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

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Discussion Overview

The discussion centers on the absence of a permanent dipole moment in a two-level quantum system when subjected to an external field. Participants explore the implications of classical and quantum perspectives on dipole moments, as well as the role of the density matrix in this context.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions why a permanent dipole moment does not exist in a two-level system, despite the classical view suggesting that displacement of charge leads to a dipole moment.
  • Another participant clarifies that a permanent dipole moment is defined as one that exists prior to the application of an external field, and distinguishes it from an induced dipole moment, which arises due to the field.
  • There is a mention of parity conservation as a reason for the prohibition of a permanent electric dipole moment.
  • A participant notes that the dipole moment due to the applied field is represented by terms in the density matrix, specifically d_{11}, d_{12}, d_{21}, d_{22}, and questions why the diagonal terms vanish.
  • Another participant states that the perturbation is a pseudoscalar, leading to the vanishing of certain matrix elements due to parity conservation.

Areas of Agreement / Disagreement

Participants express differing views on the nature of dipole moments in quantum systems, particularly regarding the definitions and implications of permanent versus induced dipole moments. The discussion remains unresolved on some aspects, particularly concerning the vanishing of diagonal terms in the density matrix.

Contextual Notes

The discussion includes assumptions about the definitions of dipole moments and the effects of parity conservation, which may not be universally agreed upon. The implications of the density matrix and its elements are also not fully resolved.

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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)?
 
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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.
 
clem said:
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 [tex]d_{11}, d_{12}, d_{21}, d_{22}[/tex] and the diagonal terms vanish, why is that?
 
The perturbation is J.E which is a pseudoscalar so <i|j.E|i> vanishes by parity conservation.
 

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