Hilbert space engineering in 4f single-molecule magnets on superconducting sur- faces

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The electronic spins of single magnetic ions have the potential to be used as quantum bits (qubits). Especially, 4f ions in single molecular magnets (SMMs) have shown very long relaxation times approaching time scales of hours at low temperatures. In solid state devices that are accessed electronically, the electronic spins need to be coupled to the conduction electrons of the leads in order to allow preparation and read out of the spin state. The interaction with the electron gas of the contacts, however, may lead to relaxation, decoherence or even Kondo screening of the spin. Recently, the role of crystal field symmetries and the hyperfine interaction to the nucleus of the 4f ions has been studied in ways to avoid relaxation. In this proposal, the next logical step in this approach will be taken to not only suppress relaxation but also to prevent decoherence and boost coherence times of the potential qubits. We will design and synthesize isotopologically pure metal-organic molecules with rare earth ions in ligand fields of four-fold or higher symmetries in order to protect magnetization tunneling and deposit these onto single crystalline and superconducting surfaces. The symmetry of the crystal field will be used to design the Hilbert space in order to forbid electron spin-flip scattering as well as nuclear spin flips. In addition, the superconducting gap will inhibit elastic scattering of electrons within the gap. In a first step, relaxation times times will be studied by the expected magnetic telegraph noise as measured with spin-polarized scanning tunneling microscopy at 25 mK. Transitions driven by hyperfine interaction can lead to magnetization tunneling at specific applied magnetic fields as evidenced in the telegraph noise. Coherence times will be investigated by coupling two magnetic ions such that Rabi oscillations should appear.