Method of Extending Hyperfine Coherence Times in Pr³⁺∶Y₂SiO₅

In this Letter, we present a method for increasing the coherence time of praseodymium hyperfine ground state transitions in Pr³⁺∶Y₂SiO₅ by the application of a specific external magnetic field. The magnitude and angle of the external field is applied such that the Zeeman splitting of a hyperfine transition is at a critical point in three dimensions, making the first order Zeeman shift vanishingly small for the transition. This reduces the influence of the magnetic interactions between the praseodymium ions and the spins in the host lattice on the transition frequency. Using this method a phase memory time of 82 ms was observed, a value 2 orders of magnitude greater than previously reported. It is shown that the residual dephasing is amenable to quantum error correction.