Probing decoherence in molecular 4f qubits

We probe herein the fundamental factors that induce decoherence in ensembles of molecular magnetic materials. This is done by pulse Electron Paramagnetic Resonance measurements at X-band (∼9.6 GHz) on single crystals of Gd@Y(trensal) at 0.5, 10^-1, 10^-2 and 10^-3% doping levels, using Hahn echo, partial refocusing and CPMG sequences. The phase memory time, T _m, obtained by the Hahn echo sequence at X-band is compared to the one previously determined at higher frequency/magnetic field (∼240 GHz). The combined information from these experiments allows to gain insight into the contributions to decoherence originating from various relaxation mechanisms such as spin-lattice relaxation, electron and nuclear spin diffusion and instantaneous diffusion. We show that while at high magnetic fields T _m is limited by spin-lattice relaxation seemingly attributed to a direct process, at lower fields the limiting factor is spectral diffusion. At X-band, for Gd@Y(trensal) we determine a T _m in the range 1-12 μs, at 5 K, depending on the magnetic field and concentration of Gd(trensal) in the isostructural diamagnetic host Y(trensal). Importantly, Gd@Y(trensal) displays measurable coherence at temperatures above liquid nitrogen ones, with 125 K being the upper limit. At the lowest dilution level of 10 and under dynamic decoupling conditions, the ratio of T _m versus the time it takes to implement a quantum gate, T _G, reaches the order of 10⁴, in the example of a single qubit π-rotation, which corresponds to an upper limit of gate fidelity of the order of 99.99%, reaching thus the lower limit of qubit figure of merit required for implementations in quantum information technologies.