An official website of the United States government
Experimental demonstrations of modified chemical structure and reactivity under strong light–matter coupling have spurred theoretical and computational efforts to uncover underlying mechanisms. Ab initio cavity quantum electrodynamics (QED) combines quantum chemistry with cavity QED to investigate these phenomena in detail. Unitary transformations of ab initio cavity QED Hamiltonians have been used to make them more computationally tractable. We analyze one such transformation, the coherent state transformation, using perturbation theory. Applying perturbation theory up to third order for ground state energies and potential energy surfaces of several molecular systems under electronic strong coupling, we show that the coherent state transformation yields better agreement with exact ground state energies. We examine one specific case using perturbation theory up to ninth order and find that coherent state transformation performs better up to fifth order but converges more slowly to the exact ground state energy at higher orders. In addition, we apply perturbation theory up to second order for cavity mode states under bilinear coupling, elucidating how the coherent state transformation accelerates the convergence of the photonic subspace toward the complete basis limit and renders molecular ion energies origin invariant. These findings contribute valuable insights into computational advantages of the coherent state transformation in the context of ab initio cavity quantum electrodynamics methods.
more »
« less
Comparing parameterized and self-consistent approaches to ab initio cavity quantum electrodynamics for electronic strong coupling
Molecules under strong or ultra-strong light–matter coupling present an intriguing route to modify chemical structure, properties, and reactivity. A rigorous theoretical treatment of such systems requires handling matter and photon degrees of freedom on an equal quantum mechanical footing. In the regime of molecular electronic strong or ultra-strong coupling to one or a few molecules, it is desirable to treat the molecular electronic degrees of freedom using the tools of ab initio quantum chemistry, yielding an approach referred to as ab initio cavity quantum electrodynamics (ai-QED), where the photon degrees of freedom are treated at the level of cavity QED. We analyze two complementary approaches to ai-QED: (1) a parameterized ai-QED, a two-step approach where the matter degrees of freedom are computed using existing electronic structure theories, enabling the construction of rigorous ai-QED Hamiltonians in a basis of many-electron eigenstates, and (2) self-consistent ai-QED, a one-step approach where electronic structure methods are generalized to include coupling between electronic and photon degrees of freedom. Although these approaches are equivalent in their exact limits, we identify a disparity between the projection of the two-body dipole self-energy operator that appears in the parameterized approach and its exact counterpart in the self-consistent approach. We provide a theoretical argument that this disparity resolves only under the limit of a complete orbital basis and a complete many-electron basis for the projection. We present numerical results highlighting this disparity and its resolution in a particularly simple molecular system of helium hydride cation, where it is possible to approach these two complete basis limits simultaneously. In this same helium hydride system, we examine and compare the practical issue of the computational cost required to converge each approach toward the complete orbital and many-electron bases limit. Finally, we assess the aspect of photonic convergence for polar and charged species, finding comparable behavior between parameterized and self-consistent approaches.
more »
« less
- PAR ID:
- 10593778
- Publisher / Repository:
- American Institute of Physics
- Date Published:
- Journal Name:
- The Journal of Chemical Physics
- Volume:
- 161
- Issue:
- 17
- ISSN:
- 0021-9606
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Coupling molecules to a quantized radiation field inside an optical cavity has shown great promise in modifying chemical reactivity. It was recently proposed that strong light-matter interactions are able to differentiate endo/exo products of a Diels-Alder reaction at the transition state. Using the recently developed parameterized quantum electrodynamic \textit{ab initio} polariton chemistry approach along with time-dependent density functional theory, we theoretically confirm that the ground state selectivity of a Diels-Alder reaction can be fundamentally changed by strongly coupling to the cavity, generating preferential endo or exo isomers which are formed with equal probability for the same reaction outside the cavity. This provides an important and necessary benchmark with the high-level self-consistent QED coupled cluster approach. In addition, by computing the ground state difference density, we show that the cavity induces a redistribution of electron density from intramolecular $$\pi$$-bonding orbitals to intermolecular bonding orbitals, thus providing chemically relavent description of the cavity-induced changes to the ground state chemistry and thus changes to the molecular orbital theory inside the cavity. We extend this exploration to an arbitrary cavity polarization vector which leads to critical polarization angles that maximize the endo=/exo selectivity of the reaction. Finally, we decompose the energy contributions from the Hamiltonian and provide discussion relating to the dominent dipole self-energy effects on the ground state.more » « less
-
Cavity QED experiments are natural hosts for non-equilibrium phases of matter supported by photon-mediated interactions. In this work, we consider a cavity QED simulation of the BCS model of superfluidity, by studying regimes where the cavity photons act as dynamical degrees of freedom instead of mere mediators of the interaction via virtual processes. We find an enhancement of long time coherence following a quench whenever the cavity frequency is tuned into resonance with the atoms. We discuss how this is equivalent to enhancement of non-equilibrium superfluidity and highlight similarities to an analogous phenomena recently studied in solid state quantum optics. We also discuss the conditions for observing this enhanced resonant pairing in experiments by including the effect of photon losses and inhomogeneous coupling in our analysis.more » « less
-
We develop a microscopic diagrammatic theory for cavity-mediated photon scattering in a topological one-dimensional insulator described by the Su–Schrieffer–Heeger model. Within the velocity-gauge formulation, we derive the photon self-energy and vertex corrections arising from virtual electron–hole excitations coupled to a quantized cavity mode, and we evaluate the resulting polariton dispersion and two-photon correlation spectra. Our analysis shows that vacuum fluctuations of the cavity field induce a momentum-resolved self-energy that mixes conduction and valence bands through virtual photon exchange, producing interband hybridization and avoided crossings in the electronic dispersion. This “cavity dressing” is symmetry-dependent, vanishing at the Brillouin-zone edge where the dipole matrix element is zero, and its strength is controlled by the spatial coherence range ζ≈(lc/a)2 of virtual excitations. We further examine how the cavity modifies nonlinear optical observables, including the Kerr nonlinearity and biphoton spectral entanglement, and identify the regimes where these effects become sensitive to the underlying topological phase. The theoretical framework established here provides a unified description of light–matter coupling in topological and polaritonic systems, bridging solid-state cavity QED with the emerging field of cavity-modified quantum materials. Our results suggest that engineered photonic environments can coherently reshape the electronic landscape of topological insulators, offering new routes to control collective electronic and optical phenomena through vacuum-field fluctuations.more » « less
-
We present an ab initio method for computing vibro-polariton and phonon-polariton spectra of molecules and solids coupled to the photon modes of optical cavities. We demonstrate that if interactions of cavity photon modes with both nuclear and electronic degrees of freedom are treated on the level of the cavity Born–Oppenheimer approximation, spectra can be expressed in terms of the matter response to electric fields and nuclear displacements, which are readily available in standard density functional perturbation theory implementations. In this framework, results over a range of cavity parameters can be obtained without the need for additional electronic structure calculations, enabling efficient calculations on a wide range of parameters. Furthermore, this approach enables results to be more readily interpreted in terms of the more familiar cavity-independent molecular electric field response properties, such as polarizability and Born effective charges, which enter into the vibro-polariton calculation. Using corresponding electric field response properties of bulk insulating systems, we are also able to obtain the Γ point phonon-polariton spectra of two dimensional (2D) insulators. Results for a selection of cavity-coupled molecular and 2D crystal systems are presented to demonstrate the method.more » « less
