Direct Measurement of the Soft Mode Driving a Quantum Phase Transition

Abstract

Quantum phase transitions in spin systems are supposed to be accompanied by a soft collective mode, which has not been seen in experiments. Here, we directly measure the low energy excitation modes of a well-known realization of the Ising model in transverse field, LiHoF₄, using microwave spectroscopy techniques to probe energies well 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 'electronuclear' modes, arising from coupling of the spin-1/2 Ising electronic spins to a bath of spin-7/2 Ho nuclear spins. The lowest-lying electronuclear mode softens at the approach to the quantum critical point from below and above, a softening that can be quenched with the application of a longitudinal magnetic field. The electronuclear mode structure has direct implications for the Ising systems that serve as the building blocks of adiabatic quantum computers and quantum annealers.