The basic principle is to control quantum interference phenomena, typically by shaping the phase of laser pulses.
[1][2] 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.
[9] Two interlinked developments accelerated the field of coherent control: experimentally, it was the development of pulse shaping by a spatial light modulator[10][11] and its employment in coherent control.
[12] The second development was the idea of automatic feedback control[13] and its experimental realization.
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.
[16][17][18] Controllability of a closed quantum system has been addressed by Tarn and Clark.
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.
It therefore follows from the negative answer to Hilbert's tenth problem that quantum optimal controllability is in general undecidable.
For example, what is the minimum time required to achieve a control objective?
The speed limit can be calculated by quantizing Ulam's control conjecture.
The most well studied method is Stimulated raman adiabatic passage STIRAP [24] which employs an auxiliary state to achieve complete state-to-state population transfer.
[6][7] For state-to-state control the objective is defined as the maximum overlap at the final time T with the state
The time dependent control Hamiltonian has the typical form: where
Different algorithms have been applied for obtaining the control field such as the Krotov method.
A related method has been called tracking [29] Some applications of coherent control are Another important issue is the spectral selectivity of two photon resonant excitation coherent control.
[43] A similar but non-resonant two photon excitation from the 1s1s to the 1s3s state of the He atom was investigated with ab-initio quantum mechanics es well[44].
These concepts can be applied to single pulse Raman spectroscopy and microscopy.