Topological defects: Data analysis

PW P. Wcisło PA P. Ablewski KB K. Beloy SB S. Bilicki MB M. Bober RB R. Brown RF R. Fasano RC R. Ciuryło HH H. Hachisu TI T. Ido JL J. Lodewyck AL A. Ludlow WM W. McGrew PM P. Morzyński DN D. Nicolodi MS M. Schioppo MS M. Sekido RT R. Le Targat PW P. Wolf XZ X. Zhang BZ B. Zjawin MZ M. Zawada

This protocol is extracted from research article:

New bounds on dark matter coupling from a global network of optical atomic clocks

**
Sci Adv**,
Dec 7, 2018;
DOI:
10.1126/sciadv.aau4869

New bounds on dark matter coupling from a global network of optical atomic clocks

Procedure

For nonzero DM-SM coupling, a topological defect will manifest as a transient perturbation of the fine-structure constant. We denoted its magnitude and duration as δα and *T*, respectively. The corresponding perturbation of the relative cavity-atom frequency encoded in *r*_{i}(*t*) depends on the atom sensitivity *K*_{α} and for two different clocks *A* and *B* can be written as

We defined normalized signals as *t*_{B} − *t*_{A} is the duration of the cross-correlated signals. For square events, the shape of their cross correlation is triangular with full width at half maximum equal to *T* and amplitude

This gives the constraint on the transient variations in the fine-structure constant (see Eq. 1). For the quadratic coupling, *8*). The DM field is assumed to be zero outside the topological defects.

The simplest model of DM topological defects requires at least two free parameters whose values have to be arbitrarily chosen; in our case, these parameters are the defect size, *d*, and the time between consecutive encounters with topological defects, T. We repeated our analysis for every combination of these two parameters within the ranges we accessed with our network. For given values of *d* and T, we cross-correlated the two *A*_{0}, yields the noise level corresponding to the transient variations in α (Eq. 1), and strength of the DM-SM coupling (Eq. 3) (see black lines in Fig. 3). This approach is analogous to the VLBI technique used in radio astronomy.

To give a proper statistical interpretation of our results, we also calculated the 5 and 95% CLs (see the green and red lines, respectively, in Fig. 3). To calculate the CLs, we repeated (100 times) the above algorithm of maximal *A*_{0} determination, artificially shifting one of the *d*), we selected the five smallest and largest elements, which yields the 5 and 95% CLs. We treated the 95% CL as an actual constraint determined in this work; hence, the black line in the top right panel in Fig. 3 should statistically (i.e., without any common component) exceed the red line 95% CL one time per every 20 values in *d* (the step in *d* is 300 km). This is consistent with Fig. 3, which indicates that at present level of accuracy, we did not observe any signature of hypothetical DM.

In the dataset considered here, the time of overlap of at least three clocks was considerably smaller than the time of overlap of two clocks. Therefore, without losing the strength of the constraint, we could restrict our analysis to simultaneous comparison of two clocks at a given time. For more than two simultaneous *η*_{T} = 1, i.e., the lengths of the cross-correlated *T*_{c}.

Note: The content above has been extracted from a research article, so it may not display correctly.

Q&A

Your question will be posted on the Bio-101 website. We will send your questions to the authors of this protocol and Bio-protocol community members who are experienced with this method. you will be informed using the email address associated with your Bio-protocol account.