Theory of phonon dynamics in an ion trap

TL;DR

This paper develops a comprehensive theory for the non-equilibrium phonon dynamics in trapped ion systems, focusing on cooling, entanglement, and optimal protocols under various driving conditions, with considerations for experimental implementation.

Contribution

It extends previous work by analyzing non-linear and periodic drives, identifying optimal protocols, and addressing noise effects for realistic experimental setups.

Findings

Optimal ramp protocols for minimal cooling and entanglement time identified

Noise effects from laser fluctuations qualitatively addressed

Theoretical framework applicable to experimental trapped ion systems

Abstract

We develop a theory to address the non-equilibrium dynamics of phonons in a one-dimensional trapped ion system. We elaborate our earlier results obtained in Phys. Rev. Lett. {\bf 111}, 170406 (2013) to chart out the mechanism of dynamics-induced cooling and entanglement generation between phonons in these systems when subjected to a linear ramp protocol inducing site-specific tuning of on-site interactions between the phonons. We further extend these studies to non-linear ramps and periodic drive protocols and identify the optimal ramp protocol for minimal cooling and entanglement generation time. We qualitatively address the effect of noise arising out of fluctuation of the intensity of the laser used to generate entanglement and provide a detailed discussion of a realistic experimental setup which may serve as a test bed for our theory.