What is the meaning of phase in relation to laser states?

[kaje]

Hi,
What does it mean when we say that the in the case of absence of a phase reference, the laser would produce a Poissonian mixture of number states?.. I got confused actually between the meaning of the phase in classical sense and quantum in this regard. Regards

 

[DrDu]

The quantum state ##|\psi\rangle= c_0|0\rangle+c_1 |1 \rangle +c_2|2\rangle \ldots ## is a superposition of number states.
If the square of the coefficients ##|c_i|^2## follows a Poisson distribution and ##c_{n+1}/c_n \sim \exp(i\phi)##, then this state is a coherent state with phase ##\phi## which is as close as you can get in QM to a classical state.