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arXiv:1911.08427 · ACS Photonics

Relevance of the Quadratic Diamagnetic and Self-Polarization Terms in Cavity Quantum Electrodynamics

Christian Schäfer, Michael Ruggenthaler, Vasil Rokaj, Ángel Rubio

Published Feb 26, 2020• 3 citations
arXivHTMLPDF

Abstract

Abstract Experiments at the interface of quantum optics and chemistry have revealed that strong coupling between light and matter can substantially modify the chemical and physical properties of molecules and solids. While the theoretical description of such situations is usually based on nonrelativistic quantum electrodynamics, which contains quadratic light–matter coupling terms, it is commonplace to disregard these terms and restrict the treatment to purely bilinear couplings. In this work, we clarify the physical origin and the substantial impact of the most common quadratic terms, the diamagnetic and self-polarization terms, and highlight why neglecting them can lead to rather unphysical results. Specifically, we demonstrate their relevance by showing that neglecting these terms leads to the loss of gauge invariance, basis set dependence, disintegration (loss of bound states) of any system in the basis set limit, unphysical radiation of the ground state, and an artificial dependence on the static dipole. Besides providing important guidance for modeling of strongly coupled light–matter systems, the presented results also indicate conditions under which those effects might become accessible.

DOI
10.1021/acsphotonics.9b01649

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Abstract Experiments at the interface of quantum optics and chemistry have revealed that strong coupling between light and matter can substantially modify the chemical and physical properties of molecules and solids. While the theoretical description of such situations is usually based on nonrelativistic quantum electrodynamics, which contains quadratic light–matter coupling terms, it is commonplace to disregard these terms and restrict the treatment to purely bilinear couplings. In this work, we clarify the physical origin and the substantial impact of the most common quadratic terms, the diamagnetic and self-polarization terms, and highlight why neglecting them can lead to rather unphysical results. Specifically, we demonstrate their relevance by showing that neglecting these terms leads to the loss of gauge invariance, basis set dependence, disintegration (loss of bound states) of any system in the basis set limit, unphysical radiation of the ground state, and an artificial dependence on the static dipole. Besides providing important guidance for modeling of strongly coupled light–matter systems, the presented results also indicate conditions under which those effects might become accessible.
Experiments at the interface of quantum optics and chemistry have revealed that strong coupling between light and matter can substantially modify the chemical and physical properties of molecules and solids. While the theoretical description of such situations is usually based on nonrelativistic quantum electrodynamics, which contains quadratic light-matter coupling terms, it is commonplace to disregard these terms and restrict the treatment to purely bilinear couplings. In this work, we clarify the physical origin and the substantial impact of the most common quadratic terms, the diamagnetic and self-polarization terms, and highlight why neglecting them can lead to rather unphysical results. Specifically, we demonstrate their relevance by showing that neglecting these terms leads to the loss of gauge invariance, basis set dependence, disintegration (loss of bound states) of any system in the basis set limit, unphysical radiation of the ground state, and an artificial dependence on the static dipole. Besides providing important guidance for modeling of strongly coupled light-matter systems, the presented results also indicate conditions under which those effects might become accessible.
Cavity Quantum Electrodynamics (Cavity-QED) offers a powerful framework for controlling light-matter interactions, yet first-principles approaches commonly assume ideal, lossless cavity fields. Here, we introduce a minimal extension to the Pauli-Fierz Hamiltonian that accounts for cavity dissipation through the experimentally accessible cavity quality factor Q. The electromagnetic field is described as a damped harmonic oscillator within the very weak damping approximation. In this framework, cavity losses only enter the light-matter interaction and dipole self-energy terms, without introducing additional photonic degrees of freedom. A time-dependent unitary transformation yields a real-valued Hermitian Hamiltonian that can be incorporated into existing ab-initio QED methods without additional computational cost or changes in scaling. We combined the approach to the QED-CCSD method and investigated the effects of cavity dissipation on the optical spectrum of a p-nitroaniline molecule under strong light-matter coupling. We found that, for realistic quality factors, cavity dissipation can reduce the Rabi splitting by more than 20% compared to the ideal-cavity limit, even though the system remains in the strong-coupling regime. Convergence towards the ideal-cavity limit then requires substantially higher quality factors than those needed to establish strong coupling. These results demonstrate that cavity dissipation can significantly affect polaritonic energetics and highlight the importance of incorporating experimentally realistic cavity losses into quantitative ab-initio Cavity-QED simulations to accurately guide experimental protocols.
