1. Mark Rodenberger, Nima Dinyari, and Xiaolu Cheng
Numerical Quantum Optics Term Project: Feedback cooling of a mechanical oscillator
Mark Rodenberger, Nima Dinyari, and Xiaolu Cheng

2. System

3. Stochastic Master Equation (SME)

4. Adiabatic Elimination

5. Reduced System Dynamics
The resulting SME for only the oscillating mirror looks like this:
It may be put into the form of a Schrödinger equation:

6. The scaled photocurrent from the homodyne measurement is given by:

7. Rescaling

8. After Rescaling
So after all of that rescaling we arrive at the following Schrödinger equation:

9. Values Used in Rescaling

10. Programming
Followed a similar procedure as Project two, Problem three:
Evolve system of motion for half a step using sderk.f90
Evolve system for the momentum part using the split operator
Finish evolving the system for the last half step with sderk.f90

11. Using Feedback to Cool
We use measurement record in a feedback loop to adjust the laser power to cool motion of mirror.
We adjust the power to critically damp the system.