Optimal control of laser cooling: A theory of purity<br/><br/>increasing transformations

Monday, March 2, 2009 - 11:10am - 11:40am
EE/CS 3-180
David Tannor (Weizmann Institute of Science)
The powerful techniques of Optimal Control Theory (OCT), used
in recent years to design laser pulse sequences to control
chemical bond breaking, are applied to the problem of laser
cooling in an open system. The result is a striking new
mechanism in which spontaneous emission builds coherences
between all the populated levels creating a pure state, only at
the end of the process transferring the amplitude to the lowest
energy state. This novel mechanism accelerates the cooling
process by exploiting the cooling induced by spontaneous
emission to all the ground electronic state levels, not just
the lowest level. The mechanism suggests the calibration of
cooling in terms of increasing purity of the system as measured
by the quantity Tr(rho2). An analytical theory of the cooling
mechanism is developed in terms of a two-stage interplay
between the control fields and the spontaneous emission. One
of the main results of the analytical theory is a differential
equation for the optimal cooling rate. The key components of
the theory – the definition of cooling as purity increase;
the invariance of purity to control fields; and the maximum
rate of approach to absolute zero – correspond to the zeroth,
second and third law of thermodynamics, providing a
thermodynamic framework for laser cooling. The formulation of
cooling in terms of the coherence measure Tr(rho2) has an
additional, interesting implication: that our results carry
over immediately to the problem of control of quantum
decoherence, suggesting both a new mechanism and fundamental
limitations on the control of that process.
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