CP(N-1) Quantum Field Theories with Alkaline-Earth Atoms in Optical Lattices

TL;DR

This paper proposes a method to simulate (1+1)-dimensional CP(N-1) quantum field theories using alkaline-earth atoms in optical lattices, enabling exploration of features like asymptotic freedom and theta vacua.

Contribution

It introduces a cold atom implementation that realizes the continuum limit of CP(N-1) theories through a ladder system of SU(N) spins derived from alkaline-earth atoms.

Findings

Monte Carlo results support the feasibility of the continuum limit.

Protocol for adiabatic ground state preparation is outlined.

Proposals for experiments on phase diagrams at non-zero density.

Abstract

We propose a cold atom implementation to attain the continuum limit of (1+1)-d CP(N-1) quantum field theories. These theories share important features with (3+1)-d QCD, such as asymptotic freedom and $\theta$ vacua. Moreover, their continuum limit can be accessed via the mechanism of dimensional reduction. In our scheme, the CP(N-1) degrees of freedom emerge at low energies from a ladder system of SU(N) quantum spins, where the N spin states are embodied by the nuclear Zeeman states of alkaline-earth atoms, trapped in an optical lattice. Based on Monte Carlo results, we establish that the continuum limit can be demonstrated by an atomic quantum simulation by employing the feature of asymptotic freedom. We discuss a protocol for the adiabatic state preparation of the ground state of the system, the real-time evolution of a false $\theta$-vacuum state after a quench, and we propose experiments to unravel the phase diagram at non-zero density.