Classical analog of two quantum-optic phenomena in metamaterials

Abstract

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.