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arXiv:1612.02263 · Annalen der Physik

All‐Optical Photonic Band Control in a Quantum Metamaterial

Didier Felbacq, Emmanuel Rousseau

Published Jul 17, 2017• 5 citations
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Abstract

Abstract Metamaterials made of periodic collections of dielectric nanorods are considered theoretically. When quantum resonators are embedded within the nanorods, one obtains a quantum metamaterial, whose electromagnetic properties depend upon the state of the quantum resonators. The theoretical model predicts that when the resonators are pumped and reach the inversion regime, the quantum metamaterial exhibits an all‐optical switchable conduction band. The phenomenon can be described by considering the pole stucture of the scattering matrix of the metamaterial.

DOI
10.1002/andp.201600371

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Abstract Metamaterials made of periodic collections of dielectric nanorods are considered theoretically. When quantum resonators are embedded within the nanorods, one obtains a quantum metamaterial, whose electromagnetic properties depend upon the state of the quantum resonators. The theoretical model predicts that when the resonators are pumped and reach the inversion regime, the quantum metamaterial exhibits an all‐optical switchable conduction band. The phenomenon can be described by considering the pole stucture of the scattering matrix of the metamaterial.
In the present work, we present a metamaterial made of a periodic collection of dielectric resonators in which a quantum oscillator (denoted QO in the following) is inserted. The geometry at stake here is much more complicated than the textbook 1D cavity usually dealt with theoretically in quantum optics. We do provide a treatment essentially based on the scattering matrix non-perturbative approach, in order to investigate the various effects that could be expected to exist in such structures.The theoretical methods used are the Feshbach projection method associated with multiple scattering theory. First, the phenomenology for one scatterer with a QO inserted is presented, then the collective behavior of a finite periodic set of such scatterers is investigated and it is shown that it is possible to open and close a conduction band according to the state of the oscillators when the inserted quantum oscillators are put in the inversion regime by means of a pump field. They add gain to the system, allowing to reach the amplification regime in the vicinity of the Mie resonances of the dielectric resonators. When the transition frequency is situated at the photonic band gap edge, it creates switchable conducting modes within the bandgap.
We theoretically demonstrate the possibility of dynamically controlling the response of metamaterials at optical frequencies using the well known phenomenon of coherent control. Our results predict a variety of effects ranging from dramatic reduction of losses associated with the resonant response of metamaterials to switchable ultraslow to superluminal propagation of pulses governed by the magnetic field of the incident wave. These effects, generic to all metamaterials having a resonant response, involve embedding the metamaterial in resonant dispersive coherent atomic/molecular media. These effects may be utilized for narrow band switching applications and detectors for radiation below predetermined cut-off frequencies.
Two independent significant developments have challenged our understanding of light-matter interaction, one, involves the artificially structured materials known as metamaterials, and the other, relates to the coherent control of quantum systems via the quantum interference route. We theoretically demonstrate that one can engineer the electromagnetic response of composite metamaterials using coherent quantum interference effects. In particular, we predict that these composite materials can show a variety of effects ranging from dramatic reduction of losses to switchable ultraslow-to-superluminal pulse propagation. We propose parametric control of the metamaterials by active tuning of the capacitance of the structures, which is most efficiently engineered by embedding the metamaterial structures within a coherent atomic/molecular medium. This leads to dramatic frequency dependent features, such as significantly reduced dissipation accompanied by enhanced filling fraction. For a Split-ring resonator medium with magnetic properties, the associated splitting of the negative permeability band can be exploited for narrow band switching applications at near infrared frequencies involving just a single layer of such composite metamaterials.
We theoretically demonstrate control of the plasmalike effective response of a metamaterial composed of aligned metallic nanorods when the electric field of the incident radiation is parallel to the nanorods. By embedding this metamaterial in a coherent atomic/molecular medium, for example, silver nanorod arrays submerged in sodium vapor, we can make the metamaterial transmittive in the forbidden frequency region below its plasma frequency. This phenomenon is enabled by having Lorentz absorbers or other coherent processes in the background medium, which provide a large positive dielectric permittivity in the vicinity of the resonance, thereby rendering the effective permittivity positive. In particular, processes such as electromagnetically induced transparency are shown to provide additional control to switch and tune the new transmission bands.
We experimentally demonstrate the active control of a plasmonic metamaterial operating in the quantum regime. A two-dimensional metamaterial consisting of unit cells made from gold nanorods is investigated. Using an external laser, we control the temperature of the metamaterial and carry out quantum process tomography on single-photon polarization-encoded qubits sent through, characterizing the metamaterial as a variable quantum channel. The overall polarization response can be tuned by up to 33% for particular nanorod dimensions. To explain the results, we develop a theoretical model and find that the experimental results match the predicted behavior well. This work goes beyond the use of simple passive quantum plasmonic systems and shows that external control of plasmonic elements enables a flexible device that can be used for quantum state engineering.
We illustrate a mechanism based on coherent optical nonlinearities to realize optically tunable photonic crystals built from media supporting electromagnetically induced transparency. These exhibit specific periodic patterns where a light probe can experience a fully developed photonic band-gap with negligible absorption. An analytical method based on a two-mode approximation is developed to study the optical response of such a periodically modulated medium driven into a regime of standing-wave electromagnetically induced transparency. A comparison with a transfer matrix approach and with techniques based on the coupled Maxwell–Liouville equations shows that our method is very accurate to describe the optical properties of such photonic metamaterials in the frequency region of interest. Nearly perfect reflectivities may be attained for ultracold 87Rb atoms samples which are seen to reflect with little loss and deformation light pulses whose frequency components are contained within the gap. When the same mechanism is implemented for inhomogeneously broadened optical transitions of nitrogen-vacancy centers in diamond, which is more amenable to device applications, fully developed photonic band-gap structures with negligible absorption, reflectivities very close to unity and sufficiently large bandwidths may also be attained. We further examine more flexible schemes based on four level systems under double driving conditions showing more accurate and efficient coherent optical control of the photonic band-gap. The remarkable experimental simplicity of the schemes that we presented is set to ease quantum nonlinear optics applications.