# Decay terms in Optical Bloch Equations

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In the Optical Bloch Equations (https://en.wikipedia.org/wiki/Maxwell%E2%80%93Bloch_equations) it is imposed that the populations decay at a rate $\gamma$, and that the coherences decay at $\frac{\gamma}{2}$.

I can see why the populations should decay at $\gamma$ (i.e. via Wigner-Weiskoppf theory) but how do we arrive at $\frac{\gamma}{2}$ for the coherences?

My motivation in asking this question is in trying to extend the OBE's to a three-level Vee system, where is is not obvious what decay rate to assign to the excited state coherence terms (i.e. $\rho_{e_1e_2}$).

This post imported from StackExchange Physics at 2016-11-24 08:30 (UTC), posted by SE-user user2640461

asked Nov 12, 2016
edited Nov 24, 2016
Some progress on this: imposing that the populations decay at $\gamma$ forces the coherences to decay with a rate of at least $\frac{\gamma}{2}$ in order to preserve positivity of the density matrix. As to why they decay exactly at that rate and no faster, perhaps you can demand that the decay be minimally decoherent. There is no compelling reason why the coherences should decay any faster than they need to.

This post imported from StackExchange Physics at 2016-11-24 08:30 (UTC), posted by SE-user user2640461

The wikipedia page you link to gives a derivation, and you can see that the factor 1/2 comes from the Lindblad terms. The form of the latter is dictated by the requirement that they can be written in the form of a sum of double commutators.

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