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arXiv:2110.06189

Non-Uniqueness of Non-Linear Optical Response

Gerard McCaul, Alexander F. King, Denys I. Bondar

Published Oct 12, 2021• 1 citation
arXivHTMLPDF

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. In this work, we demonstrate 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, we show that multiple candidate driving field exists, which will all generate the same response. Consequently, it is possible 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. This non-uniqueness phenomenon may in future be utilised to engineer internal system states without modifying its optical response.

DOI
10.48550/arxiv.2110.06189

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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. In this work, we demonstrate 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, we show that multiple candidate driving field exists, which will all generate the same response. Consequently, it is possible 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. This non-uniqueness phenomenon may in future be utilised to engineer internal system states without modifying its 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.
Introduction Lasers are part of a large class of non-linear systems which covers a great deal of scientific domains, including physics, chemistry, biology, sociology, etc. All these non-linear systems have common properties and present universal features which become more and more extensive as new studies are performed. In recent years, the interest in these non-linear systems has considerably increased. In particular, it is now well established that the role of fluctuations in non-equilibrium systems is far more relevant than in systems at thermodynamical equilibrium, and the study of their influence on stationary and transient states has become very important. Among the different aspects presented by the non-linearity in lasers, two of them will be particularly studied here: (i) The first one is the optical bistability (OB). An optical system is bistable if it has two output states I for the same value of the excitation A over some range of excitation values (see Gibbs, 1985, for a recent review). A typical response curve of such a system is given in Figure 5.1. Here, the system is defined as bistable between A ↓ and A ↑ , where the effectively occupied state depends on the history of the input parameter (see the caption to Figure 5.1). If OB is a common phenomenon in different fields, the OB transient phenomena have far more general features.
Correlated systems are a wide class of materials in which the strong electron-electron repulsion is the origin of very fascinating and unusual properties, among which metal-to-insulator transitions and high temperature superconductivity are the most striking examples. In the recent years, the fast development of non-adiabatic probing techniques opened new interesting perspectives for the investigation of such materials in non-equilibrium conditions. In this thesis, we discuss the theoretical description of few relevant cases which represent different examples of non-equilibrium phenomena in correlated materials. In particular, we will focus on the dynamics following a sudden excitation and the coupling to an external driving field. As a first example we consider the dynamics across a phase transition, namely we explore the possibility of driving a phase transition as the result of a sudden excitation, as e.g. the coupling with a short light pulse. We consider systems showing different equilibrium phases and study the conditions under which the off-equilibrium dynamics may lead to non-trivial dynamical phase transitions. A different case is represented by the dynamics induced by a driving electric field. This problem is particularly relevant for the possible applications of correlated materials in electronic devices. Here we consider the paradigmatic case of a correlated material coupled to external sources which impose a finite bias across the system. We analyze the formation and the properties of the non-equilibrium stationary states in which a finite current flows through the system. This allows us to study the non-linear response properties of a correlated system. In this context, a particularly relevant aspect is the problem of the dielectric breakdown of a Mott insulator, namely the formation of conducting states in the Mott insulating phase. In this thesis we explore different mechanisms leading to such possibility. First we discuss a quantum tunneling mechanism of carriers driven across the insulating gap by the effect of strong electric-fields. Eventually, we discuss the possibility of a resistive transition from an insulating to a metallic state induced by the application of an external electric-field.
Light-matter strong coupling has been the subject of much attention in recent decades, giving optical systems unique features. However, properties of a system with strong coupling are determined by the properties of its components and are thus difficult to control. Here, we propose Floquet engineering, a technique of controlling the energy levels of a quantum system using external fields, as a method of manipulating a hybrid system of a molecule strongly coupled to a single-mode resonator. We show that an external field can change the relative positions of levels in an open strongly coupled system, leading to a change in the rates of transitions between them. We demonstrate that if the frequency of the pumping wave is close to polariton transitions in the hybrid system, nonmonotonic dependence of fluorescence and scattering amplitudes on pump intensity with a narrow resonance-like response occurs. We show that this phenomenon occurs due to hybridization of the lower and upper polaritons with substantially different excitation numbers caused by the pumping affecting polariton states of the system. This occurs when the Rabi interaction with the coherent field is comparable to the field-matter coupling constant, which in turn needs to be sufficient for the manifestation of strong coupling. This nonmonotonic dependence of the fluorescence and scattering amplitudes on pump rate intensity paves the way for the creation of nonlinear optical devices.