Optical Bloch equations with multiply connected states
Abstract
The optical Bloch equations, which give the time evolution of the elements of the density matrix of an atomic system subject to radiation, are generalized so that they can be applied when transitions between pairs of states can proceed by more than one stimulated route. The case considered is that for which the time scale of interest in the problem is long compared with that set by the differences in detuning of the radiation fields stimulating via the different routes. It is shown that the Bloch equations then reduce to the standard form of linear differential equations with constant coefficients. The theory is applied to a twostate system driven by two lasers with different intensities and frequencies and to a threestate Λsystem with one laser driving one transition and two driving the second. It is also shown that the theory reproduces well the observed response of a cold ^{40}Ca^{+} ion when subject to a single laser frequency driving the 4S_{1/2}4P_{1/2} transition and a laser with two strong sidebands driving 3D_{3/2}4P_{1/2}.
 Publication:

Journal of Physics B Atomic Molecular Physics
 Pub Date:
 April 2008
 DOI:
 10.1088/09534075/41/8/085502
 Bibcode:
 2008JPhB...41h5502S