Quantum filter reduction for measurement-feedback control via unsupervised manifold learning
We derive simple models for the dynamics of a single atom coupled to a cavity field mode in the absorptive bistable parameter regime by projecting the time evolution of the state of the system onto a suitably chosen nonlinear low-dimensional manifold, which is found by use of local tangent space alignment. The output field from the cavity is detected with a homodyne detector allowing observation of quantum jumps of the system between states with different average numbers of photons in the cavity. We find that the models, which are significantly faster to integrate numerically than the full stochastic master equation, largely reproduce the dynamics of the system, and we demonstrate that they are sufficiently accurate to facilitate feedback control of the state of the system based on the predictions of the models alone.
Additional Information© 2009 Deutsche Physikalische Gesellschaft & Institute of Physics. Received 7 May 2009; published 30 October 2009. AEBN acknowledges financial support from the Danish Minister of Science, Technology and Innovation through an elite research scholarship. This work has been supported by the NSF under award CCF-0622246, and by DARPA-MTO under award W911NF-09-1-0045. Part of Focus on Quantum Control (http://www.iop.org/EJ/abstract/1367-2630/11/10/105030)
Published - Nielsen2009p6350New_J_Phys.pdf