Matter Wave Scattering from Ultracold Atoms in an Optical Lattice

TL;DR

This paper investigates how matter wave scattering can be used to non-destructively identify the quantum phase (superfluid or Mott insulator) of ultracold atoms in an optical lattice, providing analytical and numerical insights.

Contribution

It introduces a method to determine the many-body phase of atoms in an optical lattice via matter wave scattering, combining analytical calculations with numerical simulations.

Findings

Scattering cross sections are strongly affected by the many-body phase.

Analytical expressions are derived in the first Born approximation.

Numerical diagonalization reveals phase transition signatures.

Abstract

We study matter wave scattering from an ultracold, many body atomic system trapped in an optical lattice. We determine the angular cross section that a matter wave probe sees and show that it is strongly affected by the many body phase, superfluid or Mott insulator, of the target lattice. We determine these cross sections analytically in the first Born approximation, and we examine the variation at intermediate points in the phase transition by numerically diagonalizing the Bose Hubbard Hamiltonian for a small lattice. We show that matter wave scattering offers a convenient method for non-destructively probing the quantum many body phase transition of atoms in an optical lattice.