Open quantum system modeling of optically trapped nanoparticles

Abstract

In this thesis we develop an open quantum system model for a levitating particle trapped in an optical cavity by external optical tweezers. First we define optical forces and see how they can be used to trap particles in optical tweezers. We study Stokes and Anti-Stokes processes and show that blue detuned optical cavities can be used to cool trapped particles to their quantum ground states. We derive the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) master equation for a general open quantum system, and present its quantum state diffusion (QSD) unravelling into an ensemble of pure states. Then we derive the GKSL equation for our system, and use the QSD equations to find differential equations for parameters of an ansatz state. We find the time dependent norm for the pure states in the QSD ensemble and show how we can use it to calculate the expectation values for observables in our system.