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Spontaneous Emission in 2D Arbitrary Inhomogeneous Environment

PF Qiao, Wei Sha, Y Chen, Wallace C. H. Choy, Weng Cho Chew

Published Jan 1, 2011• 0 citations
OpenAlex

Abstract

Control of spontaneously emitted light lies at the heart of quantum optics. It is essential for diverse applications ranging from lasers, light-emitting diodes, solar cells, and quantum information. According to the quantum electrodynamics theory, the spontaneous emission (SE) of an atom can be a weak-coupling radiation process due to the vacuum fluctuations of electromagnetic field. A suitable modification of inhomogeneous environment is required so that the vacuum fluctuations controlling the SE can be manipulated. Inhibiting unwanted SE and boosting desired ones will promote the novel optoelectronic designs tailored to industrial standard. The local density of states (LDOS) counts the number of electromagnetic modes where photons can be emitted at the specific location of the emitter, and can be interpreted as the density of vacuum fluctuations. The inhibition or enhancement of SE boils down to how the LDOS of photons is controlled. In this work, the SE of the excited atoms in 2D arbitrary inhomogeneous environment has been systematically studied. The LDOS determines the radiation dynamics of a point source (for 3D) or a line source (for 2D). In particular, it also determines the SE rate, and the LDOS is represented by the electric dyadic Green’s function. The numerical solution of the electric Green’s tensor has been accurately obtained by the finite-difference frequency-domain method with the proper approximations of the monopole and dipole sources. The SE of the atoms in the photonic crystal and plasmonic metal plates has been comprehensively and comparatively investigated. For both systems, the SE strongly depends on their respective dispersion relations and could be modified or tuned by the finite-structure or finite-size effects. This work is important for the SE engineering and optimized design of optoelectronic devices.

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The spontaneous emission (SE) of the excited atoms in a two-dimensional (2D) arbitrary inhomogeneous environment has been systematically studied. The local density of states, which determines the radiation dynamics of a point source (for 3D) or a line source (for 2D), in particular, the SE rate, is represented by the electric dyadic Green's function. The numerical solution of the electric Green's tensor has been accurately obtained with the finite-difference frequency-domain method with the proper approximations of the monopole and dipole sources. The SE of atoms in photonic crystal and plasmonic metal plates has been comprehensively and comparatively investigated. For both the photonic crystal and plasmonic plates systems, the SEs depend on their respective dispersion relations and could be modified by the finite-structure or finite-size effects. This work is important for SE engineering and the optimized design of optoelectronic devices.

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Defining a quantum mechanical wavefunction for photons is one of the remaining open problems in quantum physics. Thus quantum states of light are usually treated within the realm of second quantization. Consequently, spontaneous emission (SE) in arbitrary photonic media is often described by Fock space Hamiltonians. Here, we present a real space formulation of the SE process that can capture the physics of the problem accurately under different coupling conditions. Starting from first principles, we map the unitary evolution of a dressed two-level quantum emitter onto the problem of electromagnetic radiation from a self-interacting complex harmonic oscillator. Our formalism naturally leads to an efficient computational scheme of SE dynamics using finite difference time domain method without the need for calculating the photonic eigenmodes of the surrounding environment. In contrast to earlier investigations, our computational framework provides a unified numerical treatment for both weak and strong coupling regimes alike. We illustrate the versatility of our scheme by considering several different examples.

