The effect of electron interactions on the universal properties of systems with optimized off-resonant intrinsic hyperpolarizability

Abstract

Because of the potentially large number of important applications of nonlinear optics, researchers have expended a great deal of effort to optimize the second-order molecular nonlinear-optical response, called the hyperpolarizability. The focus of our present studies is the intrinsic hyperpolarizability, which is a scale-invariant quantity that removes the effects of simple scaling, thus being the relevant quantity for comparing molecules of varying sizes. Past theoretical studies have focused on structural properties that optimize the intrinsic hyperpolarizability, which have characterized the structure of the quantum system based on the potential energy function, placement of nuclei, geometry, and the effects of external electric and magnetic fields. Those previous studies focused on single-electron models under the influence of an average potential. In the present studies, we generalize our calculations to two-electron systems and include electron interactions. As with the single-electron studies, universal properties are found that are common to all systems-be they molecules, nanoparticles, or quantum gases-when the hyperpolarizability is near the fundamental limit.

Maximizing the hyperpolarizability poorly determines the potential

“…It is apparent that both quantities converge with increasing number of parameters, x 10 to 55% of the maximum possible value while less rapidly ∆x 10 ≈ 1.26. Thus there appears to be, consistent with earlier work, a rather specific optimum value of x 10 and a less clear optimum choice for ∆x 10 . To further understand this we examined the derivatives of these parameters in the direction of each of the various eigenvectors of the hessian.…”

“…With n electrons, the maximum possible hyperpolarizability is predicted to be n 3/2 times that for a single electron. In fact this can be achieved in a system in which there are strong attractive interactions between the electrons that consequently move as a single quasi-particle in a potential similar that calculated above [10]. This mechanism is likely only to be realizable in exotic systems due to the Coulomb repulsion of the electrons.…”

“…The largest eigenvector with the largest eigenvalue seems quite strongly to constrain a linear combination of them, which is largely ∆x 10 and the next largest eigenvalue constrains another combination that is largely x 10 . The fact that ∆x 10 is largely controlled by the largest eigenvalue is unusual given that x 10 converges more quickly than∆x 10 . Nevertheless these quantities appear at first sight to offer a superior indication of how far a particular potential is from the optimum because deviations from the optimum alter them linearly, while the hyperpolarizability is only altered quadratically.…”

Hybrid quantum systems for enhanced nonlinear optical susceptibilities

“…However, it has been shown that the peak values of the nonlinear response are unchanged when another electron is added, nor when interactions between them are included. [15] Therefore, the important result is that a peak exists, though it will most likely not be at the predicted values given here. Thus, our work is intended to show that a fabrication effort of such hybrid systems based on dipoles and nanwires is likely to be fruitful in producing quantum systems that have record nonlinear response.…”

Lowest-order relativistic corrections to the fundamental limits of nonlinear-optical coefficients

“…[24][25][26][27][28][29][30][31][32] Another approach to breach the gap involves a systematic search for new classes of organic nonlinear optical molecules with multipolar chargedensity analysis from crystallographic data. [33][34][35] New abstract methods of calculating large nonlinear responses have also been studied for low-dimensional quantum graphs.…”