Proposal for the Quantum Simulation of the CP(2) Model on Optical Lattices

TL;DR

This paper proposes a method to simulate the 2d CP(2) model, which shares features with QCD, using ultra-cold atoms in optical lattices, enabling exploration of complex quantum phenomena without sign problem issues.

Contribution

It introduces an experimental setup for quantum simulation of the CP(2) model using ultra-cold alkaline-earth atoms on optical lattices, bridging theoretical models and practical quantum experiments.

Findings

Numerical results for correlation length.

Analysis of real-time decay of false vacuum.

Potential to explore theta-vacua and phase diagram at finite chemical potentials.

Abstract

The 2d CP(N-1) models share a number of features with QCD, like asymptotic freedom, a dynamically generated mass gap and topological sectors. They have been formulated and analysed successfully in the framework of the so-called D-theory, which provides a smooth access to the continuum limit. In that framework, we propose an experimental set-up for the quantum simulation of the CP(2) model. It is based on ultra-cold Alkaline-Earth Atoms (AEAs) located on the sites of an optical lattice, where the nuclear spins represent the relevant degrees of freedom. We present numerical results for the correlation length and for the real time decay of a false vacuum, to be compared with such a future experiment. The latter could also enable the exploration of theta-vacua and of the phase diagram at finite chemical potentials, since it does not suffer from any sign problem.