Coherent control

Coherent control is a quantum mechanical based method for controlling dynamical processes by light. The basic principle is to control quantum interference phenomena typically by shaping the phase of a laser pulses. The basic ideas have proliferated finding vast application in spectroscopy mass spectra, quantum information processing, laser cooling, ultracold physics and more.

The initial idea was to control the outcome of chemical reactions. Two approaches were pursued: In the time domain a pump dump scheme where the control is the time delay between pulses and in the frequency domain, interfering pathways controlled by one and three photons. The two basic methods eventually merged with the introduction of optimal control theory .

Experimental realisations soon followed. In the time domain and in the frequency domain. Two interlinked developments accelerated the field of coherent control: Experimentally it was the development of pulse shaping by a spatial light modulator and its employment in coherent control. The second development was the idea of automatic feedback control and its experimental realization .

Coherent control aims to steer a quantum system from an initial state to a target state via an external field. For given initial and final (target) states the coherent control is termed state-to-state control. A generalisation is steering simultaneously an arbitrary set of initial pure states to an arbitrary set of final states, i.e. controlling a unitary transformation. Such an application sets the foundation for a quantum gate operation.

Controllability of a closed quantum system has been addressed by Tarn and Clark. Their theorem based in control theory states that for a finite dimensional closed quantum system, the system is completely controllable, i.e. an arbitrary unitary transformation of the system can be realized by an appropriate application of the controls, if the control operators and the unperturbed Hamiltonian generate the Lie algebra of all Hermitian operators. Complete controllability implies state-to-state controllability.

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