Direct Measurement of the Soft Mode Driving 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. An important question remains of whether critical excitations remain in the presence of an external spin bath, as is the case for many real-world implementations of quantum systems. Addressing this issue is necessary for connecting theory and modeling to observations and device design. 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 experiments. Instead of the single excitation expected for a simple quantum Ising system, we find and characterize a remarkable array of modes arising from coupling of the spin-1/2 Ising electronic spins to a bath of spin-7/2 Ho nuclear spins, the lowest of which indeed softens at the quantum critical point. 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.