UC Berkeley

Feedback control allows a wide range of systems to be stabilized to out-of-equilibrium states. In quantum systems, feedback control takes two forms: incoherent control, in which projective measurements are made of the system state and the measurement results are used to inform changes to the system Hamiltonian, bringing the system towards its desired state; and coherent control, in which the system is allowed to interact coherently with an auxiliary quantum system, such that Hamiltonian dynamics coherently drive the system of interest into its desired state.

An ultracold atomic gas coupled to a high-finesse optical cavity offers a convenient testbed for both of these forms of quantum feedback. Light escaping from the cavity mode carries information about the state of the atomic sample; this information can be processed externally and used to inform changes to external magnetic fields, to trapping parameters, and to the amplitude or frequency of light used to pump the cavity, effecting changes to the system's Hamiltonian and driving the atoms towards a desired state. Meanwhile, the atomic sample continually exchanges information with the cavity field through coherent interactions; by treating the atomic sample as the system of interest and the light field as an auxiliary controller, a Hamiltonian can be engineered such that these coherent interactions drive the atomic sample towards a desired state without the need for any external control.

In this dissertation, I will re-introduce the elder of the two atom–cavity experiments currently active in the Stamper-Kurn group at Berkeley—dubbed the E3 apparatus—and will describe how it can be used to examine quantum feedback. I will discuss two instances of this, in particular: a coherent quantum feedback system, in which the energy of the collective atomic spin is autonomously stabilized to a set point conditioned on the detuning of the pump light from cavity resonance; and an incoherent feedback system, in which light escaping from the cavity offers a real-time measurement of the number of atoms present in the cavity during evaporative cooling, which is then used to stabilize to a desired atom number. Along the way, I will discuss other interesting findings that have been made along the way, as well as techniques that we've found particularly useful.