Reciprocal Asymptotically Decoupled Hamiltonian for Cavity Quantum Electrodynamics

We develop a new theoretical framework for describing light-matter interactions in cavity quantum electrodynamics (QED), optimized for efficient convergence at arbitrarily strong coupling strengths and is naturally applicable to low-dimensional materials. This new Hamiltonian is obtained by applying...

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Bibliographic Details
Published in:arXiv.org 2023-11
Main Authors: Taylor, Michael A D, Weight, Braden M, Pengfei Huo3
Format: Article
Language:English
Subjects:
Asymptotic properties
Convergence
Coupling
Dipoles
Mathematical analysis
Polaritons
Quantum electrodynamics
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Summary:We develop a new theoretical framework for describing light-matter interactions in cavity quantum electrodynamics (QED), optimized for efficient convergence at arbitrarily strong coupling strengths and is naturally applicable to low-dimensional materials. This new Hamiltonian is obtained by applying a unitary gauge transformation on the p\(\cdot\)A Hamiltonian, with a shift on both the matter coordinate and the photonic coordinate, then performing a phase rotation and transforming in the reciprocal space of the matter. By formulating the light-matter interaction in terms of an upper-bounded effective coupling parameter, this method allows one to easily converge eigenspectra calculations for any coupling strength, even far into the ultra-strong and deep-strong coupling regimes. We refer to this new approach as the Reciprocal Asymptotically Decoupled (RAD) Hamiltonian. The RAD Hamiltonian allows for a fast convergence of the polariton eigenspectrum with a much smaller matter and photon basis, compared to the commonly used p\(\cdot\)A or dipole gauge Hamiltonians. The RAD Hamiltonian also allows one to go beyond the commonly used long-wavelength approximation and accurately describes the spatial variations of the field inside the cavity, which ensures the conservation of momentum between light and matter.
ISSN:2331-8422