Homogeneous and inhomogenous relaxation time

[KFC]

Consider two-level system, the relaxation time (T1) and the coherence relaxation time (T2). I wonder what's the relation between T1, T2 in homogeneous and inhomogeneous case?

Here is my thoughts. For inhomogeneous case, all atoms are behave independently, the 'random' phase relation will add up to lower the degree of coherence, hence, T2 will be smaller to that for homogeneous case, right?

If my statement is correct, T1 is same for bother inhomogeneous and homogeneous cases (right?). Hence, T1/T2 (inhomo.) > T1/T2 (homo) ?

And I remember (but not sure if it is correct), there is a relation between T1 and T2, says T1\geq 2T2. How does this relation come from? Is that true for both homogeneous and inhomogeneous case? What does it imply physically if T1/T2 ?

 

[azntoon]

Yes, your statement is correct. In the inhomogeneous case, the random phase relation will lower the degree of coherence, thus reducing T2 relative to the homogeneous case. Therefore, you can expect that T1/T2 (inhomo) > T1/T2 (homo). The relation between T1 and T2 is often known as the Heisenberg Uncertainty Principle which states that T1 ≥ 2T2. This is true in both homogeneous and inhomogeneous cases, and it implies that the more information one knows about a system, the more uncertainty exists about its behaviour.