Discrepancy between representation of Pauli operators and states

[Benjamin Butler]

Hi there, I recently started using QuTiP, and I'm working through the "Quantum mechanics lectures with QuTiP" found here: https://qutip.org/qutip-tutorials/

Unless I am missing something it appears to me that the matrix representation QuTiP uses for the Pauli matrices is different to the one it uses for basis(N, n), create(N), etc. 

To be more specific: the destroy(2) operator should produce the zero vector when it acts on the ground state. destroy(2) * basis(2, 0) = (0, 0)^T, thus identifying basis(2, 0) as the ground state. This vector has the (arbitrary) matrix representation in QuTiP of basis(2, 0) = (1, 0)^T. The excited state is therefore basis(2 ,1) = (0, 1)^T. However, in the definitions of the Pauli operators the exact opposite representation seems to have been chosen, i.e., the form of sigmaz defined in QuTiP only makes sense if the excited state is basis(2, 0) = (1, 0)^T -- unless there is an alternative definition of the Pauli operators with a different sign convention? The definition I know for the Z operator is |e><e| - |g><g|, which corresponds to many textbooks. 

Note also that the built in 2 level raising operator does not have the same matrix form as create(2) etc, which they should if a consistent representation is being used.

Best,

Ben