Using excited states and degeneracies to enhance the electric polarizability and first hyperpolarizability

Abstract

We investigate the efficacy of boosting the nonlinear-optical response by using novel systems such as those in an excited state or with a degenerate ground state. By applying the Three Level Ansatz (TLA) and using the Thomas-Reiche-Kuhn (TRK) sum rules as constraints, we find the electric polarizability and first hyperpolarizability of excited state systems to be bounded, but larger than those derived for a system in the ground state. It is shown that a system with a degenerate ground state can have divergent polarizabilities and that such divergences are real and not relics of a pathology in the perturbation theory. Furthermore, we demonstrate that these divergences only occur on time scales short compared to the relaxation time of the population difference to an equilibrium value. Such systems provide a way to get ultra-large nonlinear optical response.We discuss examples of huge enhancements in molecules and double quantum dots using a double quantum well as a model. arXiv:1805.06977v2 [physics.optics]

Which way does stimulated emission go?

“…the inverted polarizability has opposite sign and equal magnitude. This 4-level model ignores contributions to the polarizability from additional excited levels, which can in principle provide larger scattering than non-inverted, ground state systems [27].…”

Giant Stark effect in coupled quantum wells: Analytical model

“…It is essential for several device applications and as a diagnostic tool [1][2][3][4]. For these reasons, systematic searches for structures and molecules exhibiting a large Stark effect have been reported [5][6][7][8][9]. Such structures are expected to exhibit large linear and nonlinear optical response due to their large polarizability and hyperpolarizabilities.…”

“…Thus, materials possessing near-degenerate (E (0) m ≈ E (0) n ) and dipole-coupled pairs of states are natural candidates for useful materials. Their large response to (weak) electric fields constitutes an example of a "giant" Stark effect [9].…”

Which Way Does Stimulated Emission Go?

“…In fact, outside of the strongly pumped limit, the only effect that the dump field has on P 4π is through the lowering of the equilibrium excited state population ρ 11 , and P 4π actually decreases with increasing Γ d . In the weakly dumped, linear excitation regime, the coherent part of the |1⟩→ |2⟩ dipole response to the incoming field E i can be described by a polarizability, ⟨ d ( t )⟩ = d 12 ρ 12 = α E i /2. Writing the electric field magnitude E i in terms of d 12 , Ω i and γ as d 12 Ω i /γ = (3ϵ 0 λ 3 /8 π 2 ) E i gives the explicit expression for α inv in the fully inverted limit: Using eq and eq , we confirm that σ R /σ stim = γ/Γ ≪ 1. As a side note, comparing to the polarizability of a noninverted 2-level system with the same dipole matrix element d 12 and a nonradiative relaxation rate Γ ≫ γ, the inverted polarizability has opposite sign and equal magnitude. This 4-level model ignores contributions to the polarizability from additional excited levels, which can in principle provide larger scattering than noninverted, ground state systems …”

“…This 4-level model ignores contributions to the polarizability from additional excited levels, which can in principle provide larger scattering than noninverted, ground state systems …”