Search for: All records

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. 

Understanding and controlling spin relaxation in molecular qubits is essential for developing chemically tunable quantum information platforms. We present a first-principles-parametrized analytical framework for evaluating spin relaxation dynamics in vanadyl phthalocyanine (VOPc) and its oxygenated derivative, VOPc(OH)8. By expanding the spin Hamiltonian in vibrational normal modes and computing both linear and quadratic spin–phonon coupling tensors via finite differences of the g-tensor, we construct a relaxation tensor that enters a Lindblad-type master equation, capturing both direct (one-phonon) and Raman (two-phonon) processes. A mode-resolved analysis reveals that relaxation is funneled through only a handful of low-frequency vibrations: in VOPc, three out-of-plane distortions of the phthalocyanine ring and V–O unit dominate, whereas in VOPc(OH)8, the additional oxygens shift these modes downward and suppress two of them, leaving a single strongly coupled mode as the main decoherence pathway. Both longitudinal (T1) and transverse (T2) relaxation are governed by this same set of vibrational modes, indicating that coherence loss is controlled by a common microscopic mechanism. This mode-selective picture offers a design strategy for engineering longer-lived molecular qubits. 

We consider the quantum dynamics of a pair of coupled quantum oscillators coupled to a common correlated dissipative environment. The resulting equations of motion for both the operator moments and covariances can be integrated analytically using the Lyapunov equations. We find that for fully correlated and fully anti-correlated environments, the oscillators relax into a phase-synchronized state that persists for long-times when the two oscillators are nearly resonant and (essentially) forever if the two oscillators are in resonance. We identify an exceptional point that indicates the onset of broken symmetry between an unsynchronized and synchronized dynamical phase of the system as correlations within the environment are increased. We also show that the environmental noise correlation leads to quantum entanglement, and all the correlations between the two oscillators are purely quantum mechanical in origin. This work provides a robust mathematical foundation for understanding how long-lived exciton coherences can be linked to vibronic correlation effects.