Journal of Optics•Nov 5, 2015•2 citations
Control of spontaneously emitted light lies at the heart of quantum optics. It is essential for diverse applications ranging from lasers, light-emitting diodes, solar cells, and quantum information. According to the quantum electrodynamics theory, the spontaneous emission (SE) of an atom can be a weak-coupling radiation process due to the vacuum fluctuations of electromagnetic field. A suitable modification of inhomogeneous environment is required so that the vacuum fluctuations controlling the SE can be manipulated. Inhibiting unwanted SE and boosting desired ones will promote the novel optoelectronic designs tailored to industrial standard. The local density of states (LDOS) counts the number of electromagnetic modes where photons can be emitted at the specific location of the emitter, and can be interpreted as the density of vacuum fluctuations. The inhibition or enhancement of SE boils down to how the LDOS of photons is controlled. In this work, the SE of the excited atoms in 2D arbitrary inhomogeneous environment has been systematically studied. The LDOS determines the radiation dynamics of a point source (for 3D) or a line source (for 2D). In particular, it also determines the SE rate, and the LDOS is represented by the electric dyadic Green’s function. The numerical solution of the electric Green’s tensor has been accurately obtained by the finite-difference frequency-domain method with the proper approximations of the monopole and dipole sources. The SE of the atoms in the photonic crystal and plasmonic metal plates has been comprehensively and comparatively investigated. For both systems, the SE strongly depends on their respective dispersion relations and could be modified or tuned by the finite-structure or finite-size effects. This work is important for the SE engineering and optimized design of optoelectronic devices.
The spontaneous emission (SE) of the excited atoms in a two-dimensional (2D) arbitrary inhomogeneous environment has been systematically studied. The local density of states, which determines the radiation dynamics of a point source (for 3D) or a line source (for 2D), in particular, the SE rate, is represented by the electric dyadic Green's function. The numerical solution of the electric Green's tensor has been accurately obtained with the finite-difference frequency-domain method with the proper approximations of the monopole and dipole sources. The SE of atoms in photonic crystal and plasmonic metal plates has been comprehensively and comparatively investigated. For both the photonic crystal and plasmonic plates systems, the SEs depend on their respective dispersion relations and could be modified by the finite-structure or finite-size effects. This work is important for SE engineering and the optimized design of optoelectronic devices.
In certain three-dimensional crystals, a frequency range exist for all polarizations for which light is not allowed to propagate in any direction, called the 3D photonic band gap: a frequency range where the density of vacuum fluctuations vanishes in an ideal infinitely large and perfect system. The complete absence of vacuum fluctuations can be interpreted as zero density of states and vice versa. It is well known that the characteristics of spontaneous emission of light depend strongly on the environment of the light source. According to quantum electrodynamics, the emission rate of a two-level quantum emitter as described by Fermi’s “golden rule”, is factorized into one part describing the emitter’s properties and a second part describing the effect of the environment on the light field via the local density of optical state (LDOS). The radiative decay rate of the emitters is proportional to the LDOS. The absence of vacuum fluctuations or the zero LDOS leads to complete inhibition of the spontaneous emission. While many great advances towards a band gap have been made, no complete inhibition has ever been observed to date. In this thesis, for the first time, we have studied the spontaneous emission of PbS quantum dots inside real 3D photonic band gap crystal as a function of frequency throughout the band gap. In our experiments we have observed an inhibited emission of 18x in the band gap. The time-resolved decay curves show evidence for intriguing finite-size effects whereby vacuum fluctuations tunnel into the band gap. Unfortunately, most theories assume crystals of infinite extent, where the inhibition in the band gap is also infinite, as vacuum fluctuations don’t exist inside the crystal. Here we propose an original model to calculate the LDOS in the band gap of a finite photonic crystal based on tunneling of the vacuum fluctuations into the crystal. We validate our model for the one-dimensional situation with a direct comparison to the analytic calculations which exist for one-dimensional photonic crystals. For three dimensional crystals, the theory shows an excellent match to the experiment.
In applications like quantum cryptography and quantum computation, it is desirable to obtain single photon sources which can produce a train of single photons on demand at a high repetition rate, especially at or near room temperature. Such single-photon sources can be realized by tailoring the photonic environment of the quantum emitter. The photonic environment determines the local density of states, into which the photon can be emitted. A number of structures such as interfaces, cavities and waveguides have already been used to modify the spontaneous emission (SE) rate; nevertheless there is still room for improving the overall efficiency of the single-photon sources, e.g., by inventing new ways of enhancing light-matter interaction.
Matter coupled to light can emit photons. In the absence of an external field this process is known as spontaneous emission. The radiation properties depends in detail the nature of the emitter. In this thesis we consider a two level point-source emitter, and examine how the emission is affected by engineering the local environment. We begin by studying analytically how embedding an emitter in a multi-layer cylindrical structure with radius much smaller than the emission wavelength alters the intensity of the emitted light. We find that for carefully chosen metal-dielectric interfaces, the emission can be strongly enhanced by the plasmonic effect. With this intuition, we experimentally study an InGaN semiconductor quantum dot-in-wire structure as our two level emitter, and manipulate the local field environment by coupling to a lossy plasmonic cavity. We find that the strong enhancement of the field around the quantum dot due to the metal more than compensates for the non-radiative losses, leading to order-of-magnitude increases in the radiative spontaneous emission rate, as well as overall brightness. We then examine how the emission of light can be affected by other nearby emitters. The cooperative effects are strongly dependent on the dimension of the system which controls the electromagnetic mode overlap of the emitters. We present a unified formalism capturing how these cooperative effects change from one dimension to the next. Cooperative light scattering between emitters underpins collective effects such as super- and sub-radiance, and we numerically investigate how our previous results give rise to the key experimental signatures that can be used to identify those phenomena. Specifically, we study how the superadiant decay rate scales with the size of a 222-dimensional atomic cloud, and how cooperative effects between a small number of emitters alter the emission spectrum of strongly driven resonance fluorescence.
Impressive progress has been achieved in controlling the spontaneous emission rate for emitters in Nanophotonic structures, such as microcavities, photonic crystals and nano-antennas. In all cases, however, the modification of the emission is stationary in time. Thus, the emission rate is time-independent and the distribution of photon emission times are stochastic and follow an exponential distribution in the weak coupling regime. In this paper, by using fast all-optical switching of a microcavity, the cavity resonance is tuned within tens of picosesonds. This drastically changes the local optical density of states at the emission frequency within the emission lifetime of the emitters. This paper theoretically studied an ensemble of two-level sources with a time dependent decay rate and have derived the excited state population and emitted intensity as a function of time for continuous wave and pulsed excitation. Deterministic bursts of dramatically enhanced or inhibited emission intensity within short intervals. Thereby, we control the photon distribution to show behavior that strongly deviates from single exponential decay. This can be used to protect quantum information systems against decoherence and to realize non-Markovian dynamics in cavity quantum electrodynamics.
Defining a quantum mechanical wavefunction for photons is one of the remaining open problems in quantum physics. Thus quantum states of light are usually treated within the realm of second quantization. Consequently, spontaneous emission (SE) in arbitrary photonic media is often described by Fock space Hamiltonians. Here, we present a real space formulation of the SE process that can capture the physics of the problem accurately under different coupling conditions. Starting from first principles, we map the unitary evolution of a dressed two-level quantum emitter onto the problem of electromagnetic radiation from a self-interacting complex harmonic oscillator. Our formalism naturally leads to an efficient computational scheme of SE dynamics using finite difference time domain method without the need for calculating the photonic eigenmodes of the surrounding environment. In contrast to earlier investigations, our computational framework provides a unified numerical treatment for both weak and strong coupling regimes alike. We illustrate the versatility of our scheme by considering several different examples.