Decoherence of quantum systems due to uncontrolled fluctuations of the
environment presents fundamental obstacles in quantum science. `Clock'
transitions which are insensitive to such fluctuations are used to improve
coherence, however, they are not present in all systems or for arbitrary system
parameters. Here, we create a trio of synthetic clock transitions using
continuous dynamical decoupling in a spin-1 Bose-Einstein condensate in which
we observe a reduction of sensitivity to magnetic field noise of up to four
orders of magnitude; this work complements the parallel work by Anderson et al.
(submitted, 2017). In addition, using a concatenated scheme, we demonstrate
suppression of sensitivity to fluctuations in our control fields. These
field-insensitive states represent an ideal foundation for the next generation
of cold atom experiments focused on fragile many-body phases relevant to
quantum magnetism, artificial gauge fields, and topological matter.Comment: 8 pages, 4 figures, Supplemental material
