Optical Rotation Approach to Search for the Electric Dipole Moment of the Electron

Round 1

Reviewer 1 Report

This is a very interesting and important paper. The authors suggest realistic experiments and perform necessary calculations for the new method of the measurement of the time reversal and parity violation effects using Faraday rotation of the light polarisation plan in electric field. I recommend this excellent paper for the publication. I have only one minor comment about the references and history of this effect. 

   Measurement of the electron EDM using the Faraday rotation technique was suggested in

Effects of parity nonconservation in diatomic molecules.  O.P. Sushkov,

 V.V.Flambaum.  JETP 48, 608-611, 1978 (ZhETF 75(10), 1208, 1978).

Corresponding experiment was started by D. Melik-Pashaev (D.Budker), M. Zolotorev and L.M. Barkov at the Institute of Nuclear Physics, Novosibirsk. There found a way to enhance this effect using a non-linear optics phenomenon and experimentally  demonstrated existence of this enhancement using ordinary Faraday rotation in magnetic field. I believe the authors can find corresponding references in their Ref. [34] which is a direct continuation of the D. Melik-Pashaev (D.Budker), M. Zolotorev and L.M. Barkov activity at Novosibirsk continued in Berkeley.

Author Response

I have only one minor comment about the references and history of this effect. 

   Measurement of the electron EDM using the Faraday rotation technique was suggested in

Effects of parity nonconservation in diatomic molecules.  O.P. Sushkov,

 V.V.Flambaum.  JETP 48, 608-611, 1978 (ZhETF 75(10), 1208, 1978).

We would like to thank the Reviewer for this comment. In the revised version of our manuscript in the second paragraph of the Introduction after the sentence "In [34] the possible existence of such an effect was discussed" the new sentence "Measurement of the eEDM using the Faraday rotation technique was suggested in [35]" was added. Also the new reference [35] (in the revised version) -  O.P. Sushkov, V.V.Flambaum.  JETP 48, 608-611, 1978 (ZhETF 75(10), 1208, 1978) - was added. 

Reviewer 2 Report

This work presents calculations of the optical rotation due to PT violating effects in atoms. The calculations are in support of planned experiments which may achieve record limits on the electron EDM. 

This work my be published in "Atoms", and is already at appropriate length. Nevertheless the following points should be addressed, if only in a sentence or two:

1. The abstract could more closely reflect the first sentence of the conclusion: what does this paper show about each of the species mentioned?

2. Missing from the introduction is discussion of other PT-violating effects, such as nucleon interactions. See review of Ginges & Flambaum, Phys. Rep. 397, 63 (2004), which should be cited. Would this affect the determination of optical rotation in the case of non-zero nuclear spin, which is discussed by the authors?

3. The theory section is fine but there is no discussion of the methods of calculation beyond "one can apply powerful quantum chemistry methods that take into account electron correlation". It is not immediately clear to me whether such calculations have been performed in this work or whether this paper is simply using values of eEDM enhancement factors from other works. In particular what is the relationship of this work to [40]?

Author Response

The abstract could more closely reflect the first sentence of the conclusion: what does this paper show about each of the species mentioned?

 According to the Reviewer comment in the revised version of the manuscript we added the sentence "The results show that the magnetic dipole transitions in the Tl and Pb atoms as well as the electric dipole transitions in the Ra, Hg and Cs atoms are favorable for the observation of the P,T -odd Faraday optical rotation" in the abstract .

2. Missing from the introduction is discussion of other PT-violating effects, such as nucleon interactions. See review of Ginges & Flambaum, Phys. Rep. 397, 63 (2004), which should be cited. Would this affect the determination of optical rotation in the case of non-zero nuclear spin, which is discussed by the authors?

We agree with the comment of the Reviewer. In the revised version we added one sentence in the first paragraph of the Introduction after the 10th sentence " Note, that we do not consider here other sources of P,T-violation effects including spin-dependent effects such as the interaction of the nuclear magnetic quadrupole moment with electrons [9] which will be considered elsewhere". Also the new reference [9] - Ginges & Flambaum, Phys. Rep. 397, 63 (2004) - was added.

3. The theory section is fine but there is no discussion of the methods of calculation beyond "one can apply powerful quantum chemistry methods that take into account electron correlation". It is not immediately clear to me whether such calculations have been performed in this work or whether this paper is simply using values of eEDM enhancement factors from other works. In particular what is the relationship of this work to [40]?

According to the Reviewer comment we deleted the sentence before the Eq.(12). Instead of it, we added the following text: "Such calculations of matrix elements (10) as well as transition amplitudes in the numerator of Eq. (5) for atoms under consideration were performed in Refs. [18, 42]. For this the relativistic coupled cluster method within the Dirac-Coulomb Hamiltonian has been used"  

Moderate English changes required 

Some minor cosmetic changes in English were performed all over the text of the manuscript.