Effects of Local Fields on Spontaneous Emission in Dielectric Media

Abstract

The local-field renormalization of the spontaneous emission rate in a dielectric is explicitly obtained from a fully microscopic quantum-electrodynamical, many-body derivation of Langevin-Bloch operator equations for two-level atoms embedded in an absorptive and dispersive, linear dielectric host. We find that the dielectric local-field enhancement of the spontaneous emission rate is smaller than indicated by previous studies.In the formative period of nonlinear optics, Bloembergen taught us that the nonlinear optical effects of a dilute collection of atoms that are embedded in a dielectric host are enhanced by local-field effects [1]. Now, in the era of quantum optics, researchers are again looking at the interaction of dielectric materials, the radiation field, and resonant atoms. Central to these investigations are efforts to quantize the electromagnetic field in dielectrics. One widely used technique is to quantize the macroscopic Maxwell equations in which the classical constitutive relations have been assumed [2][3][4][5][6][7]. In the microscopic approach, a generalized Hopfield transformation, based on Fano diagonalization, is used to obtain the coupled polariton modes of the coupled field-oscillator system [8][9][10]. These quantization methods are well-established for dielectrics with negligible absorption and techniques to deal with the special requirements of quantizing the electromagnetic field in absorbing dielectrics are beginning to emerge [5][6][7]9,10].Since Purcell first predicted the alteration of the emission rate of an excited atom due to an optical cavity [11], it has become well known that the observed spontaneous emission rate of an atom depends on its environment. When the quantized coupled field-dielectric theories are applied to the spontaneous emission of a two-level atom embedded in an absorptionless dielectric, the relationis obtained [3,4,7,8,10]. Here, n is the linear index of refraction and ℓ is the dielectric local-field enhancement factor, Γ 0 is the vacuum spontaneous emission rate, and Γ diel SE is the enhanced spontaneous emission rate in the dielectric. Both the Lorentz virtual-cavity model ℓ = (n 2 + 2)/3 and the Onsanger real-cavity model ℓ = 3n 2 /(2n 2 + 1) have been utilized in various studies of local-field effects on spontaneous emission.One of the key features of these approaches of applying the quantization of fields in dielectrics to spontaneous emission is that the oscillators that comprise the dielectric host are assumed to be unaffected by the presence of the embedded atom. The dielectric medium, as well as the field, is treated as a local condition at the site of a resonant atom such that the atom interacts with an all-pervasive, nonlocal, quantized effective field, the vacuum polariton modes, rather than the local vacuum radiation field modes and the oscillators. Because the near-dipole-dipole interaction is the fundamental interaction underlying the Lorentz local field, a many-body approach that explicitly deals with the vacuum radiation field modes and the...

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“…In the absence of local field enhancement (L=1), the enhancement factor from the dielectric effect is n. There are many local field models: for the real-cavity model, L=(3n 2 )/(2n 2 +2) [46]; virtual cavity, L=(n 2 +2)/3 [44,47]; and the Crenshaw model, L=((n 2 +2)/3n) 1/2 [48]. Experimental studies in the index range of 1.3-1.7 have shown agreement with the real cavity model.…”