The use of quantum light to probe exciton properties in semiconductor and molecular nanostructures typically occurs in the low-intensity regime. A substantial enhancement of exciton-photon coupling can be achieved with photonic cavities, where excitons hybridize with cavity modes to form polariton states. To provide a theoretical framework for interpreting emerging experimental efforts in this direction, we develop a scattering theory describing the interaction of frequency-entangled photon pairs with cavity polariton and bipolariton states under various coupling regimes. Employing the Tavis-Cummings model in combination with our scattering approach, we present a quantitative analysis of how the interaction of the entangled photon pair with the polariton or bipolariton modifies its joint spectral amplitude (JSA). Specifically, we examine the effects of the cavity-mode steady-state population, exciton-cavity coupling strength, and different forms of the input photon JSA. Our results show that the entanglement entropy of the scattered photons is highly sensitive to the interplay between the input JSA and the spectral line shapes of the polariton resonances, emphasizing the cavity filtering effects. We suggest that biphoton-scattering quantum light spectroscopy best serves as a sensitive probe of polariton and bipolariton states in the photon-vacuum cavity state. Our approach is not only robust to various regimes of cavity-exciton coupling, but also amenable to extensions beyond the Tavis-Cummings model, enabling the representation of a broad class of molecular systems and solid state quantum materials.

Multiparticle correlations of exciton polaritons and reservoir excitons in the strong light-matter coupling regime dictate the quantum dynamics of optical microcavities. In this work, we examine the many-body exciton-polariton dynamics in a Fabry-P & eacute;rot microcavity of a two-dimensional metal-halide semiconductor over timescales involving polariton (<<1 ps) and exciton (>>1 ps) scattering. We find enhanced exciton nonlinear dynamics in the microcavity versus the bare semiconductor, concomitant with ultrafast polariton scattering dynamics. We measure, by means of coherent spectroscopy, the coupling between exciton polaritons, bright excitons, and reservoir excitons that highlight the complex scattering landscape that fundamentally drives polariton condensation.

We present a concise review and perspective on noise-induced synchronisation and coherence protection in open quantum systems, with emphasis on recent work involving coupled spins, oscillators, and anyons. When local environments exhibit internal correlations, the structure of the noise determines which collective modes become decoherence-protected. This leads to steady-state entanglement, phase locking, and exceptional points (EPs) in the Liouvillian spectrum, signalling a collapse of the mode basis and the emergence of non-dissipative stabilised dynamics. Using a Lindblad framework, we show that symmetry in the noise correlations acts as a control parameter-protecting symmetric or antisymmetric modes depending on the sign of the correlation. In the pure-dephasing limit, coherence decay mirrors the Anderson-Kubo model, where the effective fluctuation strength scales as $\sigma <^>2\lpar 1 \pm \xi \rpar$sigma 2(1 +/-xi), and the dynamical regime (Gaussian vs. Lorentzian) is set by the ratio $\sigma / \gamma$sigma/gamma. Thus, the environment not only drives decoherence but can also selectively suppress it through symmetry filtering. We also revisit historical and conceptual origins of this idea, beginning with Huygens' synchronised pendulum clocks and culminating in modern non-Hermitian dynamics. Correlated noise-though classically stochastic-can organise quantum dynamics and protect coherence without direct control over the system. These insights offer a unifying view of synchronisation in classical and quantum regimes, with implications for quantum sensing, engineered decoherence, and long-lived coherence in complex environments such as biological light-harvesting complexes or avian magnetoreception.

We develop a stochastic framework for anyonic systems in which the exchange phase is promoted from a fixed parameter to a fluctuating quantity. Starting from the Stratonovich stochastic Liouville equation, we perform the Stratonovich-Itô conversion to obtain a Lindblad master equation that ties the dissipator directly to the distorted anyon algebra. This construction produces a statistics-dependent dephasing channel, with rates determined by the eigenstructure of the real-symmetric correlation matrix Ξ. The eigenvectors of Ξ select which collective exchange currents-equivalently, which irreducible representations of the system-are protected from stochastic dephasing, providing a natural mechanism for decoherence-free subspaces and noise-induced exceptional points. The key result of our analysis is the universality of the optimal statistical angle: in the minimal two-site model with balanced gain and loss, the protected mode always minimizes its dephasing at θ⋆=π/2, independent of the specific form of Ξ. This robustness highlights a simple design rule for optimizing coherence in noisy anyonic systems, with direct implications for ultracold atomic realizations and other emerging platforms for fractional statistics.

