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Journal of Modern Optics

Optical resonance near the edge of a photonic band gap (PBG): turning the effects of a PBG on/off using a resonant driving field

Mesfin Woldeyohannes, Mohammed Shutayfi

Published Dec 6, 2018• 1 citation
Publisher

Abstract

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.

DOI
10.1080/09500340.2018.1550222

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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 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.
Summary form only given. Unlike semiconductors which facilitate the coherent propagation of electrons, photonic band gap (PBG) materials execute their novel functions through the coherent localization of photons. When a PBG material is doped with impurity atoms which have an electronic transition that lies within the gap, spontaneous emission of light from the atom is inhibited. Inside the gap, the photon forms a bound state to the atom. Outside the gap, radiative dynamics in the colored vacuum is highly nonMarkovian. I discuss the influence of these memory effects on laser action. When spontaneous emission is absent, the next order radiative effect (resonance dipole-dipole interaction between atoms) must be incorporated, leading to anomalous nonlinear optical effects which occur at a much lower threshold than in ordinary vacuum. I describe the collective switching of two-level atoms near a photonic band edge, by external laser field, from a passive stare to one exhibiting population inversion. This effect is forbidden in ordinary vacuum. Finally, I discuss the prospects for a phase sensitive, single (3-level) atom quantum memory device, onto which information may be written by an external laser pulse. By scattering polarized photons (flying qubit) this system may execute certain quantum logic operations.
A method of laser control of absorption and dispersion of two-level quantum system (atoms, ions, quantum dots) embedded into photonic band gap (PBG) material via variation of intensity and frequency of an external laser field is proposed. It is shown that in order to provide an effective control, the frequency of atomic transition should be located at the photonic band edge near the bottom of the PBG. The method is based on the laser induced Mollow splitting of the atomic energy levels and strong dependence of the decay rates of the so-called dressed states on the frequency of the Mollow splitting due to photonic band edge. This enables us to control absorption and dispersion of a signal laser field, which is near-resonant to the quantum transition of dopant.
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 describe all-optical transistor action in photonic band gap materials doped with active atoms. In the presence of a photonic band gap (PBG) material, a coherent laser beam with the frequency slightly detuned from the resonant atomic transition frequency can drive a collection of two-level atoms to an almost totally inverted state, a phenomenon strictly forbidden in ordinary vacuum. By changing the laser field intensity in the neighborhood of a threshold value, it is possible to drive the atomic system through a transition from states in which the atoms populate preferentially the ground level to almost totally inverted states. In this process, the atomic system switches from a passive medium (highly absorptive) to a active medium (highly amplifying). The switching action in a PBG material is not associated with operating near a narrow cavity resonance with conventional trade-off between switching time and switching threshold intensity. Rather it is associated with an abrupt discontinuity in the engineered broad band electromagnetic density of states of the PBG material. We demonstrate all-optical transistor action in PBG materials by analyzing the absorption spectrum of a second probe laser beam and we show that the probe beam experience a substantial differential gain by slight intensity modulations in the control laser field.
A method of dynamic control of absorption and dispersion of a two-level quantum system (atoms, ions or quantum dots) doping a photonic band gap (PBG) material via variation of the intensity and frequency of an external laser field is proposed. The frequency of an optical transition should be inside a PBG and located near or at a photonic band edge. In this case the laser field 'dresses' the quantum system (Mollow splitting) while the decay rates of the dressed states become very different due to a photonic band edge and depend on the form of spectral density of electromagnetic modes as well as intensity and frequency of the laser field. This enables us to control absorption and dispersion of a signal laser field, which is near resonant to the quantum transition of a dopant.