page_title: Semiconductor luminescence equations
section_title: Interpretation and consequences
hierarchical_section_title: Semiconductor luminescence equations / Interpretation and consequences
caption_attribution_description: English: Build-up of photon-assisted polarization (Π correlation) that is initiated by the spontaneous-emission source.
context_page_description: The semiconductor luminescence equations describe luminescence of semiconductors resulting from spontaneous recombination of electronic excitations, producing a flux of spontaneously emitted light. This description established the first step toward semiconductor quantum optics because the SLEs simultaneously includes the quantized light–matter interaction and the Coulomb-interaction coupling among electronic excitations within a semiconductor. The SLEs are one of the most accurate methods to describe light emission in semiconductors and they are suited for a systematic modeling of semiconductor emission ranging from excitonic luminescence to lasers.
  Due to randomness of the vacuum-field fluctuations, semiconductor luminescence is incoherent whereas the extensions of the SLEs include the possibility to study resonance fluorescence resulting from optical pumping with coherent laser light. At this level, one is often interested to control and access higher-order photon-correlation effects, distinct many-body states, as well as light–semiconductor entanglement.
context_section_description: Microscopically, the luminescence processes are initiated whenever the semiconductor is excited because at least the electron and hole distributions, that enter the spontaneous-emission source, are nonvanishing. As a result,  is finite and it drives the photon-assisted processes for all those  values that correspond to the excited  states. This means that  is simultaneously generated for many  values. Since the Coulomb interaction couples  with all  values, the characteristic transition energy follows from the exciton energy, not the bare kinetic energy of an electron–hole pair. More mathematically, the homogeneous part of the  dynamics has eigenenergies that are defined by the generalized Wannier equation not the free-carrier energies. For low electron–hole densities, the Wannier equation produces a set of bound eigenstates which define the exciton resonances.
  Therefore,  shows a discrete set of exciton resonances regardless which many-body state initiated the emission through the spontaneous-emission source. These resonances are directly transferred to excitonic peaks in the luminescence itself. This yields an unexpected consequence; the excitonic resonance can equally well originate from an electron–hole plasma or the presence of excitons. At first, this consequence of SLEs seems counterintuitive because in few-particle picture an unbound electron–hole pair cannot recombine and release energy corresponding to the exciton resonance because that energy is well below the energy an unbound electron–hole pair possesses.
  However, the excitonic plasma luminescence is a genuine many-body effect where plasma emits collectively to the exciton resonance. Namely, when a high number of electronic states participate in the emission of a single photon, one can always distribute the energy of initial many-body state between the one photon at exciton energy and remaining many-body state (with one electron–hole pair removed) without violating the energy conservation. The Coulomb interaction mediates such energy rearrangements very efficiently. A thorough analysis of energy and many-body state rearrangement is given in Ref.
  In general, excitonic plasma luminescence explains many nonequilibrium emission properties observed in present-day semiconductor luminescence experiments. In fact, the dominance of excitonic plasma luminescence has been measured in both quantum-well and quantum-dot systems. Only when excitons are present abundantly, the role of excitonic plasma luminescence can be ignored.
caption: Buildup of photon-assisted polarization (Π correlation) that is initiated by the spontaneous-emission source. The buildup occurs equally for all momentum states. In a many-body system, a photon (wave arrow) is generated collectively through multiple coupled Π-transition correlations.
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