We investigate the Polariton induced conical intersection (PICI) created from coupling a diatomic molecule with the quantized photon mode inside an optical cavity, and the corresponding Berry Phase effects. We use the rigorous Pauli–Fierz Hamiltonian to describe the quantum light-matter interactions between a LiF molecule and the cavity, and use the exact quantum propagation to investigate the polariton quantum dynamics. The molecular rotations relative to the cavity polarization direction play a role as the tuning mode of the PICI, resulting in an effective CI even within a diatomic molecule. To clearly demonstrate the dynamical effects of the Berry phase, we construct two additional models that have the same Born–Oppenheimer surface, but the effects of the geometric phase are removed. We find that when the initial wavefunction is placed in the lower polaritonic surface, the Berry phase causes a π phase-shift in the wavefunction after the encirclement around the CI, indicated from the nuclear probability distribution. On the other hand, when the initial wavefunction is placed in the upper polaritonic surface, the geometric phase significantly influences the couplings between polaritonic states and therefore, the population dynamics between them. These BP effects are further demonstrated through the photo-fragment angular distribution. PICI created from the quantized radiation field has the promise to open up new possibilities to modulate photochemical reactivities.
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Representation and conservation of angular momentum in the Born–Oppenheimer theory of polyatomic molecules
This paper concerns the representation of angular momentum operators in the Born–Oppenheimer theory of polyatomic molecules and the various forms of the associated conservation laws. Topics addressed include the question of whether these conservation laws are exactly equivalent or only to some order of the Born–Oppenheimer parameter κ = ( m/ M) 1/4 and what the correlation is between angular momentum quantum numbers in the various representations. These questions are addressed in both problems involving a single potential energy surface and those with multiple, strongly coupled surfaces and in both the electrostatic model and those for which fine structure and electron spin are important. The analysis leads to an examination of the transformation laws under rotations of the electronic Hamiltonian; of the basis states, both adiabatic and diabatic, along with their phase conventions; of the potential energy matrix; and of the derivative couplings. These transformation laws are placed in the geometrical context of the structures in the nuclear configuration space that are induced by rotations, which include the rotational orbits or fibers, the surfaces upon which the orientation of the molecule changes but not its shape, and the section, an initial value surface that cuts transversally through the fibers. Finally, it is suggested that the usual Born–Oppenheimer approximation can be replaced by a dressing transformation, that is, a sequence of unitary transformations that block-diagonalize the Hamiltonian. When the dressing transformation is carried out, we find that the angular momentum operator does not change. This is a part of a system of exact equivalences among various representations of angular momentum operators in Born–Oppenheimer theory. Our analysis accommodates large-amplitude motions and is not dependent on small-amplitude expansions about an equilibrium position. Our analysis applies to noncollinear configurations of a polyatomic molecule; this covers all but a subset of measure zero (the collinear configurations) in the nuclear configuration space.
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- Award ID(s):
- 2102402
- NSF-PAR ID:
- 10418876
- Date Published:
- Journal Name:
- The Journal of Chemical Physics
- Volume:
- 158
- Issue:
- 10
- ISSN:
- 0021-9606
- Page Range / eLocation ID:
- 104302
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1063/5.0143809
