No Permanent Dipole Moment in Two-Level System w/External Field

[KFC]

In two-level system, with external field applied, why there is no permant dipole moment? In classical point of view, dipole moment is coming from displacement of positive and negative charge. In quantum case, inside the atom, even no external field, there is certain probability for the electron be anywhere around the nucleus. Hence, the displacement should induced a dispole moment, but text says there is no such dipole moment, why?

By the way, if we consider the density matrix, what does the off-diagonal element refer to? How the off-diagonal element correspons to the induced dipole moment (with external field applied)?

 

[Meir Achuz]

A "permanent dipole moment" means that the dipole moment was there before the field was applied. For this case the energy shift is proportional to the field strength. A dipole moment caused by the field is called an "induced dipole moment", and the energy is proportional to the square of the field strength. A permanent electric dipole moment is forbidden by parity conservation.

 

[KFC]

A "permanent dipole moment" means that the dipole moment was there before the field was applied. For this case the energy shift is proportional to the field strength. A dipole moment caused by the field is called an "induced dipole moment", and the energy is proportional to the square of the field strength. A permanent electric dipole moment is forbidden by parity conservation.

In the text, the dipole moment due to applied field is written as $$d_{11}, d_{12}, d_{21}, d_{22}$$ and the diagonal terms vanish, why is that?

 

[Meir Achuz]

The perturbation is J.E which is a pseudoscalar so <i|j.E|i> vanishes by parity conservation.