Creating triple-NOON states with ultracold atoms via chaos-assisted tunneling

TL;DR

This paper proposes a method to efficiently generate triple-NOON states with ultracold atoms in a three-site lattice by using chaos-assisted tunneling, significantly reducing the required evolution time.

Contribution

It introduces a chaos-assisted tunneling protocol that enables rapid creation of triple-NOON states in ultracold atom systems, enhancing practical feasibility.

Findings

Triple-NOON states can be generated with N=5 particles in a few seconds.

Periodic driving induces classical chaos, speeding up collective tunneling.

The superposition purity remains high despite the speed-up.

Abstract

Triple-NOON states are superpositions of the form $e^{i \varphi_1} |{N,0,0}\rangle + e^{i \varphi_2} |{0,N,0}\rangle + e^{i \varphi_3} |{0,0,N}\rangle$ involving $N$ bosonic quanta distributed over three modes. We theoretically show how such highly entangled states can be generated with interacting ultracold bosonic atoms in a symmetric three-site lattice. The basic protocol consists in preparing all atoms on one site of the lattice and then letting the system evolve during a specific time such that collective tunneling of the atoms to the other two sites takes place. The key point put forward here is that this evolution time can be reduced by several orders of magnitude via the application of a periodic driving of the lattice, thereby rendering this protocol feasible in practice. This driving is suitably tuned such that classical chaos is generated in the entire accessible phase space except for the Planck cells that host the states participating at the above triple-NOON superposition. Chaos-assisted tunneling can then give rise to a dramatic speed-up of this collective tunneling process, without significantly affecting the purity of this superposition. A triple-NOON state containing $N = 5$ particles can thereby be realized with $^{87}$Rb atoms on time scales of the order of a few seconds.