Towards a Programmable Quantum Simulator based on Spins in Diamond

Recent work has demonstrated the precise characterisation of a cluster of ¹³C nuclear spins around a single NV center in diamond [1]. Such systems provide an opportunity for the realisation of a programmable analogue quantum simulator [2, 3]. Here, I will present our progress in controlling such spin clusters, including collective initialisation [4], individual readout and individual and global control pulses. Our knowledge of both the nuclear-nuclear and electron-nuclear coupling strengths allows us to engineer a range of (Floquet) Hamiltonians to study many-body phenomena. We prepare the system as a discrete time crystal (DTC) under Floquet driving and study the thermalisation characteristics for different initial states. Additionally, we explore the spread of entanglement through the cluster using out-of-time-order correlators (OTOCs) and the estimation of entanglement entropy. These results establish a new type of quantum simulator for many-body spin physics.

[1]: van de Stolpe et al., Nat. Commun. 15:2006 (2024)

[2]: Randall et al., Science 374, 1474 (2021)

[3]: Bradley et al., Phys. Rev. X 9, 031045 (2019)

[4]: Schwartz et al., Sci. Adv. 4, eaat8978 (2018)