Microscopic approach to the quantized light-matter interaction in semiconductor nanostructures: Complex coupled dynamics of excitons, biexcitons, and photons

We present a microscopic and fully quantized model to investigate the interaction between semiconductor nanostructures and quantum light fields including the many-body Coloumb interaction between photoexcited electrons and holes. Our approach describes the coupled dynamics of the quantum light field and single and double electron-hole pairs, i.e., excitons and biexcitons, and exactly accounts for Coulomb many-body correlations and carrier band dispersions. Using a simplified yet exact approach, we study a one-dimensional two-band system interacting with a single-mode, two-photon quantum state within a Tavis$\unicode{x2013}$Cummings framework. By employing an exact coherent factorization scheme, the computational complexity is reduced significantly enabling numerical simulations. We also derive a simplified model which includes only the bound $1s$-exciton and biexciton states for comparison. Our simulations reveal distinct single- and two-photon Rabi oscillations, corresponding to photon-exciton and exciton-biexciton transitions. We demonstrate, in particular, that biexciton continuum states significantly modify the dynamics in a way that cannot be captured by simplified models which consider only bound states. Our findings emphasize the importance of a comprehensive microscopic modeling in order to accurately describe quantum optical phenomena of interacting electronic many-body systems.

💡 Research Summary

The authors develop a fully quantum‑mechanical microscopic model for the interaction of a semiconductor nanostructure with a single‑mode quantum light field. The electronic system is represented by a one‑dimensional two‑band tight‑binding model with spin‑degenerate valence and conduction bands. The Hamiltonian consists of three parts: (i) the free electron‑hole and photon energies, (ii) a Tavis‑Cummings light‑matter coupling that creates or annihilates an electron‑hole pair together with a photon, and (iii) the full Coulomb interaction among electrons and holes, described by a regularized 1/r potential. The light‑matter matrix element Mₑₕ(k) is taken to be momentum‑independent and incorporates the polarization selection rules.

The system is initialized in a two‑photon Fock state while the electronic subsystem is in its vacuum (no excitons). By applying the Heisenberg equation of motion to all operators, the authors identify a closed set of 15 expectation values that can become non‑zero for this initial condition. Direct integration of the resulting hierarchy would scale as O(K⁸) with the number of k‑points, which is computationally prohibitive.

To overcome this, an exact coherent factorization scheme is introduced. All relevant expectation values are expressed in terms of three “coherences”: (1) L = ⟨b†b†⟩₍coh₎, the two‑photon coherence, (2) Xₑₕ(k) = ⟨b†α†ₑ,kβ†ₕ,−k⟩₍coh₎, the photon‑exciton coherence, and (3) Bₑₕ′ₑ′ₕ(k₁,k₂,k₃), the biexciton coherence that depends on three momenta because of momentum conservation. This reduces the computational scaling to O(K³). The resulting equations of motion are:

iħ∂ₜL = −2ħω_c L + 2∑_{k,e,h}Mₑₕ(k) Xₑₕ(k)
iħ∂ₜXₑₕ(k) =