Fig. 1: Bath purification by conditional selective measurements and it’s posterior (persistent) effects.

a Schematic description: Conditional selective measurements of the state of the central probe-spin (S) surrounded by a spin bath in the star configuration. The conditional measurements consist of photon-emission detection from the decayed state or non-detection from the initial state. A sequence of measurement events collapses the spin-bath toward a low entropy state with resolvable, partly-(red) or fully-polarized (orange) spins. b The success probability, p_m of m positive measurement outcomes: solid red— for a probe subject to uncorrelated (Markovian) measurement sequence (solid red) that leaves the spin-bath unchanged, dashed orange—for a probe subject to correlated measurements that purify the bath. The success probability exponentially decays with m for uncorrelated measurements, while it saturates for correlated measurements. c Simulated bath spectrum P(ω_j) plotted for the cases prior to measurements (red—thermal bath) and after the conditional (selective) measurement sequences (CT) M_0,4 (orange) and M_4,0 (blue). Both (orange and blue) posterior spectra are much narrower than the prior spectrum, indicating low-entropy steady-states of the bath. The orange spectrum peaked at bath states with zero magnetic fields, whereas the blue spectrum peaked at higher magnetic field values of the bath spins. d Probe coherence decay prior (red) and posterior to measurements (orange, blue) for the spectra shown in (c). The orange curve is in the quantum Zeno (QZE) regime (decay slowdown) while the blue curve is in the anti-Zeno (AZE) regime (decay speedup). These curves are simulated for a bath of N = 8 spins that are randomly (inhomogeneously) coupled to the probe spin. The timescale between measurements is chosen to be τ = 0.6 μs, such that it is close to the bare \({T}_{2}^{*}\) obtained from the prior FID (red solid-line in d). (see te section “Results”, Supplementary Note 3).