# Coherent population trapping

Could anyone explain me (or give reference to a book) what is coherent population
trapping (in optics). Is it somehow connected with Electromagnetically Induced
Transparency (I also don't know how it works). Thanks for any replies.

Cthugha
EIT is basically a quantum interference effect in 3-level systems.

A simplifying explanation:
Consider you have a system with 3 levels 1, 2 and 3. The transitions 1->3 and 2->3 can be excited optically. If you now excite transition 1->3 with a resonant and coherent light beam, it will be absorbed. You might see Rabi oscillations.
If you additionally excite transition 2->3 resonantly with a coherent light beam, the situation is more difficult. At some pump strength of 2->3 you will get a destructive interference of the probability amplitudes regarding transitions from 1->3. So the probability amplitudes 1->3 and 2->3->1 (or 2->3->1->3) cancel out, making the material transparent at the 1->3 transition. Coherent population trapping is more or less the same effect, but here the focus is on the population of the state for which the transition amplitudes cancel and not on the light field.

I am not too familiar with books covering this topic. One book I know is "Lasers without Inversion and Electromagnetically Induced Transparency" by Sher Alam. It gives a very understandable, but not extremely theoretical introduction. It is ok for getting into the topic, but might be a bit shallow if you want to go into every single detail.

Thanks for your replay, Cthugha. I only wonder if direct transition 1->3 is first or
second-order effect (have dipol moment between 1 and 3 to be zero) - maybe it's not important here.

Redbelly98
Staff Emeritus
Homework Helper
The idea is that 1 & 3 are both ground states, and 2 is an excited state. So 1<->3 transitions are not induced by the optical field. Something like this:

Code:
    2 ---
/ \
/   \
/     \
1 ---     --- 3