We derive the Lindblad master equation that governs dissipative dynamics in anyon oscillators and extend the formalism to multiple coupled oscillator systems using symmetric and antisymmetric operators. We also formulate adjoint equations in the Heisenberg picture. By analyzing the eigenvalues and normal modes of the coupled system, we obtain the complete equations of motion for the creation and annihilation operators. A unitary transformation diagonalizes the two-anyon Hamiltonian and reveals anyon-modified normal modes. Our analysis demonstrates that tuning $\xi$ allows selective protection of normal modes from dissipation, with implications for topological quantum systems.

We develop a Lyapunov-based framework to model the evolution of entangled biphotons interacting with cavity and material modes. Using Gaussian-preserving dynamics and Møller operators, we map input joint spectral amplitudes to experimentally measurable joint spectral intensities. Our model reproduces key features of observed spectra and reveals off-diagonal correlations arising from cavity decay, providing a scalable and tractable tool for quantum spectroscopic analysis.

Quantum statistics dictate how particles exchange and correlate-but in two-dimensional systems, these rules extend beyond bosons and fermions to anyons, quasiparticles with continuously tunable exchange phases. Here, we develop a Lindblad framework for anyonic oscillators and show that fractional statistics enable statistical control of decoherence in open quantum systems. By varying the anyonic phase and environmental correlations, we demonstrate tunable mode protection, identify exceptional points in the dissipative spectrum, and reveal temperature-dependent coherence bifurcations. We also demonstrate that signatures of the statistical phase should also be manifest in 2D coherent spectroscopic probes of these systems. These results establish the exchange phase as a functional control parameter for engineering dissipation-resilient quantum states.

We develop a diagrammatic theory of cavity-mediated photon-photon interactions in a topological insulator using the SSH model. The fourth-order vertex Γ^(4)(ω_1,ω_2) governs spectral entanglement and Kerr nonlinearity, leading to a nonlinear topological phase diagram. We also compute the electronic self-energy from vacuum photon exchange and identify symmetry-imposed limits on band renormalization. These results link band geometry to the emergence of light-matter correlations.

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.

We present a velocity-gauge formalism for computing nonlinear current response functions in periodic systems and apply it to the Su-Schrieffer-Heeger (SSH) model as a minimal topological testbed. By retaining the full minimal coupling Hamiltonian and avoiding the rotating wave approximation, we construct gauge-consistent expressions for the linear and third-order current susceptibilities using retarded Green's functions. Our results reveal how nonlinear optical spectra encode not only energy-level transitions but also interband phase coherence and topological winding. In the topological phase, the third-order response exhibits characteristic phase inversions and spectral asymmetries that are absent in the trivial phase. These features reflect geometric changes in the Bloch eigenstates and highlight the role of virtual pathways in shaping the nonlinear signal. Our framework offers a robust and extensible platform for modeling nonlinear light-matter interactions in topological materials beyond the dipole approximation and the standard Coulomb-gauge formulation in molecular spectroscopy.

Recent advances in quantum light spectroscopy highlight the potential of using entangled photons as a sensitive probe for many-body dynamics and material correlations. However, a comprehensive theory to explain experimental results remains elusive, primarily due to the complexity of the Hilbert space and the intricate interactions and nonlinearities inherent in material systems. In this work, we introduce a tractable model based on a finite-sized correlation matrix governed by a bilinear bosonic Hamiltonian, enabling efficient simulations through Gaussian-preserving dynamics. We apply this framework to compute the output joint spectral intensity (JSI) and von Neumann entropy of frequency-entangled biphotons, and find close agreement with experimental observations in empty microcavities. Our results reveal the emergence of off-diagonal spectral correlations that can be interpreted as irreversible decay of cavity excitations into the biphoton continua. This approach offers a powerful theoretical tool for interpreting quantum spectroscopic data and paves the way for probing more complex light-matter interactions in materials.

We develop a theoretical framework for electron transfer (ET) at graphene defects, treating the surface as a Dirac cone with a localized defect state coupled to a vibrational environment. Using a polaron transformation combined with a modified density of states, we derive an explicit expression for the ET rate that incorporates both vibrational reorganization and fractionalized quasiparticle statistics. We show that fractional statistics, modeled through a power-law density of states, suppress low-energy ET near resonance and introduce tunable deviations from conventional Marcus-like kinetics. Our results suggest that strain, defect engineering, or chemical modification could stabilize fractional excitations in graphene-based catalysts, offering new strategies for controlling surface reactivity. These findings provide a foundation for future experimental and computational investigations into the role of topology and fractional statistics in chemical electron transfer.

