  We apply quantum filtering and control to a particle in a harmonic trap under
continuous position measurement, and show that a simple static feedback law can
be used to cool the system. The final steady state is Gaussian and dependent on
the feedback strength and coupling between the system and probe. In the limit
of weak coupling this final state becomes the ground state. An earlier model by
Haine et. al. (PRA 69, 2004) without measurement back-action showed dark
states: states that did not display error signals, thus remaining unaffected by
the control. This paper shows that for a realistic measurement process this is
not true, which indicates that a Bose-Einstein condensate may be driven towards
the ground state from any arbitrary initial state.
