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Physical Review B

Resonance fluorescence of semiconductor quantum dots: Signatures of the electron-phonon interaction

Kwang Jun Ahn, Jens Förstner, A. Knorr

Published Apr 22, 2005• 58 citations
Publisher

Abstract

Using a fully quantized description of strongly confined electrons interacting with acoustic phonons and the photon field, the nonstationary resonance-fluorescence spectra of a semiconductor quantum dot are investigated. For excitation pulses with durations approaching typical electron-phonon scattering times, the virtual quantum processes yield an observable electron-phonon sideband broadening.

DOI
10.1103/physrevb.71.153309

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•Jan 1, 2010•1 citation
Using a fully quantized description of strongly confined electrons interacting with acoustic phonons and the photon field, the nonstationary resonance-fluorescence spectra of a semiconductor quantum dot are investigated. For excitation pulses with durations approaching typical electron-phonon scattering times, the virtual quantum processes yield an observable electron-phonon sideband broadening.
A model of semiconductor quantum dots coupled to phonons and laser light, which is relevant in the limit of strong electronic confinement, is investigated. For an arbitrary sequence of excitations by ultrafast pulses, analytical solutions are obtained for all pertinent density-matrix elements. The results are nonperturbative with respect to the coupling to both phonons and laser light. The derivation depends neither on a particular choice of electronic wave functions nor on a particular wave-vector dependence of the phonon interaction or phonon dispersion. All components of the density matrix exhibit oscillatory dependences on the pulse areas of the exciting pulses analogously to the Rabi oscillations known from simple two-level systems. Three typical applications of the general results are worked out: (a) the influence of phonons on four-wave-mixing spectra, (b) the coherent control of electronic dot occupations in the presence of phonons, and (c) the dynamics of phonon correlations including the formation of a stable polaron spatially localized in the dot and the emission of a pulsed phonon wave packet that leaves the dot.
We study the resonance fluorescence spectra of a driven quantum dot placed inside a high-Q semiconductor cavity and interacting with an acoustic phonon bath. The dynamics is calculated using a time-convolutionless master equation in the polaron frame. We predict pronounced spectral broadening of the Mollow sidebands through off-resonant cavity emission which, for small cavity-coupling rates, increases quadratically with the Rabi frequency in direct agreement with recent experiments using semiconductor micropillars [S. M. Ulrich et al., preceding Letter, Phys. Rev. Lett. 106, 247402 (2011)]. We also demonstrate that, surprisingly, phonon coupling actually helps resolve signatures of the elusive second rungs of the Jaynes-Cummings ladder states via off-resonant cavity feeding. Both multiphonon and multiphoton effects are shown to play a qualitatively important role on the fluorescence spectra.
Introduction Quantum optics provides a complete description of the resonant interaction of light and a material system. The light scattered as a result of this interaction – the resonance fluorescence – provides a means to monitor and affect the material system's dynamics and also allows for the generation of nonclassical states of the electromagnetic field. Initial theoretical studies characterizing resonance fluorescence addressed fundamental questions regarding the necessity of quantizing the electromagnetic field. This is a particularly illustrative period in optical physics where multiple theories existed that might describe resonance fluorescence – semi-classical optical Bloch equations [1, 2] or quantum electrodynamics [4, 3] – and experimental evidence was necessary to identify the appropriate theoretical framework. Indeed, experiments in 1974 and 1977 investigating the resonance fluorescence lineshape [5, 6] and the photon statistics of the scattered light [7] vindicated the full quantum electrodynamical description of light-matter interaction over other models. In the subsequent 30 years, resonance fluorescence has been used as a high-resolution spectroscopic probe of a variety of physical systems, as a means to investigate quantum coherence in atomic gases and, with the current interest in quantum information science (QIS), as a tool for quantum-state preparation, measurement and control in trapped ions [8]. During this same time period, advances in material science have ushered in an era where it is possible to grow and fabricate solid-state devices at length scales commensurate with the quantum confinement of electrons and holes. It is only recently that resonance fluorescence has been observed from the prototypical artificial nanostructure exhibiting three-dimensional quantum confinement – a single semiconductor quantum dot (QD) [9].
We present a microscopic description of the photon statistics and phonon signatures in the quantum light emission from semiconductor quantum dots. Using higher-order Born approximation, time-resolved optical emission and scattering spectra are calculated in the weak coupling regime. In the strong coupling regime, a mathematical induction method is presented to calculate the longitudinal optical (LO) phonon-assisted quantum dot cavity-QED. The phonon interaction at room temperature has a strong impact on the quantum correlation of the cavity field and enhances the non-classicality of the cavity field, initially prepared in a thermal state.
The work presented in this dissertation contains the first observation of spin-resolved resonance fluorescence from a single quantum dot and its application of direct measurement of electron spin dynamics. The Mollow triplet and the Mollow quintuplet, which are the hallmarks of resonance fluorescence, are presented as the non-spin-resolved and spin-resolved resonance fluorescence spectrum, respectively. The negligible laser background contribution, the near pure radiative broadened spectrum and the anti-bunching photon statistics imply the sideband photons are background-free and near transform-limited single photons. This demonstration is a promising step towards the heralded single photon generation and electron spin readout. Instead of resolving spectrum, an alternative spin-readout scheme by counting resonance fluorescence photons under moderate laser power is demonstrated. The measurements of n-shot time-resolved resonance fluorescence readout are carried out to reveal electron spin dynamics of the measurement induced back action and the spin relaxation. Hyperfine interaction and heavy- light hole mixing are identified as the relevant mechanisms for the back action and phonon-assistant spin-orbit interaction dominates the spin relaxation. After a detailed discussion on charge-spin configurations in coupled quantum dots system, the single-shot readout on electron spin are proposed.