Microscopic Theory of Polaron-Polariton Dispersion and Propagation

Abstract: We develop an analytical microscopic theory to describe the polaron-polariton dispersion, formed by hybridizing excitons, photons, and phonons, and their coherent dynamics inside optical cavities. Starting from a microscopic light-matter Hamiltonian, we derive a simple analytical model by pursuing a non-perturbative treatment of the phonon and photon couplings to excitons. Within our theoretical framework, the phonons are treated as classical fields that are then quantized via the Floquet formalism. We show that, to a good approximation, the entire polaron-polariton system can be described using a band picture despite the phonons breaking translational symmetry. Our theory also sheds light on the long-lived coherent ballistic motion of exciton-polaritons with high excitonic character that propagate with group velocities lower than is expected from pure exciton-polariton bands, offering a microscopic explanation for these puzzling experimental observations.

• The paper presents a novel analytical framework for polaron-polariton dispersion using a generalized Holstein-Tavis-Cummings Hamiltonian.
• It employs a mixed quantum-classical method with Floquet analysis to capture detailed phonon-exciton-photon couplings and decoherence effects.
• The model explains long-lived coherent propagation and phonon-induced band renormalization, providing insights for photonic and quantum device design.

Analytical Microscopic Theory of Polaron-Polariton Dispersion

This paper introduces a novel analytical framework aimed at elucidating the complex dynamics and dispersion of polaron-polaritons. The polaron-polariton results from the interaction and hybridization between excitons, photons, and phonons within optical cavities. The intricate nature of these hybrid quasi-particles and their behavior underlies numerous emerging phenomena and applications in quantum materials and photonics. The authors propose a non-perturbative approach, achieving a robust analytical model that integrates light-matter interactions and phonon influences in a theoretically consistent manner.

The core of this research is the development of a generalized multimode Holstein-Tavis-Cummings Hamiltonian. The model encapsulates interactions beyond the standard long-wavelength approximation, accommodating detailed phonon-exciton-photon couplings. This Hamiltonian is treated within a mixed quantum-classical paradigm, with phonons conceptualized as classical fields undergoing quantization through the Floquet formalism. The analytical model resulting from this treatment advances our understanding of how phonons disrupt translational symmetry in excitonic systems, contributing to decoherence phenomena traditionally encountered.

The theoretical insights provided hold significant implications. By employing a variational treatment and Floquet analysis, the model affords a quasi-band structure that approximates polaron-polariton dispersions with high precision. This modeling not only mirrors experimental results in terms of polariton spectra but also elucidates phenomena such as phonon-induced band renormalization and vibronic spectral splitting.

Particularly noteworthy is the model's explanation of long-lived coherent ballistic motion observed in exciton-polaritons possessing high excitonic character. The presence of vibronic structures introduced by phonon interactions results in renormalized group velocities lower than those predicted by exciton-polariton band slopes. This outcome is critical for designing photonic and optoelectronic devices, as it provides foundational insights into controlling excitonic transport properties.

Furthermore, the paper explores the implications of these findings for enhanced light-matter interaction under cavity confinement. By demonstrating the quasi-decoupling of reciprocal space subspaces in the presence of coherent phonon fields, the work suggests mechanisms by which optical cavities may suppress decoherence, promoting sustained coherent propagation of polaritons. Such insights could be transformative for advancing quantum information processing capabilities and optimizing material platforms for coherent light transport.

In a broader perspective, this research opens avenues for further exploration into microcavity systems and their quantum dynamics. Future investigations might extend these theoretical frameworks to more complex material geometries or integrate additional quantum field interactions. Altogether, the study substantially contributes to the theoretical armature required for progressing photonic and material sciences, impacting how researchers might engineer quantum systems exhibiting controlled light-matter interaction characteristics in practical settings. The analytical techniques and results presented offer a scaffold for subsequent experimental validation and model refinement, potentially inciting further breakthroughs in the manipulation and understanding of polaritonic systems.