Ion chains in high-finesse cavities

TL;DR

This paper studies how chains of ions in high-finesse cavities exhibit bistability, can be cooled to low vibrational occupation, and show entanglement between vibrations and cavity field, with potential for quantum control.

Contribution

It introduces a detailed analysis of ion chain dynamics in high-finesse cavities, revealing bistable states, cooling mechanisms, and entanglement properties not previously characterized.

Findings

Bistable equilibrium configurations of ion chains are identified.

Vibrational modes can be cooled to low occupation numbers via cavity scattering.

Vibrations become entangled with cavity field fluctuations at steady state.

Abstract

We analyze the dynamics of a chain of singly-charged ions confined in a linear Paul trap and which couple with the mode of a high-finesse optical resonator. In these settings the ions interact via the Coulomb repulsion and are subject to the mechanical forces due to scattering of cavity photons. We show that the interplay of these interactions can give rise to bistable equilibrium configurations, into which the chain can be cooled by cavity-enhanced photon scattering. We characterize the resulting equilibrium structures by determining the stationary state in the semiclassical limit for both cavity field and crystal motion. The mean occupation of the vibrational modes at steady state is evaluated, showing that the vibrational modes coupled to the cavity can be simultaneously cooled to low occupation numbers. It is also found that at steady state the vibrations are entangled with the cavity field fluctuations. The entanglement is quantified by means of the logarithmic negativity. The spectrum of the light at the cavity output is evaluated and the features signaling entanglement are here identified.