Hello, this is my first thread here and i have a question regarding coherent population trapping and the dark state. I am from Germany, so please excuse me, when my english isnt very good. This is what I found on wikipedia:(adsbygoogle = window.adsbygoogle || []).push({});

http://en.wikipedia.org/wiki/Dark_state

in the section "Three-level systems" they give a semiclassical Hamiltonian and solve Schrödingers eq. However, in the end they give solutions for the functions c_i(t) and i think especially c_3(t) is interesting. In the text they say, that with the right initial conditions, we can gain c_3(t)=0, wich is exactliy what is needed for electromagnetically Induced Transparency to work. When I try to find the initial conditions on my own, i would set c_3(t)=0, and would gain the solution

(1) c_3(0)=0

(2) c_1(0)*Ω_p=c_2(0)*Ω_c

The second equation allows the values c_1(0)=Ω_c/Ω and c_2(0)=Ω_p/Ω, wich would give the state:

|ψ(t)> = (Ω_c*Exp(-i*ω_1*t)|1> + Ω_p*Exp(-i*ω_2*t)|2>)/Ω

Wikipedia though, as well as other literatures, states the dark state as:

|D> = (Ω_c*|1> + Ω_p*|2>)/Ω

Apperently i am missing something crucial here. my questions now are the followong:

1. Where have the exponential expressions gone? Or how do i get the dark state |D>

2. Equation (2) leaves space for more than one solution. does that mean, there is more than one way to set up two lasers, to induce coherent population trapping in a medium?

Thank you for your time.

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# Dark state & schrödinger equation

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