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and hence δk = 0 and the M1 transition is completely suppressed. In practice, E − = E + − δ E due to the small but nonzero transmission of the back mirror in the cavity. Since | δ E| ≪ E , | δk | ≈ | δ E / E| ≪ 1. Thus, although the M1 transition amplitude is not strictly zero, it is highly suppressed. 

Without loss of generality, the quantities β , ζ , and M are assumed to be real. In general, the rate R$_{M}$ given by Eq. (1) includes terms proportional to β M (Stark-M1 interference) and βζ (Stark-PV interference). 

A careful choice of field geometry allows for additional suppression of undesirable Stark-M1 interference. From Eq. (3), it is evident that the Stark-PV interference is proportional to the rotational invariant 

which is P-odd and T-even. In the present experimental apparatus the electric field, E , is applied orthogonally to the magnetic field, B , and collinearly with the axis of the linearly-polarized standing light wave, as shown in Fig. 2. 

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This geometry is such that the M1 and Stark-induced amplitudes are out of phase. Thus, they do not interfere and therefore do not produce spurious PV-mimicking ef- fects (see Section IV). 

In the ideal case where we neglect the apparatus im- perfections, the static magnetic and electric fields are B = B ˆ z and E = E ˆ x , respectively, and the light stand- ing wave has an electric field 

## III. PV SIGNATURE: IDEAL CASE 

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With this field orientation (see Fig. 2), Eqs. (1) through (4) yield 

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where terms of order ζ 2 and higher are neglected, and δk = 0 is assumed. 

In order to isolate the Stark-PV interference term from the dominant Stark-induced transition rate, we modulate the electric field: E = E$_{dc}$ + ˜ E$_{0}$ cos( ωt ), where ˜ E$_{0}$ is the modulation amplitude, ω is the modulation frequency, and E$_{dc}$ provides a DC bias. Then Eqs. (7) and (8) become 

where R [ n ] M is the amplitude of the n th harmonic of the transition rate R$_{M}$ . The dominant Stark-induced con- tribution, which oscillates at twice the modulation fre- quency, is 

On the other hand, the amplitude R [1] M contains the Stark-PV interference term: 

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The term R [0] M is a constant “background”: 

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For an arbitrary polarization angle θ , all three Zee- man components of the transition, as shown in Fig. 3a, are present while scanning over the spectral profile of the transition. The first-harmonic signal due to Stark-PV in- terference has a characteristic signature: the sign of the oscillating terms for the two extreme components of the transition is opposite to that of the central component. The second-harmonic signal provides a reference for the lineshape since it is free from interference effects linear in E (Fig. 3b). With a non-zero DC component present in the applied electric field, a signature identical to that in the second harmonic will also appear in the first har- monic, Fig. 3c. The latter can be used to increase the first-harmonic signal above the noise, which makes the profile analysis more reliable. 

To obtain the PV term from the measured first- and second-harmonic transition rates, we first normalize the first-harmonic signals R [1] M by their second-harmonic 

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