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Results in Physics

Quantum master equation for coupling mechanism of metamaterial

Wei Huang, Songyi Liu, Shi-Ting Cao, Chu Guo, Shan Yin, Xinwei Du, Wentao Zhang

Published Feb 5, 2022• 10 citations
Publisher

Abstract

In this paper, we present a full quantum description for coupling mechanism of the metamaterial. We start the derivation from quantum master equation to fit the spectrum of THz metamaterial. Therefore we can employ the quantum master equation to describe the coupling of metamaterial, such as the electromagnetically induced transparency (EIT) and bound state in the continuum (BIC). In this paper, we build up a bridge between the quantum mechanism and coupling mechanism of metamaterial, so-called quantum–classical analogies. Based on our theory, we can find the more quantum phenomenon with corresponding to the coupling phenomenon of the metamaterial.

DOI
10.1016/j.rinp.2022.105262

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Journal of Physics D Applied Physics•Mar 25, 2022•59 citations
In this paper, we present a full quantum description for coupling mechanism of the metamaterial. We start the derivation from quantum master equation to fit the spectrum of THz metamaterial. Therefore we can employ the quantum master equation to describe the coupling of metamaterial, such as the electromagnetically induced transparency (EIT) and bound state in the continuum (BIC). In this paper, we build up a bridge between the quantum mechanism and coupling mechanism of metamaterial, so-called quantum–classical analogies. Based on our theory, we can find the more quantum phenomenon with corresponding to the coupling phenomenon of the metamaterial.
Electromagnetically induced transparency (EIT) in terahertz (THz) metamaterials relies on the coherent coupling between a radiative (bright) mode and a subradiant (dark) mode. Understanding the dynamic interplay between the bright and dark modes holds the key to manipulate the mutual interference and hence the transparency. Here, we use nonlinear 2D-THz spectroscopy to scrutinize the dynamics through nonlinearities of the EIT-like phenomenon in a metamaterial platform that comprises of two coupled resonators. From the temporal profiles of the nonlinear pump-probe and photon-echo signals, we found that the bright mode relaxation time is almost twice the time for the coherent exchange of energy between the two coupled resonators. The multi-peak nature of photon-echo signal and the corresponding temporal signatures further provides a direct visualization of the interference between the dressed states that drives the transparency window in our THz metamaterial. A time-resolved density matrix model accurately describes the observed features, including the cross-peak behavior and the temporal dynamics, establishing the coherent mode coupling as the origin of the transparency window.
\n With a metamaterial structure, the phenomenology observed in quantum electromagnetically induced transparency is reproduced. Through the parametric comparison between quantum and classical systems, the physical mechanism of this novel phenomenon has been explained directly in our analysis. In addition, we use another metamaterial structure to mimic a tripod four-level atom and reveal the analog of electromagnetically induced absorption. Our theoretical and experimental studies may not only bring an intuitive understanding of quantum interference in atomic system, but also provide useful guidelines for the design of microwave devices based on metamaterials.\n
We theoretically investigate the classical analog of electromagnetically induced transparency (EIT) and electromagnetically induced absorption (EIA) in a planar metamaterial at optical frequency, which originates from destructive and constructive interference between dark and radiative elements.The metamaterial consists of two coupled resonators with different geometries.An EIT-like transparent window with low absorption is observed and found to be strongly affected by resonant states of the resonators.The transition between the EIT and EIA is achieved by changing the split width and coupling distance.The absorption is enhanced up to 2.5 times compared with the dipolar case.The excitation of the dark mode is very important for EIT-and EIA-like responses of the proposed metamaterial.The EIT and EIA phenomena offer a potential method for manipulating electromagnetic response in metamaterial-based devices.
We show that by treating the weak probe field as a perturbation to the strong coupling fields in the atomic system and using the perturbative method in a master equation, the features of linear response of phenomena of electromagnetically induced transparency (EIT) can be uniformly demonstrated, regardless of the details of atomic energy level configuration. We compare our estimation with both typical and atypical EIT-observed configurations and find that our model indeed provides a description of the sharp transmission window in central area of typical EIT curve. It can also be inferred hereby that for various systems other than atomic gas, as long as the description of the system’s dynamics comes down to the simplified form of master equation, the corresponding EIT analogs and EIT-like phenomena can also be explained in this way.
We show that by treating the weak probe field as a perturbation to the strong coupling fields in the atomic system and using the perturbative method in a master equation, the features of linear response of phenomena of electromagnetically induced transparency (EIT) can be uniformly demonstrated, regardless of the details of atomic energy level configuration. We compare our estimation with both typical and atypical EIT-observed configurations and find that our model indeed provides a description of the sharp transmission window in central area of typical EIT curve. It can also be inferred hereby that for various systems other than atomic gas, as long as the description of the system’s dynamics comes down to the simplified form of master equation, the corresponding EIT analogs and EIT-like phenomena can also be explained in this way.
Abstract Electromagnetically induced transparency (EIT) stems from a quantum system, where an opaque atomic medium appears the narrow transparent state within a wide absorption area. This phenomenon can be achieved by quantum interference of pumping light and detecting light at different energy levels of transitions. In the generation process of EIT effect, in addition to transparent state, the atomic medium is usually accompanied with a strong dispersion effect, which will bright about a significant reduction of light velocity, thus realizing many important applications, such as slow light propagations. Although the EIT effect has many important applications, its application scenarios are greatly limited due to the fact that EIT realization usually requires specific and complicated conditions, such as refrigeration temperature, high intensity laser, etc. Recently, the analogue of EIT effect in metamaterial has attracted increasing attentions due to its advantages such as controllable room temperature and large operating bandwidth. Metamaterial analogue of EIT effect has become a new research focus. In this article, we review current research progresses on EIT metamaterials. Firstly, we describe the theoretical models for analyzing EIT metamaterials, including the mechanical oscillator model and the equivalent circuit model. Then, we describe the simulations, designs and experiments of passive EIT metamaterials with fixed structures and active EIT metamaterials with tunable elements. Furthermore, the applications of EIT metamaterials in the areas of slow lights, sensings, absorptions and other fields are also reviewed. Finally, the possible directions and key issues of future EIT metamaterial researches are prospected.