Metamaterials are artificial structures that display properties beyond those available in naturally occurring materials, for instance, it can show negative permeability or negative refractive index made of ordinary materials. On the other hand, metamaterials are resonant materials in general and can be seen as the combination of the electric resonator and the magnetic resonator. Based on this background, the coupling of the cavity mode with the metamaterials in the linear region has been theoretically investigated. We find that magnetic resonators can induce normal mode splitting as the electric resonator does, and the normal mode splitting induced by the metamaterials containing both electric and magnetic resonators is larger than that by only electric resonator. When the resonant frequencies of the electric and the magnetic resonators have the opposite deviations from the cavity frequency, transmission spectrum shows a three-peak shape in which two normal mode-splitting peaks and one revived cavity mode. Of most interest is that the full width at half-maximum (FWAM) of the revived cavity mode is much narrower than that of the empty cavity under certain conditions. This provides a new way to improve the quality factor of the cavity without increasing the reflectivity of the cavity walls.
Metamaterials are artificial structures that display properties beyond those available in naturally occurring materials, for instance, it can show negative permeability or negative refractive index made of ordinary materials. On the other hand, metamaterials are resonant materials in general and can be seen as the combination of the electric resonator and the magnetic resonator. Based on this background, the coupling of the cavity mode with the metamaterials in the linear region has been theoretically investigated. We find that magnetic resonators can induce normal mode splitting as the electric resonator does, and the normal mode splitting induced by the metamaterials containing both electric and magnetic resonators is larger than that by only electric resonator. When the resonant frequencies of the electric and the magnetic resonators have the opposite deviations from the cavity frequency, transmission spectrum shows a three-peak shape in which two normal mode-splitting peaks and one revived cavity mode. Of most interest is that the full width at half-maximum (FWAM) of the revived cavity mode is much narrower than that of the empty cavity under certain conditions. This provides a new way to improve the quality factor of the cavity without increasing the reflectivity of the cavity walls.
In cavity quantum electrodynamics (cQED), how an atom behaves in a cavity is what people care about. The coupling strength (g) between cavity field and atoms plays a fundamental role in various QED effects including Rabi splitting. In the solid-state case, when an atomic-like two-level system such as a single quantum dot (QD) is placed into a cavity, Rabi splitting would occur if g is strong enough. In the classical limit, when a QD in a cavity changes into a classical oscillator, the normal-mode splitting would also take place. It is known that g relies on the local fields at the places of the QDs or classical oscillators inside the cavity. However, for both cases, the traditional cavity modes involved are all in the form of standing waves and the localized fields are position-dependent. To ensure strong coupling between QDs or classical oscillators and photons, they should be placed right at the place where the cavity field is maximum, which is very challenging. How is the positional uncertainty overcome? Recently, the peculiar behaviors of electromagnetic (EM) fields inside zero-index metamaterial (ZIM) in which permittivity and/or permeability are zero have aroused considerable interest. In ZIMs the propagating phase everywhere is the same and the effective wavelength is infinite, which strongly changes the scattering and mode properties of the EM waves. In addition to the above characteristics, the fields in ZIM could be homogeneous as required by Maxwell equations. While the special properties of ZIMs are investigated, the fabrication of ZIMs is widely studied. It is found that a two dimensional (2D) photonic crystal consisting of a square lattice of dielectric rods with accidental degeneracy can behave as a loss-free ZIM at Dirac point. To overcome the positional uncertainty, in this paper we propose a cavity filled with effective zero-index metamaterial (ZIM). When the ZIM is embedded in a cavity, the enhanced homogeneous fields can occur under the resonance condition. Finally, experimental verification in microwave regime is conducted. In the experiments, we utilize a composite right/left-handed transmission line with deep subwavelength unit cell to mimic a ZIM and use a metallic split ring resonator (SRR) as a magnetic resonator whose resonance frequency is determined by structural parameters. The experimental results that in general agree well with the simulations demonstrate nearly position-independent normal-mode splitting.
