Low-field dephasing time of an optically polarized NV- spin bath beyond the P1 limit in diamond: a cluster-correlation-expansion and exact spin-bath study

Dense ensembles of nitrogen-vacancy (NV-) centres in nitrogen-rich diamond dephase on the electron spins of the substitutional nitrogen (P1) centres. If the paramagnetic nitrogen is instead converted into NV- centres, the laser that initializes the sensor also pumps the bath into m s = 0, a state with no moment along its own axis. Using cluster-correlation-expansion (CCE) calculations, combined with an exact solver for probe-bath exchange and with no adjustable parameter, this paper asks whether such an optically polarized NV- bath dephases a sensor more slowly than a P1 bath of the same density. The answer is set by the field. In a field along [111], three quarters of the bath centres lie off the field axis, and the moment of their m s = 0 state along the field grows from 0.04 at 25 G to 0.46 at 300 G and 0.81 at 800 G. At 25 G the polarized bath is therefore nearly silent: at 10 17 cm-3 the dephasing time T 2* of a separately addressed 15 NV- probe is 112 us, six times the 18.1 us of a P1 bath, and still 2.4 times at 90 % polarization; an ensemble measurement gains a factor of two. At 300 G the advantage over P1 shrinks to 1.4, and at 800 G the polarized bath dephases faster than P1. The field dependence of every bath, P1 included, follows the mean moment of its centres along the field. For the Hahn echo, exchange with on-axis bath centres and bath relaxation (T 1 = 6 ms) limit the gain to 1.2 times the P1 value at 25 G. Optical polarization of an NV- bath at low field therefore offers dephasing times beyond the P1 limit of nitrogen-rich diamond.