Understanding physical properties of quantum emitters strongly interacting with quantized electromagnetic modes is one of the primary goals in the emergent field of waveguide quantum electrodynamics (QED). When the light-matter coupling strength is comparable to or even exceeds energies of elementary excitations, conventional approaches based on perturbative treatment of light-matter interactions, two-level description of matter excitations, and photon-number truncation are no longer sufficient. Here we study in and out of equilibrium properties of waveguide QED in such nonperturbative regimes on the basis of a comprehensive and rigorous theoretical approach using an asymptotic decoupling unitary transformation. We uncover several surprising features ranging from symmetry-protected many-body bound states in the continuum to strong renormalization of the effective mass and potential; the latter may explain recent experiments demonstrating cavity-induced changes in chemical reactivity as well as enhancements of ferromagnetism or superconductivity. To illustrate our general results with concrete examples, we use our formalism to study a model of coupled cavity arrays, which is relevant to experiments in superconducting qubits interacting with microwave resonators or atoms coupled to photonic crystals. We examine the relation between our results and delocalization-localization transition in the spin-boson model; notably, we point out that a reentrant transition can occur in the regimes where the coupling strength becomes the dominant energy scale. We also discuss applications of our results to other problems in different fields, including quantum optics, condensed matter physics, and quantum chemistry.
The field of Polaritonic Chemistry studies molecules strongly coupled to the light field of optical cavities. The resulting modification of the potential energy landscape has been demonstrated to enable control over the chemical and physical properties of materials and molecular ensembles. This thesis extends the Tavis–Cummings model to describe molecules under strong light–matter coupling, incorporating static dipole moments and dipole self-energy contributions derived from the Pauli–Fierz Hamiltonian. These additional terms are shown to be essential for reproducing cavity-modified molecular dynamics and spectra. Simulations on the nuclear wavefunction propagation of MgH+ molecules demonstrate the impact of these terms, while an effective two-level system model accurately captures the behavior of large ensembles. Beyond single excitations, the thesis also explores the higher excitation manifolds of the Tavis-Cummings model, which reveals that allowing for more than a single excitation makes the reaction of the involved polaritons entropically more favorable. Open-system simulations highlight how the coherence of the system's initial state governs decay pathways and enables long-lived energy storage. Finally, a multilevel vibrational model coupled to a two-mode cavity is introduced, where a Raman scheme enables selective mixing of vibrational states. The simulation results show that continuous pumping can drive molecules into specific vibrational states while suppressing electronic excitation, both for single molecules and small ensembles. Together, these results provide new theoretical insights into the mechanisms by which optical cavities reshape molecular energy landscapes. The results suggest approaches for controlling photonic, electronic, and vibrational dynamics in strongly coupled systems, contributing to the theoretical foundation of polariton chemistry.
Strong coupling of organic molecules to the vacuum field of a nanoscale cavity can be used to modify their chemical and physical properties. We extend the Tavis-Cummings model for molecular ensembles and show that the often neglected interaction terms arising from the static dipole moment and the dipole self-energy are essential for a correct description of the light-matter interaction in polaritonic chemistry. On the basis of a full quantum description, we simulate the excited-state dynamics and spectroscopy of MgH+ molecules resonantly coupled to an optical cavity. We show that the inclusion of static dipole moments and the dipole self-energy is necessary to obtain a consistent model. We construct an efficient two-level system approach that reproduces the main features of the real molecular system and may be used to simulate larger molecular ensembles.
Constructing models for cavity quantum materials requires a careful treatment of the light-matter coupling. In general, one must specify matrix elements constructed from the material wavefunctions, which are often unknown in a tight-binding framework. The Peierls substitution is frequently used to avoid introducing these additional parameters in the multi-center dipole (or Peierls) gauge, under the assumption that contributions from intraband and interband dipole moments can be neglected. We present the derivation of the Peierls gauge description, including these dipole moment terms, in the passive view of canonical transformations. We construct a toy model for a multi-band system with two sites, which we couple to a uniform field in the Coulomb, dipole, and Peierls gauges. We find that all polarization field terms are required to describe multi-band coupling in the Peierls gauge. The Peierls substitution can only be justified under restriction to a single band in one dimension, provided one also ignores self-polarization corrections arising from bands outside the retained subspace. However, these corrections are frequently non-negligible. More generally, the Coulomb, dipole, and Peierls gauges define distinct partitions of the composite system into the light and matter subsystems. We illustrate the implications of this subsystem relativity for observables such as the photon number and on the performance of orbital truncations in each gauge.