Measuring hybridized electro-nuclear modes at a quantum phase transition

Understanding the excitations, fluctuations, and dynamics at a quantum phase transition is an important research thrust in pure condensed matter and atomic physics, as well as applications such as adiabatic quantum annealing engines. One of the key open questions in this area is whether critical excitations remain when coupled to an external spin bath, as is present for many real-world implementations of quantum systems. Here, we directly measure the low energy excitation modes of a well-known realization of the quantum Ising model in transverse field, LiHoF₄, using microwave spectroscopy techniques to probe energies below what is accessible via neutron scattering. We also measure the effect of a longitudinal magnetic field on the gap of the low energy collective mode. These results suggest that quantum criticality persists in the presence of a spin bath and that similar modes may exist in other quantum Ising systems, including adiabatic quantum computers.