Analysis and characterisation of a closed-loop control system for laser cooling and trapping experiment

Abstract

This research is aimed at analysing the performance of a closed-loop feedback system of an external cavity diode laser (ECDL) for a laser (Doppler) cooling and atom trapping experiment. External cavity diode lasers (ECDL) are commonly used in laser cooling exper-iments involving rubidium atoms. The laser frequency is controlled by adjusting the cavity length and the diode current. Using feedback control method, the laser is locked to an appropriate rubidium transition using a saturation absorption spectroscopy (SAS) setup together with a proportional-integral-derivative (PID) controller. At the CPUT Quantum Physics research group, we have a laser cooling and atom trapping experimental setup. This setup is a combination of multiple optical, electrical and mechanical components. We first analyse this system experimentally using test signals. By passing in basic test input signals, we were able to measure the system by identifying and extracting certain properties such as the resonant frequency, the damping constant and transient response of the system. The re-sults generated from the experimental analysis further enabled us to estimate the transfer function of the external cavity diode laser (ECDL). We then analyse the feedback setup numerically using known parameters from the experiment, and estimated parameters from the experimental analysis. We do this by first getting the mathematical model of the laser and then solving the differential equation using Euler methods in Matlab. By numerically analysing this feedback system, we are able to understand its transient behaviour. We were also able to test the system for different test scenarios e.g. tests for various controller constants, system response to different disturbance types and so on. The similarities observed between the experimental and numerical analysis pro-vide a reliable framework for future improvements when developing the feedback system. Elements such as the integrator constants, disturbance magnitudes and so on can be evaluated using the developed numerical closed-loop system.