Analog Quantum Simulation of Extremely Sub-Ohmic Spin-Boson Models

TL;DR

This paper presents a method to simulate extremely sub-Ohmic spin-boson models using color centers in h-BN membranes, enabling exploration of non-Markovian dynamics and quantum phase transitions in solid-state systems.

Contribution

It introduces a novel quantum simulation scheme for sub-Ohmic spin-boson models using engineered h-BN resonators with magnetic field gradients.

Findings

Demonstrates coherence revivals indicating non-Markovian baths

Shows spin polarization localization related to quantum phase transition

Achieves specific spectral densities through geometric engineering

Abstract

We propose a scheme for the quantum simulation of sub-Ohmic spin--boson models by color centers in free-standing hexagonal boron nitride (h-BN) membranes. The electronic spin of a color center that couples to the membrane vibrational spectrum constitute the physical model. The spin-motion coupling is provided by an external magnetic field gradient. In this study, we show that a class of spectral densities can be attained by engineering geometry and boundary conditions of the h-BN 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 sources of decoherence in solid-state quantum bits.