Place all the atoms in the lower state, set Freq=1.00 and Amp=0.05, and turn on inelastic collisions with . Run BlochApp for about 500 seconds. Toggle between and versus time. Both of these terms are moving towards zero. In the Bloch vector representation, examine the uvw versus time plot which will show that u, v, and w are all approaching zero as well. From the information in the upper and lower plots, one is forced to conclude that all the elements of the density matrix are becoming zero, as in Figure .
Figure: Rabi oscillations including inelastic collisions Freq=1.00, Amp=0.05,and
How fast are the elements of the density matrix approaching zero? Clone the versus time plot and select the Print option from the File menu. If you are working on a network and do not have a local printer, then you may have to alter the printer setup via the Windows print manager or the included printer setup item. Once you have the print out, connect the peaks of the curve. The resulting function is a decaying exponential. This type of decay is quite dramatic and easily characterized by a single decay constant, , where . is the amount of time that is required to shrink the amplitude by a factor of , which is a good number to keep in your mental calculator. The decay of the density matrix will be reexamined in a later section.
Why should inelastic collisions drive the density matrix to the zero matrix? Inelastic collisions drive atoms out of the two levels which are linked by the laser. Thus, the initial population of atoms is decreasing, which requires that the probability of being in a particular state decrease as well. When there are no atoms in the upper or lower state, then the probability of finding an atom in these states is necessarily zero. At the same time, as the atomic populations shrink towards zero the collisions dephase the dipole moment in a random fashion that destroys it as well.