法来评估，因为它们不是等高线。因此,我们将每个响应函数与相应的虚时间有序电流相关函数相关联，因为后者可以用威克定理分解。响应函数和相关函数之间的映射，适当地分析继续到真实频率，被证明是准确的。我们推导了非线性电流核满足的约束，并证明了非线性电导率的广义f和规则，所有这些都是粒子数守恒的结果。这些约束保证了非线性静态响应没有杂散。我们应用该理论来计算存在弱无序的非相互作用电子系统的规范不变非线性电导率。作为这种广义非线性响应的特例，我们讨论了它的三次谐波和瞬时太赫兹克尔信号。形式主义可用于计算电子系统（例如超导体）的对称破碎相中的非线性电导率，密度波和向列状态。
