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Physical Review A

Defect band-gap structures for triggering single-photon emission

Ho Trung Dung, L. Knöll, Dirk‐Gunnar Welsch

Published Feb 10, 2003• 10 citations
Publisher

Abstract

A three-dimensional (3D) analysis of the spontaneous decay of a single dipole embedded in a planar multilayer structure is given, with special emphasis on Kerr-tunable photonic band-gap materials for single-photon emission on demand. It is shown that the change in the density of states near a defect resonance is much more pronounced than that near the band edges. In particular, operation near the band edge as suggested from a 1D analysis is little suited for controlling the photon emission.

DOI
10.1103/physreva.67.021801

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A three-dimensional (3D) analysis of the spontaneous decay of a single dipole embedded in a planar multilayer structure is given, with special emphasis on Kerr-tunable photonic band-gap materials for single-photon emission on demand. It is shown that the change in the density of states near a defect resonance is much more pronounced than that near the band edges. In particular, operation near the band edge as suggested from a 1D analysis is little suited for controlling the photon emission.
In this article we propose to build a (semi-)deterministic photon gun by modifying the spontaneous decay in a photonic band-gap material. We show that such a device allows for deterministic and unidirectional single-photon emission with a repetition rate of the order of 100 kHz. We describe a specific realization of the 1D band-gap model by means of a 3D photonic-crystal heterostructure and the feasability of implementing such a device using Er3+ ions that produce single photons at the telecommunication wavelength of 1.55,μm, important for many applications.
The novel dynamical and spectral features of (single photon) spontaneous emission from an atomic transition near a photonic band edge are investigated by frustrating these features by spontaneous emission through another atomic transition far from the photonic band edge and deep in the photon continuum, the two atomic transitions forming the two dipole-allowed transitions of a three-level atom in a Λ configuration. Though spontaneous emission through the atomic transition far from the photonic band edge (the “far” transition) is not directly affected by the photonic band gap (PBG), it is indirectly affected by the PBG through its coupling to the atomic transition near the photonic band edge (the “near” transition) via the Λ configuration. As a result of this coupling, spontaneous emission through the “far” transition can be used as a probe to measure the strength of the effects of the PBG on spontaneous emission through the “near” transition. We have shown that the effects of the PBG on spontaneous emission via the “near” transition are strongly affected (and, therefore, can be controlled by) not only by the detuning of the “near” transition from photonic band edge but also by the vacuum decay rate of spontaneous emission through the “far” transition which is coupled to the “near” transition through the Λ configuration. In particular, we have shown that the oscillatory behavior of spontaneous emission near a photonic band edge as well as the Autler-Townes doublet of the spontaneous emission spectrum (due to the splitting of the atomic level near the photonic band edge) are strongly dependent on the decay rate of spontaneous emission through the probe transition which is far from the band edge.
We study spontaneous emission near the edge of a photonic band gap. Instead of a simple exponential decay in the vacuum, spontaneous emission displays an oscillatory behavior. A single photon-atom bound dressed state exhibits a fractional steady-state atomic population on the excited state. For a three-level atom we evaluate the spectral splitting and subnatural linewidth of spontaneous emission. In the presence of N-1 unexcited atoms we show that the collective time scale factor is equal to ${\mathit{N}}^{\mathrm{\ensuremath{\varphi}}}$, where \ensuremath{\varphi}=2/3 for an isotropic band gap and \ensuremath{\varphi}=1 or 2 for anisotropic two-dimensional or three-dimensional band edges, respectively.
We demonstrate the coherent control of spontaneous emission for a three-level atom located within a photonic band gap (PBG) material, with one resonant frequency near the edge of the PBG. Spontaneous emission from the three-level atom can be totally suppressed or strongly enhanced depending on the relative phase between the steady-state control laser coupling the two upper levels and the pump laser pulse used to create an excited state of the atom in the form of a coherent superposition of the two upper levels. Unlike the free-space case, the steady-state inversion of the atomic system is strongly dependent on the externally prescribed initial conditions. This non-zero steady-state population is achieved by virtue of the localization of light in the vicinity of the emitting atom. It is robust to decoherence effects provided that the Rabi frequency of the control laser field exceeds the rate of dephasing interactions. As a result, such a system may be relevant for a single-atom, phase-sensitive optical memory device on the atomic scale. The protected electric dipole within the PBG provides a basis for a qubit to encode information for quantum computations. A detailed literature survey on the nature, fabrication and applications of PBG materials is presented to provide context for this research.
We studied the effects of a coherent monochromatic resonant laser field driving the transition of a two-level atom embedded in a photonic band gap (PBG) material on the emission dynamics of the atom. When the transition frequency of the atom lies outside a PBG and sufficiently far from the band edge that the emission dynamics of the atom is not normally affected by the gap, the dynamic stark splitting of the upper level of the atom into two dressed states by a sufficiently strong resonant driving field can bring the lower dressed state close enough to the band edge or even inside the gap so as to be affected by the gap, providing a switchable means of extending the novel effects of atom–photon interaction near the edge of a PBG for atomic transitions outside the gap and far from the band edge. The net effect is as if a sufficiently strong resonant field driving a transition of an atom embedded in a PBG actively shifts the PBG close enough to the transition so that the gap affects the emission dynamics associated with the transition.
The phenomenon of spontaneous emission cancellation has been investigated in photonic-band-gap materials in the presence of dipole-dipole interaction. The material is densely doped with an ensemble of five-level nanoparticles. The mean field theory is used to calculate the effect of the dipole-dipole interaction whereas the linear response theory is used to calculate the expressions for the real and imaginary susceptibilities. Numerical simulations are performed for an isotropic photonic-band-gap material. Interesting results are predicted such as the control of the spontaneous emission cancellation by moving the resonance energies between the energy band and energy gap. It is also found that the photonic-band-gap material can be switched between absorptive and nonabsorptive states by changing the strength of the dipole-dipole interaction and the resonance energies in the energy band.