We demonstrate significant improvements of the spin coherence time of a dense ensemble of nitrogen-vacancy (NV) centers in diamond through optimized dynamical decoupling (DD). Cooling the sample down to $77$ K suppresses longitudinal spin relaxation
$T_1$ effects and DD microwave pulses are used to increase the transverse coherence time $T_2$ from $sim 0.7$ ms up to $sim 30$ ms. We extend previous work of single-axis (CPMG) DD towards the preservation of arbitrary spin states. Following a theoretical and experimental characterization of pulse and detuning errors, we compare the performance of various DD protocols. We identify that the optimal control scheme for preserving an arbitrary spin state is a recursive protocol, the concatenated version of the XY8 pulse sequence. The improved spin coherence might have an immediate impact on improvements of the sensitivities of AC magnetometry. Moreover, the protocol can be used on denser diamond samples to increase coherence times up to NV-NV interaction time scales, a major step towards the creation of quantum collective NV spin states.
Quantum mechanics does not provide a clear answer to the question: What was the past of a photon which went through an interferometer? Various welcher weg measurements, delayed-choice which-path experiments and weak-measurements of photons in interfe
rometers presented the past of a photon as a trajectory or a set of trajectories. We have carried out experimental weak measurements of the paths of photons going through a nested Mach-Zehnder interferometer which show a different picture: the past of a photon is not a set of continuous trajectories. The photons tell us that they have been in the parts of the interferometer which they could not have possibly reached! Our results lead to rejection of a common sense approach to the past of a quantum particle. On the other hand, they have a simple explanation within the framework of the two-state vector formalism of quantum theory.
