Non‐Uniqueness of Driving Fields Generating Non‐Linear Optical Response

Abstract

In recent years, non‐linear optical phenomena have attracted much attention, with a particular focus on the engineering and exploitation of non‐linear responses. Comparatively little study has, however, been devoted to the driving fields that generate these responses. This work demonstrates that the relationship between a driving field and the optical response it induces is non‐unique. Using a generic model for a strongly interacting system, it is shown that multiple candidate driving field exists, which will all generate the same response. Consequently, it is possible to show that the optical response is not sufficient to determine the internal dynamics of the system, and that different solutions for the driving field will do different amounts of work on a system. Physically, the work done indicates the energy absorbed by the system from the field and will therefore correspond to modifying the absorption spectrum of the material. This non‐uniqueness phenomenon may be further utilized to engineer thermodynamically efficient system states without modifying its optical response.

Dynamical Generation of Epsilon-Near-Zero Behaviour via Tracking and Feedback Control

“…In particular, tracking control [54][55][56][57][58][59][60][61] provides a method for calculating driving fields such that the evolution of a given observable tracks a specified trajectory. These methods have been deployed profitably in the context of atomic [57], molecular [55,62,63] and solid-state systems [60,61,64,65]. Complementary to this method is feedback control [66].…”

“…Though the Hamiltonian in Eq. ( 1) and subsequent analysis of the field required to induce an ENZ response are valid for any Û that will commute with electron number operators [64,65], for simulations we take our system to be a half-filled Fermi-Hubbard model (N s = N e ) [86], where N ↑ = N ↓ and onsite interaction of the form…”