# Probing Quantum States with Momentum Boosts

## TL;DR

This paper introduces a method to measure the condensate fraction in a 1D optical lattice by analyzing atom dynamics after a momentum boost, distinguishing superfluid and Mott insulator states.

## Contribution

The paper proposes a novel diagnostic technique using momentum boosts and atom dynamics to determine condensate fractions in optical lattices.

## Key findings

- Superfluid and Mott insulator states show distinct responses to lattice tilting.
- The induced current is linearly related to the condensate fraction.
- Interactions modify the slope of the current-condensate fraction relationship.

## Abstract

We present a technique to diagnose the condensate fraction in a one-dimensional optical lattice of weakly interacting bosons based on the dynamics of the trapped atoms under the influence of a momentum kick. It is shown using the Multi-Configuration Time Dependent Hartree method for Bosons (MCTDHB) that the two extreme cases of the superfluid and Mott insulator states exhibit different behaviors when the lattice is briefly tilted. The current induced by the momentum boost caused by the tilt which depends directly on the amount of phase coherence between the lattice sites is linearly proportional to the condensate fraction. The atom-atom interactions only change the slope of the linear relationship. We discuss the applications of this scheme in magnetic field gradiometery.