Optica Talk 1 (2026) - The Fokker-Planck and Langevin Equations in Cavity Quantum Electrodynamics

OPTICA student chapter seminar Speaker: Adnan Alabbar, Department of Physics and Astronomy, Texas A&M University Title: The Fokker-Planck Equation and the Langevin Equation in Cavity QED Date: Thursday, September 3rd (11:30 am) Abstract: The Fokker-Planck Equation (FPE) and the Langevin Equation (LE) are two of the most widely used tools in nonequilibrium statistical mechanics. They simplify stochastic partial differential equations that are often daunting to tackle analytically. These approximations give strong results even if many elements of the system are ignored. The general equations will be presented, along with historical background. Then, two applications will be presented. First, the FPE is applied to a problem on spontaneous emission. The master equation can be solved via Laplace transform methods. The solutions are ‘ugly,’ however, and not always amenable to manipulation. The FPE reduces them to simpler integrals with remarkable accurate results. Next, the LE is used to account for vacuum fluctuations in a cavity interacting with two-level atoms. Adiabatic elimination of the cavity mode yields an effective master equation for the atoms that can be solved with the methods mentioned above. These two approaches allow us to treat open quantum systems in a simplified manner without compromising on accuracy. About the Speaker: Adnan Alabbar is a Ph.D. student in the Department of Physics and Astronomy at Texas A&M University studying quantum optics under Girish Agarwal. He earned his B.Sc. in Physics and Mathematics from Kuwait University, worked as a research assistant in nuclear astrophysics with M. M. Sharma, and earned his M.S. in Optics from the University of Rochester under Govind Agrawal, focusing on optical solitons. Before coming to College Station, he was a Research Associate at the Kuwait Institute for Scientific Research in the Environmental and Life Sciences Research Center.