Relaxation of a Two-Level System Coupled to a Fullerene Molecule

Abstract

<p>Insight into many-body problems in quantum mechanics may be developed by solving simple models exactly using computational methods. The small size of endohedral-doped fullerene molecules allows the electronic states to be evaluated numerically using a spin model such as the Heisenberg Hamiltonian. The Lanczos algorithm is deployed to compute a few low-energy states of fullerene systems.</p> <p>Since the spin of the dopant electrons can be manipulated using external magnetic fields, the system can be used as a qubit. For sufficiently large couplings between the dopant and the fullerene, the qubit may relax by releasing energy into the carbon cage. The resulting oscillations of the qubit are found to include a high frequency component introduced when the spin accesses multiple states with different energies. The frequency and the amplitude of the qubit's oscillations also depend on the magnitude of external fields and the size of the coupling between the dopant and the fullerene.</p>