Two lifetimes are displayed below the evolution time. These lifetimes are calculated from the atomic parameters that have been discussed. They are called longitudinal and transverse lifetimes. In general lifetimes are defined as the inverse of a decay rate; the time constant, , which was discussed earlier is a lifetime. The transverse lifetime is defined as the inverse of . The longitudinal lifetime is defined as the inverse of . The former is the lifetime of the off--diagonal elements, and the latter is the lifetime of the diagonal elements. In the Bloch vector picture, the transverse lifetime controls the uv--plane, and the longitudinal lifetime controls the plane perpendicular to the uv--plane. These names are derived from nuclear magnetic resonance and refer to the lifetimes of the atom's spin when it is aligned with or perpendicular to the magnetic field.
It is easiest to observe these lifetimes when there is no electromagnetic field. Set Amp=0.00. Place all the atoms in state in which and . An initial dipole moment exists and has the magnitude of one. Run the simulation and plot vs time and the dipole moment with all the atomic parameters off. Confirm that the system is static with the dipole moment and equal to one.
Turn elastic collisions on and set . Notice that the population remains unchanged and the dipole moment decays. The values for the longitudinal and transverse lifetimes respectively are and 100. and w never change; thus, they have an infinite lifetime. The dipole moment does decay. Find the value of the dipole moment after one hundred seconds in Figure . The value should be about 0.38 which is approximately .
Figure: The transverse lifetime of the system for Freq=1.00, Amp=0.00, and
Leaving the elastic collisions on, turn spontaneous emission on and set A=0.01. The longitudinal lifetime is no longer infinite. It should have the value 100, and the transverse value should be 66.67 or . Run BlochApp again and measure the peak height of at 100 seconds, and the dipole moment at 67 seconds. Are they about 0.38? Run this experiment again with A=0.02. What are the lifetimes in this case? Are these lifetimes correct? Try a few more combinations of the parameters and include inelastic collisions. When including inelastic collisions, set because the lifetimes will not be valid if both and are non--zero. Why? (Hint: we have assumed that |1> is the ground state)
Set , , and . Turn both elastic collisions and spontaneous emission on. Make and . Make the analysis types and uvw versus time. The result is analogous to all the examples that we have examined thus far. The upper state is drained into the lower state and the dipole moment decays as in Figure . This effect has been observed in the laboratory and is called free induction decay. This phenomenon is used in laboratories to measure the transverse and longitudinal lifetimes in both atomic physics and nuclear magnetic resonance.
Figure: Free induction decay for Freq=1.00, Amp=0.00, A=0.01, and
A spin system is a true two level system because a spin is either up or down; however, our two level atom is only an approximation. There is no equivalent or term in nuclear magnetic resonance. Set and and rerun this experiment. What do you expect will be different? the same?