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Hi, i'm working on the interaction between a two level atom (|g>, |e>)

In my exercise we have to use the rotation operator :

R(t)=exp[i(σ

with σ

(1 0)

(0 -1)

If i want to represent my rotation operator in the {|g>,|e>} basis. Then i can do:

σ

( 2 0)

( 0 0)

Do my operator is :

(exp(iwt) 0 )

( 0 exp(0) )

Thanks for your answers.

In my exercise we have to use the rotation operator :

R(t)=exp[i(σ

_{z}+1)ωt/2]with σ

_{z}the pauli matrix which is in the {|g>,|e>} basis :(1 0)

(0 -1)

If i want to represent my rotation operator in the {|g>,|e>} basis. Then i can do:

σ

_{z}+1 = (1 is the identity matrix)( 2 0)

( 0 0)

Do my operator is :

(exp(iwt) 0 )

( 0 exp(0) )

Thanks for your answers.