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

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.

arXiv comment5 pages and 3 figures

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• Dynamical quantum phase transition in a system of non-interacting bosons
• Dynamical Topological Phase Transition in a Bose-Einstein Condensate
• Continuous variable multipartite vibrational entanglement
• The fractional Landau-Lifshitz-Gilbert equation
• Non-Markovianity in the time evolution of open quantum systems assessed by means of quantum state distance
• Group theoretical and ab-initio description of color center candidates in fluorographene