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 propose a quantum analogue of the Huygens clock, where the phases of two spins synchronize through their interaction with a shared environment. This environment acts like the escapement mechanism in a mechanical clock, regulating the gear train and allowing discrete timing advances. In our model, the relative phases of the two spins synchronize via a mutually correlated environment. We demonstrate that several arguments can significantly reduce the cardinality of the allowed measurements for a system of qubits, thus simplifying the problem. We present a numerically efficient method to calculate the degree of quantumness in the correlations of the final density matrix, providing a tight upper bound for rank 3 and rank 4 density matrices. We suggest a potential realization of noise-induced synchronization between two nuclear spins coupled to a common ancilla undergoing dynamical decoupling.

We propose a quantum analogue of the Huygens clock, in which the phases of two spins achieve synchronization through their interaction with a shared environment. The environment functions analogously to the escapement mechanism in a mechanical clock, regulating the gear train and permitting the advancement of timing in discrete intervals. In our proposed model, the relative phase of the two spins become synchronized through interaction with a mutual, correlated, environment. We show that for a system of qubits, several arguments can be made that significantly reduce the cardinality of the set of allowed measurements and, hence, the complexity of the problem. We present a numerically efficient method to calculate the degree of quantumness that exists in the correlations of our final density matrix. This method also provides a tight upper bound for when the system is described by rank-3 and rank-4 density matrices.

In this, we announce a new section dedicated to research articles where quantum phenomena are either evident on a macroscopic scale or significantly influence the system's emergent properties. This can lead to unique optical or mechanical attributes originating solely from quantum mechanisms. In addition, we welcome submissions on quantum theory, methodologies, and algorithms, with a particular focus on light-matter interactions and quantum many-body theory.

It is generally assumed that environmental noise arising from thermal fluctuations is detrimental to preserving coherence and entanglement in a quantum system. In the simplest sense, dephasing and decoherence are tied to energy fluctuations driven by coupling between the system and the normal modes of the bath. Here, we explore the role of noise correlation in an open-loop model quantum communication system whereby the ``sender'' and the ``receiver'' are subject to local environments with various degrees of correlation or anticorrelation. We introduce correlation within the spectral density by solving a multidimensional stochastic differential equations and introduce these into the Redfield equations of motion for the system density matrix. We find that correlation can enhance both the fidelity and purity of a maximally entangled (Bell) state. Moreover, by comparing the evolution of different initial Bell states, we show that one can effectively probe the correlation between two local environments. These observations may be useful in the design of high-fidelity quantum gates and communication protocols.

Photophysical aggregates are ubiquitous in many solid-state microstructures adopted by conjugated polymers, in which π electrons interact with those in other polymer chains or those in other chromophores along the chain. These interactions fundamentally define the electronic and optical properties of the polymer film. While valuable insight can be gained from linear excitation and photoluminescence spectra, nonlinear coherent excitation spectral lineshapes provide intricate understanding on the electronic couplings that define the aggregate and their fluctuations. Here, we discuss the coherent two-dimensional excitation lineshape of a model hairy-rod conjugated polymer. At zero population waiting time, we find a π/2 phase shift between the 0-0 and 0-1 vibronic peaks in the real and imaginary components of the complex coherent spectrum, as well as a dynamic phase rotation with population waiting time over timescales that are longer than the optical dephasing time. We conjecture that these are markers of relaxation of the photophysical aggregate down the tight manifold of the exciton band. These results highlight the potential for coherent spectroscopy via analysis of the complex spectral lineshape to become a key tool to develop structure-property relationships in complex functional materials.

Coherent nonlinear spectroscopy offers us a window into the system-bath interactions in materials. Specifically, the spectral lineshapes can reveal the nature and dynamics of the environmental fluctuations surrounding the system of interest. Here we will discuss how stochastic non-equilibrium exciton dynamics manifest in the peculiar lineshapes and how they provide mechanistic insights into the nature of exciton-phonon and exciton-exciton interactions in nanostructured derivatives of metal halide perovskites. Despite the success of such classical optical probes in unveiling the many-body physics in materials, we will elaborate on the ambiguities still present in the resultant photophysical models that stem primarily due to the high excitation intensities used in the measurements. We will also discuss alternative experimental methodologies based on quantum entangled photons, which may offer superior signal to noise ratio and thus enabling the measurement of many-body interactions at close to single photon excitation densities.