Quantum Metamaterials with Magnetic Response at Optical Frequencies

We propose novel quantum antennas and metamaterials with a strong magnetic response at optical frequencies. Our design is based on the arrangement of natural quantum emitters with only electric dipole transition moments at distances smaller than a wavelength of light but much larger than their physical size. In particular, we show that an atomic dimer can serve as a magnetic antenna at its antisymmetric mode to enhance the decay rate of a magnetic transition in its vicinity by several orders of magnitude. Furthermore, we study metasurfaces composed of atomic bilayers with and without cavities and show that they can fully reflect the electric and magnetic fields of light, thus, forming nearly perfect electric or magnetic mirrors. The proposed metamaterials will embody the intrinsic quantum functionalities of natural emitters such as atoms, ions, color center, or molecules and can be fabricated with available state-of-the-art technologies, promising several applications both in classical optics and quantum engineering.

Figure 1

Atomic dimer antenna: Optical response of two atoms placed at $z=\pm l/2$ (see insets) as a function of detuning at the antisymmetric (AS) (a) and symmetric (b) modes of the composite system, respectively. Left vertical axes (black): total scattering cross sections normalized to the free-space value $3{\lambda }^2/2\pi$ for a two-level atom on resonance. Right vertical axes (orange and blue): The real (solid curves) and imaginary (dashed curves) parts of the induced effective polarizabilities calculated using Eq. (1) and for $l=0.1{\lambda }_a$, where ${\lambda }_a$ is the wavelength detuning between the illumination and the atom. Insets display normalized total magnetic field distribution for each case, where ${\mathbf{H}}_t$, ${\mathbf{H}}_0$ are the total and incident magnetic fields, respectively.

Figure 2

Enhancing the decay rate of a magnetic transition: (a) Enhanced decay rate of a magnetic dipole emitter placed in the middle of an atomic dimer antenna for the symmetric (blue), antisymmetric (red) modes and an atomic tetramer (purple) as a function of the antenna length $l$. The tetramer antenna is composed of four identical atoms placed at ${\mathbf{r}}_{1,2}=\mp l/2{\mathbf{e}}_z,{\mathbf{r}}_{3,4}=\pm l/2{\mathbf{e}}_x$. (b),(c) Schematics of an emitter with magnetic dipole moment ${\mu }_t$ placed in the middle of an atomic dimer (b) and tetramer (c).

Figure 3

Atomic bilayer metasurface (ABM): (a) Schematics of an ABM. The symmetric and antisymmetric modes corresponding to the electric and magnetic mirrors, respectively. (b) Intensity reflection coefficient $R$ as a function of layer separation $l$ and frequency detuning $\omega -{\omega }_a$ for an ABM with period ${\mathrm{\Lambda }}_x={\mathrm{\Lambda }}_y=\mathrm{\Lambda }=0.5{\lambda }_a$. (c) Intensity transmission and reflection coefficients corresponding to a cut through (b) at $l=0.1{\lambda }_a$. Solid curves: analytical results for an infinite array with plane wave illumination. Symbols: Numerical calculations for a finite array with $15\times 15\times 2$ atoms illuminated by a Gaussian beam. (d) Real and imaginary parts of the effective induced dipole moments of different layers. (e) Real and imaginary parts of the effective electric and magnetic polarizabilities. (f) Intensity reflection coefficient as a function of angle of incidence ${\theta }_{\mathrm{inc}}^s$ (for s-polarized light) and frequency detuning for the antisymmetric mode.

Figure 4

Atomic metasurface inside a planar cavity composed of distributed Bragg reflectors (DBRs): (a) Schematics of a cavity and an atomic monolayer metasurface (AMM). (b) Transmission of the cavity loaded with the AMM shows resonance splitting as a function of its position inside the cavity ($D$). (c),(d) Same as (a),(b) but for an atomic bilayer metasurface (ABM). The quality factor of the planar cavity is taken to be $Q\approx 8.7\times {10}^3$, ${\gamma }_c\approx {10}^3{\mathrm{\Gamma }}_0$ and $L_c=3{\lambda }_a$.