Kramers-degenerated NV+113C spin systems in diamond: analytical description

Abstract

Spin systems consisted of single electronic spin S=1 of the NV center and nearby nuclear spins I=1/2 of 13 C atoms disposed in diamond lattice near the center can be used as a small register of a quantum computer or as a sensor of a magnetic field. At odd number of nuclear spins eigenvalues of the spin systems at zero external magnetic field are at least twofold degenerated (Kramers degeneration) due to time reversal invariance of the spin Hamiltonian. This degeneracy is lifted only by external magnetic field regardless of the presence of any electric (crystal) field which can also lift the degeneracy thus hindering measurement of the magnetic field. Therefore, the Kramers-degenerated spin systems can be very perspective for measurement of a local magnetic field by the NV-based single-spin quantum magnetometer. Here, we are considering analytically the simplest Kramers-degenerated spin system NV+1 13 C consisting of a single electron spin S=1 of the NV сenter coupled by hyperfine interaction with a single nuclear spin I=1/2 of 13 C atom disposed in arbitrary site of diamond lattice. Simple approximate analytical expressions are obtained for eigenvalues and eigenstates of the spin system.