In Sec. 6 on the polarization monitor of [1], we assumed a small value of $\delta$, which is incorrect. The correct approximation $\beta \ll 1$ can be derived from a general treatment of the problem with the condition $\vert (S_3/S_0)_\mathrm {atom} \vert \lesssim 0.3$, and leads to the following corrected Eq. (10):

The corrected Eq. (11) then reads:

Since $\delta$ is in general not small (but can be on the order of $10^3 \pi$), even small relative fluctuations in $\delta$ will prevent the determination of $\Delta \psi _\text {atom}$ with our method. Furthermore, a single linear retarder is not a sufficient model for a combination of linear birefringent elements, but a circular birefringence term (rotator) must also be included [2]. The latter can be non-zero even when cascading multiple linear retarders only, nor can it be assumed to be constant. This additionally prevents the determination of $\Delta \psi _\text {atom}$ from $\Delta \psi _\text {back}$. However, from the polarization-maintaining properties of our fiber we know that the variations of this angle are always below $\Delta \psi _\text {atom} \lesssim 3 ^\circ$, which is sufficient for our experiment.

In contrast to $\delta$, the beam splitter retardance $\delta _\text {BS}$ can be small, such that Eqs. (12) remain unchanged as long as polarizing effects of the beam splitter can be neglected.

The corrected Fig. 12 of [1] resulting from the above corrections is presented in Fig. 1 .

 

Fig. 1. Corrected Fig. 12 of [1] using the corrected model of polarization monitor, showing only the absolute value of circularly polarized fraction $\vert (S_3/S_0)_\text {atom} \vert$.

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