Abstract
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.
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GENERAL SCIENTIFIC SUMMARY Introduction and background. Feedback control has been investigated in detail within the framework of classical systems and it is a widely used technique, but there are several interesting possibilities in applying feedback control to quantum systems as well. A general problem in this respect, however, is that the state of a quantum system is typically described in a very high-dimensional space and it may be demanding to calculate the required feedback in real time.
Main results. We present a general technique to obtain an approximate low-dimensional model of the dynamics of a quantum system which allows fast estimation of the current state of the system. We apply the method to a single atom in an optical cavity and demonstrate that it is possible to control the system dynamics by using the approximate model to compute the required feedback.
Wider implications. The positive results for the investigated system and the generality of the method suggests that it may be used to control other quantum systems as well. The modelling procedure contains several degrees of freedom and a further line of research could be to find systematic methods to optimize the tradeoff between accuracy and simplicity of the low-dimensional models.