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Photonics North (PN)

Lasing inside microcavities without resorting to the concept of density of states: The effects of vacuum field fluctuations

Tracy Robertson, Serge Gauvin

Published Jun 1, 2017• 2 citations
Publisher

Abstract

It has long been established that inside microcavities the resulting electromagnetic (optical) confinement might lead to strong enhancement (Purcell effect) or inhibition (Kleppner effect) of spontaneous emission. In both cases, the formulation is based on the concept of density of optical modes. However, and without resorting to this concept, there is an alternative point of view entirely based on the modulation of the vacuum field fluctuations. Consequently, a different interpretation of lasing, which does not involve the concept of density of modes, is conceivable.

DOI
10.1109/pn.2017.8090588

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It has long been established that inside microcavities the resulting electromagnetic (optical) confinement might lead to strong enhancement (Purcell effect) or inhibition (Kleppner effect) of spontaneous emission. In both cases, the formulation is based on the concept of density of optical modes. However, and without resorting to this concept, there is an alternative point of view entirely based on the modulation of the vacuum field fluctuations. Consequently, a different interpretation of lasing, which does not involve the concept of density of modes, is conceivable.
In 1946 Purcell showed that the spontaneous emission rate of an atomic system could be enhanced by placing it in a conducting cavity. Later, Kleppner showed that spontaneous emission could also be inhibited if the vacuum modes coupled to the atom were excluded by a structure. Most recently, we experimentally have shown that a periodic dielectric structure could alter the spontaneous emission by Bragg scattering of vacuum fluctuations.1 The structure used was a colloidal crystal with a face-centered cubic structure whose (111) planes were separated by optical dimensions.
It is well known that spontaneous emission is not an intrinsic atomic property, but rather results from the coupling of the atom to the vacuum modes of the electromagnetic field. As such, it can be modified by tailoring the electromagnetic environment into which the atom can radiate. This was already realized by Purcell, who noted that the spontaneous emission rate can be enhanced if the atom placed inside a cavity is resonant with one of the cavity is resonant with one of the cavity modes, and by Kleppner, who discussed the opposite case of inhibited spontaneous emission. It has also been recognized that spontaneous emission need not be an irreversible process. Indeed, a system consisting of a single atom coupled to a single mode of the electromagnetic field undergoes a periodic exchange of excitation between the atom and the field. This periodic exchange remains dominant as long as the strength of the coupling between the atom and a cavity mode is itself dominant. 23 refs., 6 figs.
Spontaneous emission into micro- or nano-scale structures can be enhanced or inhibited by engineering the local density of optical states using closed quantum cavities. When electromagnetic fields are confined within small mode volumes of a high-Q symmetrical closed quantum cavity, the Purcell effect significantly accelerates the natural spontaneous emission. Due to the statistical nature of spontaneous emission, the emitted fields do not have a well-defined phase; consequently, the emission is incoherent and lacks directional control. The situation becomes more complicated in multi-mode cavities, as selecting a specific mode in a particular direction requires precise detuning between the emitter transition frequency and the cavity mode frequency to ensure strong coupling. In single-mode cavities, only the dominant mode can resonate, and only in a specific direction; thus, an appropriate transition frequency range can be easily determined. Such cavities allow for greater manipulation of the local electromagnetic density of states, facilitating effective control of the direction of spontaneous emission. This property is essential for creating efficient single-photon sources, photonic circuits, and on-chip quantum information.
Spontaneous and stimulated emission properties of electronic states depend intimately on the electromagnetic environment to which they are coupled. Microcavities are of great fundamental and practical interest largely thanks to their ability to influence these emission properties. In the weak coupling regime of cavity quantum electrodynamics, a microcavity can either enhance or inhibit spontaneous emission, while the strong coupling regime is characterized by reversible vacuum Rabi oscillations. Stimulated emission properties are also greatly influenced by the nature of the intracavity field.
The earliest studies on the subject of spontaneous emission from an excited atom via interaction with the vacuum modes of the radiation field go back to the early days of quantum mechanics. In view of the fundamental nature of the vacuum fluctuations, it was long thought that spontaneous emission could not be controlled. However, in 1946 Purcell noted that the spontaneous emission rate of the atom inside a resonant cavity can be substantially enhanced (or suppressed) over its free-space value. This is due to the dramatic change of the density of modes of the vacuum field in a cavity. The enhancement and suppression of spontaneous emission in resonant and off-resonant cavities were observed experimentally in the 1980s. It was also realized in the 1950s and 1960s that coherent driving fields can dramatically change the characteristics of the spontaneous emission. The Autler-Townes doublet and Mollow three-peak spectrum are the examples of such behavior. A dramatic narrowing of the spectral peaks were discovered in driven multilevel atomic systems in the early 1990s. The role of atomic coherence in quenching spontaneous emission fluctuations in the context of laser physics was studied in the 1980s, via the correlated spontaneous emission laser (CEL). In this case atomic coherence results in the correlation of two spontaneous emission noise events so that the spontaneous emission quantum noise is eliminated in the relative linewidth. Later, it was “discovered” that the spontaneous emission can be suppressed through quantum interference between decay channels. Properly stated, this was rediscovered since it was first discovered and explained by Lamb in the 1940s. If the dipoles of two transitions from one upper level to two lower levels are parallel, the spontaneous emission in an ordinary vacuum can be cancelled. In a nonuniform vacuum, e.g., a cavity, the quenching of spontaneous emission can be achieved, even for the orthogonal dipoles.
Abstract Inhibition and enhancement of spontaneous emission rate, first proposed by Purcell, is discussed in terms of altered density-of-modes in various types of solid-state cavities and the Purcell factor is derived for two-level atomic system. The conditions for observing Purcell factor and experimental findings in micropillars embedded with Quantum Dots (QD)s are discussed. The strong interaction between photons and matter in the form of QD excitons, dispersion relations for ground and excited states separated by Rabi splitting are discussed. Experimental photoluminescence spectra showing anticrossing of exciton lines and cavity lines by temperature and other tuning methods are used to illustrate the strong light-matter interaction. The Jayness–Cummins model based on second quantization is presented to point out Rabi oscillation, Purcell effect, and other novel features. Microcavity structures for observing cavity quantum electrodynamics effects are mentioned. Microcavity lasers predicting thresholdless operation for unity spontaneous emission coupling factors are discussed.