$ 2𝑆 0 ' 𝐼 0 ' . The presence of inphase coherences before the 'pump-refocus' block will manifest as cosine oscillations in the intensity of the refocussed echo and anti-phase coherences will manifest as sine oscillations, with the oscillation amplitudes proportional to their expectation values (see the product operator calculations in SI 11 and their relation to expectation values in SI 9.1). This has been observed previously in 4P-DEER at low temperature and high frequency, where the initial Hahn-echo acted on an almost pure initial thermal state and so generates both in-and antiphase coherences (Equation ). Operation pair