Microscopic simulations of the coupled dynamics of cavity photons, excitons, and biexcitons

The coherent interaction between quantum light and material excitations in semiconductor nanostructures is investigated using a fully quantized microscopic approach that incorporates many-body Coulomb correlations. The simulations demonstrate that the quantum dynamics is influenced by biexciton continuum states and is highly sensitive to both the frequency of the cavity mode and the strength of the light-matter coupling.

💡 Research Summary

The authors present a fully quantized microscopic study of the interaction between a semiconductor nanostructure and a single‑mode optical microcavity when the cavity field is prepared in a two‑photon Fock state. The electronic system is modeled with a two‑band tight‑binding Hamiltonian, while the cavity mode is described by bosonic creation and annihilation operators. The total Hamiltonian consists of three parts: (i) the non‑interacting electron, hole, and photon energies (HS), (ii) the light‑matter coupling term (HLM) that converts photons into electron‑hole pairs and vice‑versa with a coupling strength M0, and (iii) the Coulomb interaction term (HC) that accounts for many‑body correlations among photo‑excited carriers.

Because a two‑photon Fock state can generate at most two electron‑hole pairs, the hierarchy of Heisenberg equations of motion naturally closes without any artificial truncation. The authors therefore obtain a finite set of coupled differential equations for the expectation values of photon number ⟨b†b⟩, photon‑exciton coherences, and biexciton coherences. A coherence‑based reduction scheme further reduces the computational load by retaining only the relevant two‑photon, photon‑exciton, and biexciton coherences.

Numerical simulations are performed for realistic parameters: exciton binding energy Xb≈20.06 meV, biexciton binding energy XXb≈3.82 meV, and a light‑matter coupling M0 of 1 meV and 1.5 meV. The cavity‑exciton detuning δ = Ec − EX is varied to explore the system’s response. The main findings are:

1. Biexciton absorption resonance – A weak dip in the photon number appears at δ≈−1.9 meV, which corresponds to half the biexciton binding energy (−XXb/2). This feature is independent of M0 and signals the resonant excitation of a bound biexciton by the two‑photon field.

2. Rabi oscillations and normal‑mode splitting – Contrary to expectations, no significant absorption occurs when the cavity is resonant with the 1s exciton (δ = 0). Instead, pronounced Rabi‑type oscillations emerge at detunings well below the exciton energy. The oscillations retain an excitonic character, but their frequency and the associated normal‑mode splitting increase with M0. The authors attribute this shift to a strong effective coupling to the continuum of unbound biexciton states, an effect absent in models that include only bound states.

3. Continuum‑induced photon loss – At positive detunings around δ≈+5 meV a pronounced reduction of ⟨b†b⟩ is observed, consistent with excitation into the unbound biexciton continuum. This behavior cannot be reproduced by few‑level models that neglect the continuum.

Overall, the study demonstrates that (i) a fully quantized treatment of the two‑photon field naturally yields a closed set of equations, (ii) the biexciton continuum plays a decisive role in shaping the spectral response and normal‑mode splitting, and (iii) simplified models that retain only bound exciton and biexciton states miss essential physics such as the continuum‑induced resonance shift and weak biexciton absorption.

The authors conclude that accurate modeling of semiconductor nanostructures interacting with quantum light requires a microscopic approach that treats many‑body Coulomb correlations and the quantized field on equal footing. They suggest future extensions to multimode cavities, photon statistics beyond two photons, and the development of new truncation strategies to handle higher photon numbers.