Stochastic exciton-scattering theory of optical lineshapes: Renormalized many-body contributions

The Journal of Chemical Physics, Volume 157, Issue 5, 2022

In this research, we explore how environmental fluctuations influence the optical properties of materials. Specifically, we focus on spectral lineshapes, which are graphical representations showing how a material absorbs or emits light across different wavelengths. Understanding these lineshapes is crucial, as they provide insights into the interactions between light and matter within various environments.​

To analyze these interactions, we employ Itô calculus, a mathematical framework designed to model systems affected by random fluctuations, commonly used in fields like financial mathematics. By applying Itô calculus, we develop a stochastic model to account for the non-stationary (changing over time) background processes that occur when materials are exposed to broad-band pulsed laser stimulation. This approach allows us to simulate and understand how these random environmental factors cause variations in the observed spectral lineshapes.​

Our findings bridge the gap between observed spectral fluctuations and the underlying environmental influences, offering a more comprehensive understanding of exciton dynamics—how excited states in a material behave. This enhanced comprehension is vital for interpreting complex spectral features in condensed matter systems, which has implications for developing advanced materials and technologies in fields such as optoelectronics and photonics.

The Optical Signatures of Stochastic Processes in Many-Body Exciton Scattering

Annual Review of Physical Chemistry, Volume 74, 2022

In this research, we developed a quantum stochastic model to investigate how dynamic, non-stationary background excitations influence optical spectra in condensed-phase systems. By deriving a reduced model from a field theory description of interacting bosonic excitons, we demonstrated that optical excitons are coupled to an incoherent background through scattering mediated by screened Coulomb interactions. To model the evolution of this background population, we employed the Ornstein-Uhlenbeck process, a stochastic technique that describes the velocity of a particle undergoing Brownian motion. Our findings provide a framework for predicting coherent nonlinear spectroscopic signals, enhancing the understanding of exciton dynamics in complex materials

​Correlated Noise Enhancement of Coherence and Fidelity in Coupled Qubits

Philosophical Magazine, Volume 104, Issue 13-14, 2024 (ArXiv)

We investigate the stochastic dynamics of open quantum systems under correlated environmental noise, modeling a quantum communication setup with two interacting qubits coupled to distinct, locally fluctuating environments. By incorporating varying degrees of statistical correlation between these environments, we show that such correlations have significant, and sometimes beneficial, effects on the fidelity and purity of entangled Bell states.

Using stochastic modeling, we find that anticorrelated longitudinal noise sharpens spectral features through fluctuation cancellation, aiding purity preservation in the Φ⁺ state. In contrast, positively correlated noise better sustains the fidelity of the Ψ⁺ state. These state-dependent behaviors have direct implications for quantum protocols like teleportation and dense coding.

Our findings challenge traditional noise models that assume independence across subsystems, demonstrating that ignoring noise correlations may misrepresent decoherence and error dynamics. Importantly, we suggest that engineering specific noise correlations could serve as a viable strategy for enhancing coherence and building more robust quantum technologies.

Stochastic Modeling of Interactions in Perovskites

Mathematical modeling of stochastic processes particularly thought Ito calculus has played a fundamental role in stock market finance. A similar mathematical problem is encountered in the interaction of excitations and molecules inside chemical and physical systems. These interactions are often stochastic in nature and they influence the line-shape of the spectral signature for the system of interest. Through stochastic modeling, important insights can be obtained into the spectral features generated by these processes. My current research is focused on using numerical and analytical methods to model the stochastic interaction between excitons, calculate their spectral response, and develop machine learning methods to identify stochastic processes in experimental outputs.

My presentation at Exciton/Photon Interactions for Quantum Systems 2021 can be found here.