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 review our recent quantum stochastic model for spectroscopic lineshapes in the presence of a coevolving and nonstationary background population of excitations. Starting from a field theory description for interacting bosonic excitons, we derive a reduced model whereby optical excitons are coupled to an incoherent background via scattering as mediated by their screened Coulomb coupling. The Heisenberg equations of motion for the optical excitons are then driven by an auxiliary stochastic population variable, which we take to be the solution of an Ornstein–Uhlenbeck process. Here, we present an overview of the theoretical techniques we have developed as applied to predicting coherent nonlinear spectroscopic signals. We show how direct (Coulomb) and exchange coupling to the bath give rise to distinct spectral signatures and discuss mathematical limits on inverting spectral signatures to extract the background density of states. Expected final online publication date for the Annual Review of Physical Chemistry, Volume 74 is April 2023. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates. 

Spectral line shapes provide a window into the local environment coupled to a quantum transition in the condensed phase. In this paper, we build upon a stochastic model to account for non-stationary background processes produced by broad-band pulsed laser stimulation, as distinguished from those for stationary phonon bath. In particular, we consider the contribution of pair-fluctuations arising from the full bosonic many-body Hamiltonian within a mean-field approximation, treating the coupling to the system as a stochastic noise term. Using the Itô transformation, we consider two limiting cases for our model, which lead to a connection between the observed spectral fluctuations and the spectral density of the environment. In the first case, we consider a Brownian environment and show that this produces spectral dynamics that relax to form dressed excitonic states and recover an Anderson–Kubo-like form for the spectral correlations. In the second case, we assume that the spectrum is Anderson–Kubo like and invert to determine the corresponding background. Using the Jensen inequality, we obtain an upper limit for the spectral density for the background. The results presented here provide the technical tools for applying the stochastic model to a broad range of problems.