ConspectusThe notion that light and matter states can be hybridized the way s and p orbitals are mixed is a concept that is not familiar to most chemists and material scientists. Yet it has much potential for molecular and material sciences that is just beginning to be explored. For instance, it has already been demonstrated that the rate and yield of chemical reactions can be modified and that the conductivity of organic semiconductors and nonradiative energy transfer can be enhanced through the hybridization of electronic transitions. The hybridization is not limited to electronic transitions; it can be applied for instance to vibrational transitions to selectively perturb a given bond, opening new possibilities to change the chemical reactivity landscape and to use it as a tool in (bio)molecular science and spectroscopy. Such results are not only the consequence of the new eigenstates and energies generated by the hybridization. The hybrid light–matter states also have unusual properties: they can be d...

Hybrid Light-Matter States in a Molecular and Material Science Perspective.

Light–matter coupling with strength comparable to the bare transition frequencies of the system is called ultrastrong. This Review surveys how experiments have realized ultrastrong coupling in the past decade, the new phenomena predicted in this regime and the applications it enables. Ultrastrong coupling between light and matter has, in the past decade, transitioned from a theoretical idea to an experimental reality. It is a new regime of quantum light–matter interaction, which goes beyond weak and strong coupling to make the coupling strength comparable to the transition frequencies in the system. The achievement of weak and strong coupling has led to increased control of quantum systems and to applications such as lasers, quantum sensing, and quantum information processing. Here we review the theory of quantum systems with ultrastrong coupling, discussing entangled ground states with virtual excitations, new avenues for nonlinear optics, and connections to several important physical models. We also overview the multitude of experimental setups, including superconducting circuits, organic molecules, semiconductor polaritons, and optomechanical systems, that have now achieved ultrastrong coupling. We conclude by discussing the many potential applications that these achievements enable in physics and chemistry.

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Ultrastrong coupling between light and matter

In this work, we provide an overview of how well-established concepts in the fields of quantum chemistry and material sciences have to be adapted when the quantum nature of light becomes important in correlated matter–photon problems. We analyze model systems in optical cavities, where the matter–photon interaction is considered from the weak- to the strong-coupling limit and for individual photon modes as well as for the multimode case. We identify fundamental changes in Born–Oppenheimer surfaces, spectroscopic quantities, conical intersections, and efficiency for quantum control. We conclude by applying our recently developed quantum-electrodynamical density-functional theory to spontaneous emission and show how a straightforward approximation accurately describes the correlated electron–photon dynamics. This work paves the way to describe matter–photon interactions from first principles and addresses the emergence of new states of matter in chemistry and material science.

https://www.pnas.org/content/pnas/114/12/3026.full.pdf

Atoms and molecules in cavities, from weak to strong coupling in quantum-electrodynamics (QED) chemistry

Molecular polaritons are the optical excitations which emerge when molecular transitions interact strongly with confined electromagnetic fields. Increasing interest in the hybrid molecular-photonic materials that host these excitations stems from recent observations of their novel and tunable chemistry. Some of the remarkable functionalities exhibited by polaritons include the ability to induce long-range excitation energy transfer, enhance charge conductivity, and inhibit or accelerate chemical reactions. In this review, we explain the effective theories of molecular polaritons which form a basis for the interpretation and guidance of experiments at the strong coupling limit. The theoretical discussion is illustrated with the analysis of innovative applications of strongly coupled molecular-photonic systems to chemical phenomena of fundamental importance to future technologies.

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Polariton chemistry: controlling molecular dynamics with optical cavities

We present an overview of the general concepts of polaritonic chemistry with organic molecules, i.e., the manipulation of chemical structure that can be achieved through strong coupling between confined light modes and organic molecules. Strong coupling and the associated formation of polaritons, hybrid light–matter excitations, lead to energy shifts in such systems that can amount to a large fraction of the uncoupled transition energy. This has recently been shown to significantly alter the chemical structure of the coupled molecules, which opens the possibility to manipulate and control reactions. We discuss the current state of theory for describing these changes and present several applications, with a particular focus on the collective effects observed when many molecules are involved in strong coupling.

