Coherent control

Coherent control is a quantum mechanics-based method for controlling dynamical processes by light. The basic principle is to control quantum interference phenomena, typically by shaping the phase of laser pulses. The basic ideas have proliferated, finding vast application in spectroscopy mass spectra, quantum information processing, laser cooling, ultracold physics and more. Coherent control is a quantum mechanics-based method for controlling dynamical processes by light. The basic principle is to control quantum interference phenomena, typically by shaping the phase of 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: The two basic methods eventually merged with the introduction of optimal control theory. Experimental realizations 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 generalization 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. The computational task of finding a control field for a particular state-to-state transformation is difficult and becomes more difficult with the increase in the size of the system. This task is in the class of hard inversion problems of high computational complexity. The algorithmic task of finding the field that generates a unitary transformation scales factorial more difficult with the size of the system. This is because a larger number of state-to-state control fields have to be found without interfering with the other control fields. Once constraints are imposed controllability can be degraded. For example, what is the minimum time required to achieve a control objective? This is termed the 'quantum speed limit'.