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I would like to know why it is impossible to have a two level laser ?

Indeed if I write the equations (I neglect here the spontaneous emission), I have :

$\frac{dN_2}{dt}=W(\omega).B.(N1-N2)$ and $\frac{dN_2}{dt}=-W(\omega).B.(N1-N2)$

Where $W(\omega)$ is my energy density and B my einstein coefficient.

If i add a pump I have this :

$\frac{dN_2}{dt}=W(\omega).B.(N1-N2)+W_p$ and $\frac{dN_2}{dt}=-W(\omega).B.(N1-N2)-W_p$

If $W_p$ is high enough I can have $N_2>N_1$.

So why do we say that the inversion is not possible ?

Thank you !

StarBucK
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    The pumping term you have included probably assumes that N2 << N1. It neglects the population of N1 (imagine N1 being empty, how but still the pumping rate is a constant). It also neglects de-excitation from N2 to N1.

    The actual question is answered here. http://physics.stackexchange.com/questions/72080/lasing-in-a-2-level-system

     – Mikael Kuisma Apr 05 '16 at 00:13
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    It occurs to me that there is probably a very elegant thermodynamic argument based on the 2nd law for this. I'd bounty a answer like that. – dmckee --- ex-moderator kitten Apr 05 '16 at 00:28
  • @dmckee Maybe.... it is interesting to think about. But really, the argument in the linked answer boils down to "time-reversal symmetry means you can't bring electrons up (in a two level system) without also bringing some down." It's hard for me to imagine a simpler or more elegant argument than that. – Rococo Apr 05 '16 at 05:59
  • Thank you. I have read the other topic answers and yours (I can't comment on the other topic). If I understand well I have to change my pumping term in Wp(N1-N2) and then I see that if it makes N2 increase, when N1=N2 everything will be stationnary so I can't inverse the population.

    Also, in a hypothetical two level systems the pumping can't be by light right ? Because if I pump using light I will diminish the intensity of my laser (so the pumping must be chemical or electrical).

     – StarBucK Apr 05 '16 at 11:23

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