Light-Matter Interactions Simulated at Microscopic Level Reveal New Quantum Control Possibilities

Researchers have long sought to understand the intricate interplay between light and matter at the nanoscale, and a new study details the coupled dynamics of cavity photons, excitons, and biexcitons using fully quantized microscopic simulations. Hendrik Rose, Stefan Schumacher, and Torsten Meier, all from the Institute for Photonic Quantum Systems (PhoQS) at Paderborn University, present compelling evidence that biexciton continuum states significantly influence these dynamics. Their work demonstrates a high sensitivity to both cavity mode frequency and the strength of light-matter coupling, offering crucial insights for the development of advanced quantum photonic devices and a deeper understanding of fundamental quantum phenomena.

Quantized light-matter interactions and biexciton dynamics in semiconductor nanocavities reveal novel quantum phenomena

Scientists have developed a fully quantized microscopic approach to simulate the interaction between light and excitations within semiconductor nanostructures. The work incorporates many-body Coulomb correlations, providing a highly accurate model of quantum dynamics. Simulations reveal that biexciton continuum states significantly influence this dynamic behaviour, demonstrating a strong sensitivity to both cavity mode frequency and the strength of light-matter coupling.

This detailed analysis moves beyond semiclassical approximations, capturing quantum features like fluctuations and entanglement previously inaccessible to simpler models. The research centres on a semiconductor nanostructure embedded within a single-mode optical cavity, modelled using a two-band tight-binding approach and quantized light field treatment.
A total Hamiltonian was formulated, encompassing single-particle energies, light-matter coupling, and many-body Coulomb interactions. By formulating the dynamics in the Heisenberg picture and employing a coherence-based reduction scheme, the researchers achieved a computationally efficient yet exact solution to the system’s equations of motion.

Initial conditions involved a two-photon Fock-state for the cavity mode and the electronic system in its ground state, simplifying the complexity of the calculations. Numerical simulations of the mean photon number revealed prominent shifts in resonance frequencies depending on the detuning between the cavity photon energy and the exciton energy.

Specifically, a weak absorption feature was observed at a detuning of approximately -1.9 meV, aligning with half the biexciton binding energy and confirming the excitation of a bound biexciton state. Notably, this spectral position remained consistent regardless of the light-matter coupling strength. Rabi oscillations were also identified at detunings below the exciton energy, a phenomenon not predicted by models limited to bound states, indicating a strong coupling to the continuum of unbound biexciton states.

Furthermore, a significant reduction in the mean photon number was observed at detunings of 5 meV and above, consistent with excitation into the continuum of unbound biexciton states. These findings highlight the necessity of detailed microscopic analysis for accurately modelling semiconductor nanostructures interacting with quantum light.

Future work will focus on extending the model to incorporate multi-mode fields and explore more complex photon statistics, potentially requiring novel truncation strategies for higher photon numbers. This research was supported by the Deutsche Forschungsgemeinschaft (DFG) through the Collaborative Research Center TRR 142/3, project number 231447078, subproject A02, and benefited from computing time on the Noctua 2 high-performance computer at the NHR Center Paderborn.

Theoretical framework and derivation of coupled equations of motion are presented

A two-band tight-binding model and a quantized single-mode optical cavity form the basis of this study’s theoretical framework for investigating light-matter interactions in semiconductor nanostructures. The total Hamiltonian, defined as H = HS + HLM + HC, describes the system’s dynamics, where HS represents single-particle electronic and photonic energies, HLM governs light-matter coupling converting photons into electron-hole pairs, and HC accounts for many-body Coulomb interactions.

Formulated in the Heisenberg picture, the work employs expectation values of normal-ordered operators as dynamical variables, deriving coupled equations of motion directly from the Hamiltonian. Initial conditions were set with the cavity mode in a two-photon Fock-state and the electronic system in its ground state, resulting in a hierarchy of coupled operator equations that naturally closes without requiring truncation.

A coherence-based reduction scheme was implemented to simplify these equations, focusing on two-photon, photon-exciton, and biexcitonic coherences to capture the system’s full dynamics and significantly reduce numerical effort. The time evolution of the mean photon number, ⟨b†b⟩, was calculated using the Heisenberg equation, d dt⟨b†b⟩= i ħ⟨[H, b†b]⟩, which links the photon dynamics to material and mixed material-photonic expectation values.

Numerical simulations were performed using parameters K = 60, U0 = 20 meV, Jc = 20 meV, Jv = 2 meV, and a0/d = 0.5, with light-matter coupling strengths of M0 = 1 meV and M0 = 1.5 meV. These parameters yield exciton and biexciton binding energies of Xb ≈20.06 meV and XXb ≈3.82 meV, respectively. The resulting simulations reveal a weak absorption feature at δ ≈−1.9 meV, corresponding to half the biexciton binding energy, providing evidence for bound biexciton excitation. Furthermore, the observed spectral shift and normal-mode splitting are attributed to strong coupling with the continuum of unbound biexciton states, a phenomenon not captured by models limited to bound states.

Biexciton excitation and continuum coupling evidenced by optical simulations reveal strong light-matter interaction

Simulations reveal a transient reduction of the mean photon number at a detuning of approximately -1.9 meV, aligning with half the biexciton binding energy and demonstrating excitation of a bound biexciton state. Parameters used in the simulations included K = 60, U0 = 20 meV, Jc = 20 meV, Jv = 2 meV, and a0/d = 0.5, with light-matter coupling values of M0 = 1 meV and M0 = 1.5 meV.

Binding energies calculated from these parameters are Xb ≈20.06 meV for the 1s exciton and XXb ≈3.82 meV for the biexciton. The research demonstrates that the spectral position of the weak absorption feature remains consistent regardless of the light-matter coupling strength, M0. Rabi oscillations are observed at detunings significantly below the exciton energy, a phenomenon not replicated by models limited to bound states, indicating a strong coupling to the continuum of unbound biexciton states.

A larger light-matter coupling, M0, correlates with a larger normal-mode splitting, as evidenced in the simulations. Furthermore, a strong reduction in the mean photon number is identified at and above a detuning of approximately 5 meV, consistent with excitation into the continuum of unbound biexciton states.

This behavior is not captured by simplified models incorporating only the 1s exciton and bound biexciton states, highlighting the necessity of a detailed microscopic analysis for accurate modelling. The work establishes that the observed resonance shifts and excitonic character of the Rabi oscillations necessitate a comprehensive approach beyond simplified models.

Biexciton continua define light-matter coupling dynamics in semiconductor nanostructures and reveal fundamental exciton interactions

Researchers have employed a fully quantized microscopic model to investigate the interaction between light and semiconductor nanostructures, revealing the significant influence of biexciton continuum states on the observed dynamics. Simulations demonstrate a strong sensitivity to both the frequency of the cavity mode and the strength of the light-matter coupling, evidenced by prominent shifts in resonance frequencies and Rabi oscillations predominantly of excitonic character.

The findings also indicate weak absorption of bound biexcitons within the system. This work establishes the importance of detailed microscopic analysis for accurately modelling semiconductor nanostructures interacting with quantum light, surpassing the capabilities of simplified models that only consider bound exciton and biexciton states.

The observed reduction in mean photon number, consistent with excitation into unbound biexciton states, highlights the necessity of incorporating these states for quantitative accuracy. These results contribute to a more nuanced understanding of light-matter interactions at the nanoscale, crucial for advancements in quantum photonics and related fields.