We propose a scheme for the quantum simulation of sub-Ohmic spin-boson models by color centers in free-standing hexagonal boron nitride (hBN) membranes. The electronic spin of a color center that couples to the membrane vibrational spectrum constitutes the physical model. The spin-motion coupling is provided by an external magnetic field gradient. In this Rapid Communication, we show that a class of spectral densities can be attained by engineering geometry and boundary conditions of the hBN resonator. We then put our focus on two extreme cases, i.e., $1/f$- and white-noise spectral densities. Spin coherence and polarization dynamics are studied. Our calculations show coherence revivals at periods set by the bath characteristic frequency signaling the non-Markovian nature of the baths. The nonequilibrium dynamics of the spin polarization exhibits a coherent localization, a property peculiar to the quantum phase transition in extremely sub-Ohmic spin-boson models. Our scheme may find application in understanding the sources of decoherence in solid-state quantum bits.

• Received 8 August 2018

DOI:https://doi.org/10.1103/PhysRevA.98.040303