由能谱和跃迁偶极矩确定的多项式势给出最大的超极化率
Polynomial potentials determined from the energy spectrum and transition dipole moments that give the largest hyperpolarizabilities
摘要：
我们试图得到反问题的多项式解，即在给定能谱和跃迁偶极矩矩阵的情况下，确定力学哈密顿量的形式。我们的方法是通过找到反问题的近似解来确定多项式形式的势，然后确定该系统的哈密顿量的超极化率。我们发现，最大的超极化率接近以前潜在的优化研究的表观极限，但我们没有找到真正的潜力，必要的参数值超过这个表观极限。我们还探讨了具有正指数的半势，它不能表示为多项式，除了整数幂。这产生了一个简单的封闭的潜力，只有一个参数，扫描几乎整个范围内的固有超极化率。消失指数的极限情况下产生最大的内禀超极化率。
英文摘要：
We attempt to get a polynomial solution to the inverse problem, that is, to determine the form of the mechanical Hamiltonian when given the energy spectrum and transition dipole moment matrix. Our approach is to determine the potential in the form of a polynomial by finding an approximate solution to the inverse problem, then to determine the hyperpolarizability for that system's Hamiltonian. We find that the largest hyperpolarizabilities approach the apparent limit of previous potential optimization studies, but we do not find real potentials for the parameter values necessary to exceed this apparent limit. We also explore half potentials with positive exponent, which cannot be expressed as a polynomial except for integer powers. This yields a simple closed potential with only one parameter that scans nearly the full range of the intrinsic hyperpolarizability. The limiting case of vanishing exponent yields the largest intrinsic hyperpolarizability.
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