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Polaritonic Chemistry with Organic Molecules

In this work, we give a comprehensive derivation of an exact and numerically feasible method to perform ab initio calculations of quantum particles interacting with a quantized electromagnetic field. We present a hierarchy of density-functional-type theories that describe the interaction of charged particles with photons and introduce the appropriate Kohn-Sham schemes. We show how the evolution of a system described by quantum electrodynamics in Coulomb gauge is uniquely determined by its initial state and two reduced quantities. These two fundamental observables, the polarization of the Dirac field and the vector potential of the photon field, can be calculated by solving two coupled, nonlinear evolution equations without the need to explicitly determine the (numerically infeasible) many-body wave function of the coupled quantum system. To find reliable approximations to the implicit functionals, we present the appropriate Kohn-Sham construction. In the nonrelativistic limit, this density-functional-type theory of quantum electrodynamics reduces to the densityfunctional reformulation of the Pauli-Fierz Hamiltonian, which is based on the current density of the electrons and the vector potential of the photonfield. By making further approximations, e.g., restricting the allowed modes of the photon field, we derive further density-functional-type theories of coupled matter-photon systems for the corresponding approximate Hamiltonians. In the limit of only two sites and one mode we deduce the appropriate effective theory for the two-site Hubbard model coupled to one photonic mode. This model system is used to illustrate the basic ideas of a density-functional reformulation in great detail and we present the exact Kohn-Sham potentials for our coupled matter-photon model system.

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Quantum electrodynamical density-functional theory: Bridging quantum optics and electronic-structure theory

We propose an orbital exchange-correlation functional for applying time-dependent density functional theory to many-electron systems coupled to cavity photons. The time nonlocal equation for the electron-photon optimized effective potential (OEP) is derived. In the static limit our OEP energy functional reduces to the Lamb shift of the ground state energy. We test the new approximation in the Rabi model. It is shown that the OEP (i) reproduces quantitatively the exact ground-state energy from the weak to the deep strong coupling regime and (ii) accurately captures the dynamics entering the ultrastrong coupling regime. The present formalism opens the path to a first-principles description of correlated electron-photon systems, bridging the gap between electronic structure methods and quantum optics for real material applications.

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Optimized Effective Potential for Quantum Electrodynamical Time-Dependent Density Functional Theory

Abstract We present a scanning tunneling microscopy (STM) and ab-initio study of the anisotropic superconductivity of 2H-NbSe 2 in the charge-density-wave (CDW) phase. Differential-conductance spectra show a clear double-peak structure, which is well reproduced by density functional theory simulations enabling full k - and real-space resolution of the superconducting gap. The hollow-centered (HC) and chalcogen-centered (CC) CDW patterns observed in the experiment are mapped onto separate van der Waals layers with different electronic properties. We identify the CC layer as the high-gap region responsible for the main STM peak. Remarkably, this region belongs to the same Fermi surface sheet that is broken by the CDW gap opening. Simulations reveal a highly anisotropic distribution of the superconducting gap within single Fermi sheets, setting aside the proposed scenario of a two-gap superconductivity. Our results point to a spatially localized competition between superconductivity and CDW involving the HC regions of the crystal. 

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Real-space anisotropy of the superconducting gap in the charge-density wave material 2H-NbSe2

We present an ab initio time-dependent density functional theory study of the ultrafast demagnetization of elemental ferromagnets subject to terahertz (THz) laser pumping compared to optical laser pumping. We find that THz radiation can cause as much demagnetization as optical radiation for significantly lower-energy transfer to the sample. We show that the demagnetization efficiency of the THz pulse is related to a coherent coupling of the radiation to the electron charge dynamics. In fact, our simulations reveal that the low-frequency THz electric field enforces in-phase electron charge oscillations around the atomic centers, leading to a highly efficient spin-orbit torque switching of the magnetization. Unlike for optical pumping, at the end of the pulse a major fraction of the excited electrons is driven back to equilibrium acquiring a thermalized Fermi-Dirac distribution. 

Ab initio
 study of ultrafast demagnetization of elementary ferromagnets by terahertz versus optical pulses

We present a minimal approach to include static Coulomb interactions in Eliashberg theory of superconductivity from first principles. The method can be easily implemented in any existing Eliashberg code (isotropic or anisotropic) to avoid the standard use of the semiempirical parameter μ∗ , which adds unnecessary uncertainty to T c predictions. We evaluate the prediction accuracy of the method by simulating the superconducting properties of a set of layered superconductors, which feature unconventional Coulomb effects: CaC6, MgB2, Li-doped β-ZrNCl and YNi2B2C. We find that the estimated critical temperatures are consistent with those from ab-initio density functional theory for superconductors, and in close agreement with the experimental values.

Camilla Pellegrini

Papers

Quantum electrodynamical density-functional theory: Bridging quantum optics and electronic-structure theory

Optimized Effective Potential for Quantum Electrodynamical Time-Dependent Density Functional Theory

Real-space anisotropy of the superconducting gap in the charge-density wave material 2H-NbSe2

Ab initio study of ultrafast demagnetization of elementary ferromagnets by terahertz versus optical pulses

Eliashberg theory with ab-initio Coulomb interactions: a minimal numerical scheme applied to layered superconductors