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One quantum dot in a microcavity: nonlinear models

In this Chapter, we study, semi-analytically, light-matter coupling with nonlinearities. We fist solve the anharmonic oscillator (weakly interacting excitons), first alone, then coupled to a second harmonic oscillator (a cavity mode). Then we address the Jaynes-Cummings model (small quantum dot in a cavity). We analyze the properties of emission of all these descriptions in the presence of decoherence (dissipation and incoherent pump). Most of the results presented here have been published in the references 3, 7 and 12 from the list of my publications .^5.1

• Introduction
• The anharmonic oscillator
  • First order correlation function and power spectrum
    • SE analytical spectrum
    • Spectrum in the Steady State
  • Second order correlation function
  
  
• Linear model with excitonic interactions
  • Spectrum with the manifold method
  • Spectrum with the quantum regression formula
  
  
• The Jaynes-Cummings model
  • First order correlation function and power spectrum
  • Vanishing pump case in the manifold picture
  • Population and Statistics
  • Weights and Renormalization
  • Spectrum at Resonance
    • Point 1: very good systems and the incoherent Mollow triplet
    • Point 2: Good systems, the nonlinear doublet and role of cavity pumping
    • Point 3: decoherence and saturation
  • Spectrum with detuning
  
  
• Future work
  • Bubbles and line splittings
  
  
• Conclusions