Nonlinear coupling of continuous variables at the single quantum level

TL;DR

This paper experimentally studies nonlinear Coulomb-induced interactions between vibrational modes of cold ions, revealing frequency shifts and quantum coherence effects relevant for high-fidelity quantum gates.

Contribution

It demonstrates the first precise measurement of Kerr-type nonlinear coupling between ion vibrational modes in a linear trap.

Findings

Observed oscillation frequency shifts due to nonlinear coupling

Detected collapse and revival of quantum coherence in Ramsey experiments

Discussed implications for quantum gate fidelity

Abstract

We experimentally investigate nonlinear couplings between vibrational modes of strings of cold ions stored in linear ion traps. The nonlinearity is caused by the ions' Coulomb interaction and gives rise to a Kerr-type interaction Hamiltonian H = n_r*n_s, where n_r,n_s are phonon number operators of two interacting vibrational modes. We precisely measure the resulting oscillation frequency shift and observe a collapse and revival of the contrast in a Ramsey experiment. Implications for ion trap experiments aiming at high-fidelity quantum gate operations are discussed.