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Coherent and incoherent light scattering in the resonance fluorescence of a single molecule

G. Wrigge

Published Jan 1, 2008• 4 citations
Publisher
DOI
10.3929/ethz-a-005708655

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The nature of resonance emission of light, which appears as a mixture of (coherent) resonance scattering and (incoherent) resonance fluorescence, is considered. The basic conceptual elements which distinguish the scattering and fluorescence components for the linear excitation limit are developed in terms of a simple formulation whereby a molecule interacts with a coherent Lorentzian light pulse which increases exponentially with time for t<0 and is turned off at t = 0. These results together with the ideas, currently existing in the literature, that stochastic modulation of a molecule by its medium is essential for the appearance of fluorescence provide the basis for the further formulation of a theory which does not require the ad hoc introduction of a random potential. The theory developed considers the microscopic origins of manifest stochastic modulation effects in terms of a bath potential for the molecule–medium (bath) degrees of freedom. This potential, termed the sudden potential, is associated with the change in interaction with the medium that a molecule experiences upon intramolecular state transitions which are induced by external interactions (e.g., by light). Development of the reduced molecule–field density operator leads naturally to a separation of terms which describes scattering and (the propensity for) fluorescence. Critical to the theory is a four-time correlation function for the bath (sudden) potential. The difficulties inherent in defining absorption (spectrum) resonances and the corresponding distinctions between resonance and relaxed emission are discussed. Implications are considered for the further understanding of experimental results on molecular excitation dynamics in the gas phase and in supersonic jets. Sources of stochastic modulation other than material media are mentioned. In particular, the possibility is suggested of the pervasive existence of stochastic modulation through interaction of a molecule with the vacuum state of the radiation field. This raises questions concerning the fundamental relations between quantum mechanics and thermodynamics.

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Squeezing in resonance fluorescence processes of a laser-pumped molecule possessing permanent dipoles is shown. A weak low-frequency coherent field pumps the sample near resonance with the dynamically Stark-splitting states induced by a second stronger laser field driving the main two-level transition. The fluorescence spectrum consists of three coherently scattered spectral lines and up to nine incoherently scattered spectral lines. Compared with a similar problem yet in the absence of permanent dipoles, aditional squeezing regions are found.
Resonance fluorescence from a two-level emitter is a standard route to single-photon generation, where the emitter produces only one photon at a time, and multiphoton emission or scattering is inherently suppressed. In this study, we challenge this paradigm in the weak-excitation limit, where coherent scattering dominates. Using a single quantum dot in a microcavity, we show that the incoherent component exhibits pronounced superbunching, revealing simultaneous multiphoton scattering from a single emitter. In contrast, the total reflected field—comprising the reflected driving field and incoherent scattering—displays perfect antibunching, arising from quantum interference that cancels two-photon probability amplitudes. By spectrally filtering the reflected field, we tune the relative contributions of coherent and incoherent components, observing transitions in photon statistics from antibunching to superbunching, or to Poissonian light. Supported by master-equation simulations and an interference-based model, these results uncover the hidden but fundamental role of multiphoton dynamics in resonance fluorescence, and open avenues for generating nonclassical light in cavity and waveguide quantum electrodynamics.
The nature of resonance emission of light, which appears as a mixture of (coherent) resonance scattering and (incoherent) resonance fluorescence, is considered. The basic conceptual elements which distinguish the scattering and fluorescence components for the linear excitation limit are developed in terms of a simple formulation whereby a molecule interacts with a coherent Lorentzian light pulse which increases exponentially with time for t<0 and is turned off at t = 0. These results together with the ideas, currently existing in the literature, that stochastic modulation of a molecule by its medium is essential for the appearance of fluorescence provide the basis for the further formulation of a theory which does not require the ad hoc introduction of a random potential. The theory developed considers the microscopic origins of manifest stochastic modulation effects in terms of a bath potential for the molecule–medium (bath) degrees of freedom. This potential, termed the sudden potential, is associated with the change in interaction with the medium that a molecule experiences upon intramolecular state transitions which are induced by external interactions (e.g., by light). Development of the reduced molecule–field density operator leads naturally to a separation of terms which describes scattering and (the propensity for) fluorescence. Critical to the theory is a four-time correlation function for the bath (sudden) potential. The difficulties inherent in defining absorption (spectrum) resonances and the corresponding distinctions between resonance and relaxed emission are discussed. Implications are considered for the further understanding of experimental results on molecular excitation dynamics in the gas phase and in supersonic jets. Sources of stochastic modulation other than material media are mentioned. In particular, the possibility is suggested of the pervasive existence of stochastic modulation through interaction of a molecule with the vacuum state of the radiation field. This raises questions concerning the fundamental relations between quantum mechanics and thermodynamics.