# Momentum-space atom correlations in a Mott insulator

## TL;DR

This study explores momentum-space correlations in bosonic Mott insulators, revealing how correlations and quasi-particle spectral weight evolve with tunneling, providing insights into many-body ground states and transition dynamics.

## Contribution

It provides the first detailed measurement of three-dimensional momentum-space correlations in a Mott insulator, linking correlation lengths to in-trap size and analyzing spectral weight changes near the superfluid transition.

## Key findings

- Two-body and three-body correlations show perfect bunching with reciprocal lattice periodicity.
- Correlation length inversely proportional to in-trap size, matching incoherent lattice predictions.
- