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Physical Review A

Spontaneous decay process of a two-level atom embedded in a one-dimensional structure containing left-handed material

Jing-Ping Xu, Ya-Ping Yang, Chen Hong, Shi-Yao Zhu

Published Dec 17, 2007• 15 citations
Publisher

Abstract

The spontaneous decay process of a two-level atom embedded in a one-dimensional structure containing left-handed material (LHM) is investigated. We first consider the case of the atom being in front of a LHM layer mounted on a mirror, where it has been claimed that the atomic decay would be inhibited completely. Here we introduce dispersion and dissipation in the LHM, and find that there are two factors that weaken the inhibition of spontaneous decay. One is atomic nonradiative decay at shorter distances and the other is the instantaneous radiative decay process for larger distances. Then we discuss the decay process of an atom embedded in a one-dimensional photonic crystal composed of alternate LHM and ordinary material [right-handed material (RHM)] layers (LHM-RHM PC). Because of two special characteristics of the LHM, phase compensation and the fact that a frequency with negative index is usual near the material resonance frequency, both the radiative and nonradiative decay processes in the LHM-RHM PC are much different from those in a RHM PC. Under appropriate condition, the population evolution of atoms in a LHM-RHM PC displays oscillatory behavior.

DOI
10.1103/physreva.76.063813

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Optics Letters•Aug 27, 2008•20 citations
The spontaneous decay process of a two-level atom embedded in a one-dimensional structure containing left-handed material (LHM) is investigated. We first consider the case of the atom being in front of a LHM layer mounted on a mirror, where it has been claimed that the atomic decay would be inhibited completely. Here we introduce dispersion and dissipation in the LHM, and find that there are two factors that weaken the inhibition of spontaneous decay. One is atomic nonradiative decay at shorter distances and the other is the instantaneous radiative decay process for larger distances. Then we discuss the decay process of an atom embedded in a one-dimensional photonic crystal composed of alternate LHM and ordinary material [right-handed material (RHM)] layers (LHM-RHM PC). Because of two special characteristics of the LHM, phase compensation and the fact that a frequency with negative index is usual near the material resonance frequency, both the radiative and nonradiative decay processes in the LHM-RHM PC are much different from those in a RHM PC. Under appropriate condition, the population evolution of atoms in a LHM-RHM PC displays oscillatory behavior.
We investigate the spontaneous emission of a two-level atom in one dimensional photonic crystals composed of left-hand material (LHM) and right-hand material (RHM). A complete set of mode functions is constructed for the quantization of the radiation field. It is found that the mode functions for the frequency with in the band gap decreases exponentially from the surface to the interior of the photonic crystal which results in a much weaker field than the vacuum in the free space. The depression of the field leads to weak interaction with the atom, which leads to the suppressed spontaneous emission. Due to the strong reflection, the field in the LHM-RHM structure is much weaker than that in the RHM-RHM structure, thus the spontaneous emission is more strongly suppressed.
We investigate the spontaneous emission (SpE) of a two-level atom embedded in one-dimensional photonic crystals composed of left-hand material (LHM) and right-hand material. A complete set of mode functions is constructed for quantizing the radiation field. The radiated field distribution under the condition of impedance matching is calculated. The radiated field is focused in each layer and propagates along the direction normal to each layer due to the LHM. With such a structure we can control the propagation of the SpE field without changing the SpE rate.
Spontaneous decay of a two-level atom near the left-handed material (LHM) slab is investigated. The contributions of the guided modes and the surface-plasmon polariton (SPP) modes supported by the LHM slab to the spontaneous decay are studied at length. We find that the atomic decay near a LHM slab is much different from that near a dielectric slab or metal slab. The first---the dielectric slab with arbitrary thickness---supports at least two guided modes (one for TE polarized and one for TM polarized), but LHM slab may support none of the guided mode for certain thickness. The second---the atom near the LHM slab---may decay through both TE- and TM-polarized SPP, but the atom near the metal slab can decay only through TM-polarized SPP. The third, when the LHM slab supports only TE-polarized SPP modes, the atom near such slab cannot couple to the SPP mode when its dipole moment is perpendicular to the interface. Even if LHM contains weak loss, above analysis is also valid, and the decay rate directly related to material's losses (defined by the decay through dissipation here) can be distinguished from the total decay rate. Most interesting, we find that the decay through SPP will be larger than the decay through dissipation when the atom is placed at an appropriate position. Our results will give constructive reference to the design and fabrication of the quantum device made of LHM.
The possibility of negative optical path length in left-handed media (LHM) is shown to lead to complete suppression of spontaneous emission of an atom in front of a mirror with a layer of LHM. For the same reason two atoms put at the foci of a perfect lens formed by a parallel LHM slab [J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000)] exhibit perfect subradiance and superradiance. It is shown that these effects occur over distances that can be orders of magnitude larger than the transition wavelength and are only limited by the propagation length within the free-space decay time of the atoms. Single- and two-atom decay rates are calculated from the Greens function of the electric field in the presence of a LHM and limitations as well as potential applications are discussed.
We study the spontaneous emission of an atom embedded in a one-dimensional photonic crystal or superlattice using a classical electrodynamic theory of radiation. The rate of emission is a function of the frequency of the emitted photon, the dipole's position and orientation, as well as the geometric and material parameters of the superlattice. The emission spectrum shows an oscillatory behavior which follows the photonic band structure. For TE modes, there are frequency regions where radiative emission is completely prohibited due to the absence of modes with k//>omega/c; the radiation is then TM polarized. In addition to the radiative modes, there are always evanescent modes with k//>omega/c which are waveguided by the dielectric layers. The evanescent contribution to the spontaneous emission is dominant if a dielectric layer is in the near field region of the dipole. For TM modes, emission rates greatly vary for parallel and perpendicular dipole moments. In a photonic crystal with a high filling fraction of the dielectric and perpendicular dipoles located in the low-index layer, the decay rate can be as much as 76 times the free space value for a single atom and 50 times for a gas of atoms. We also find that the rate of emission presents a strong dependence on the atom's position.
We find that the V-type three-level Zeeman atom has the complete quantum interference when it is embedded in one-dimensional photonic crystals (1D PCs) possessing the TM-polarized complete gap. To avoid the nonradiative decay related to dissipation and the decay through surface exciton, we add two phase compensators made of ideal left-handed materials on two sides of atom, and then the total structure is equivalent to a 1D PC supporting only the radiative modes. The parameter regions (epsilon, mu) leading to the TM-polarized complete gap have been sketched out, and the influence of absorption on the quantum interference is discussed.