Recently, metamaterials with unique electromagnetic (EM) properties have attracted people’s great interest. In metamaterials, the eclectic and magnetic response to incident light can be conveniently tuned. For example, the enhancement of electric and magnetic response can bring about effective negative permittivity (epsilon) and negative permeability (mu), respectively [1,2]. Since the interactions of metamaterials and light can be manipulated by varying the structural and geometric parameters of metamaterials, metamaterials provide us a convenient platform to mimic a variety of quantum-optic phenomena such as electromagnetically induced transparency (EIT) [3] and vacuum Rabi splitting [4]. EIT in quantum optics occurs when atoms can transit via two pathways and make a destructive interference to inhibit absorption, which brings about slow-wave effect and strong group velocity dispersion [5]. However, the building process of atomic EIT is still unclear due to the very quick time evolution in the transition. EIT analog in metamaterials realized by the interference in two classical pathways can observe the dynamic process during the establishment of EIT in the time scale much larger than the atomic counterpart. Based on a waveguide structure, we study the dynamic evolution of EIT in metamaterials and reveal experimentally the parameters controlling excitation transfer during the building process of EIT [6]. The dynamic properties of classical EIT not only mimic the population transfer between energy levels in the atomic EIT, but also present a physical picture of rapid optical response that plays an important role in fast manipulating light by EIT. Moreover, we study another important problem in classical EIT, i.e., the influence of intrinsic losses on EIT. We provide systematic experimental demonstration of EIT in metamaterials with tunable intrinsic loss. It is found under the EIT condition the maximum transmittance as well as the corresponding group delay in the transmission window is nearly unchanged and only the delay bandwidth is affected by the intrinsic loss. Vacuum Rabi splitting, which appears when atoms or atom-like systems are put inside a cavity, is another important quantum phenomenon that may be applied for the quantum entanglement and computations [7]. In a cavity with high quality factor and small volume, vacuum Rabi splitting can occur for a single atom in the strong coupling regime. In general, the cavity modes are all in the form of standing waves and the cavity fields are inhomogeneous. To ensure strong coupling of an atom (or a quantum dot) and photons, we need to place the atom right at the peak(s) of the fields, which is very challenging in atomic or solid-state experiments. Moreover, in atomic experiments, a cold atom is needed. This is because a hot atom can move around the position-variant fields under thermal fluctuation, making the coupling of the atom and the cavity unstable. To overcome the position uncertainty, we propose another type of cavity filled with zero-index metamaterials (ZIMs) in which epsilon=0 and/or mu=0 . In an impedance-matched ZIM ( epsilon=mu=0), both phases and amplitudes of the EM fields are homogeneous [8]. However, in a epsilon-near-zero (ENZ) medium (epsilon=0,mu=1), although the phases of EM waves are uniform, in most cases the amplitudes of electric fields will vary in space. In practice, a highly doped semiconductor such as InGaAs can be utilized as an ENZ medium [9] and self-assembled or colloidal quantum dots could be embedded in this ENZ medium. So how to realize uniform electric fields in an ENZ medium is an important practical problem. We discover that, when an ENZ medium is inserted in the center of a two-dimensional photonic crystal with a gap that plays a role of magnetic wall, the electric fields in the ENZ medium are forced to be nearly uniform, as required by Maxwell equations and boundary conditions. Then, we embed a quantum dot in the ENZ medium confined by the magnetic-wall-like photonic barrier and obtain a nearly position-independent Rabi-like splitting. This is because the enhanced electric fields are almost same at any place of the ENZ medium. Finally, by loading lumped capacitors and inductors in a microwave transmission line, we realize a cavity with effective ZIM in which the enhanced fields are nearly homogeneous [10]. When an atom-like split ring resonator is coupled to this effective ZIM at various locations, we observe the nearly position-independent Rabi-like splitting. A ZIM-filled cavity in the strong coupling regime will provide us a new platform to study the interactions of atoms and photons in the future.
Metamaterials, or artificial materials with optical properties not known for natural materials, have recently been used to demonstrate unusual optical phenomena, such as negative refraction, perfect lenses, subwavelength components, and electromagnetic invisibility cloaks. Most of the metamaterials designed to date are periodic structures containing a single resonating element in each unit cell, such as a split-ring resonator (SRR), a cutwire, or a slab-wire pair [1]. In this contribution, we demonstrate that a metamaterial with two coupled SRRs can exhibit an effect reminiscent of electromagnetically induced transparency (EIT), a coherent process normally observed in three-level atomic media [2]. Due to this process, a small transparency window with low absorption appears in the spectral response of the metamaterial. Simultaneously, extremely steep normal dispersion is observed in the transparency window, which is useful for slow-light applications.
We theoretically study the cavity transmission spectra with three-level atoms coupled by a coherent external control field in the superstrong coupling regime (atoms-cavity coupling strength g [square root] N is near or larger than the cavity free-spectral range DeltaFSR). When satisfying the superstrong coupling condition by increasing the number of the interaction atoms, more than one FSR cavity modes interact with atoms and each mode will split three peaks, which can be well explained by the linear dispersion enhancement of electromagnetically induced transparency medium due to the largely increased atomic density in the cavity.
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 discuss the frequency dependence of the spontaneous-emission rate (power) in a Fabry-Perot microcavity containing a Lorentz dielectric, with emphasis on modifications of the spectrum under the circumstances of the strong medium-cavity coupling. With the standard-cavity tuning, the total spontaneous-emission power spectrum consists of a multiwave version of the familiar low-frequency vacuum Rabi split peak and a broad structure on the high-frequency side coming from the enhanced spontaneous emission into the continuum of the obliquely propagating waves. This form of the spectrum derives from the properties of the (single-wave) radiation-intensity spectrum of the molecule. Depending on the observation direction, the radiation-intensity spectrum exhibits either a double-peak structure characteristic of the vacuum Rabi splitting, as observed in light transmisssion and reflection experiments, or a single-peak structure describing the enhanced spontaneous emission at the corresponding cavity resonant frequency.