Dressed quantum graphs with optical nonlinearities approaching the fundamental limit

Abstract

We dress bare quantum graphs with finite delta function potentials and calculate optical nonlinearities that are found to match the fundamental limits set by potential optimization. We show that structures whose first hyperpolarizability is near the maximum are well described by only three states, the so-called three-level Ansatz, while structures with the largest second hyperpolarizability require four states. We analyze a very large set of configurations for graphs with quasi-quadratic energy spectra and show how they exhibit better response than bare graphs through exquisite optimization of the shape of the eigenfunctions enabled by the existence of the finite potentials. We also discover an exception to the universal scaling properties of the three-level model parameters and trace it to the observation that a greater number of levels are required to satisfy the sum rules even when the three-level Ansatz is satisfied and the first hyperpolarizability is at its maximum value, as specified by potential optimization. This exception in the universal scaling properties of nonlinear optical structures at the limit is traced to the discontinuity in the gradient of the eigenfunctions at the location of the delta potential. This is the first time that dressed quantum graphs have been devised and solved for their nonlinear response, and it is the first analytical model of a confined dynamic system with a simple potential energy that achieves the fundamental limits.

References in corpus (4)

• Modulated conjugation as a means for attaining a record high intrinsic hyperpolarizability
• Pushing the hyperpolarizability to the limit
• Studies on optimizing potential energy functions for maximal intrinsic hyperpolarizability
• Monte Carlo Studies of the Fundamental Limits of the Intrinsic Hyperpolarizability

Cited by in corpus (10)

• Green's function approach for quantum graphs: an overview
• Exact fundamental limits of the first and second hyperpolarizabilities
• Physics of the fundamental limits of nonlinear optics: A theoretical perspective
• Lowest-order relativistic corrections to the fundamental limits of nonlinear-optical coefficients
• Optimization of eigenstates and spectra for quasi-linear nonlinear optical systems
• Optimum topology of quasi-one dimensional nonlinear optical quantum systems
• Using excited states and degeneracies to enhance the electric polarizability and first hyperpolarizability
• Maximizing the hyperpolarizability of 1D potentials with multiple electrons
• General solution to nonlinear optical quantum graphs using Dalgarno-Lewis summation techniques
• Static hyperpolarizability of space-fractional quantum systems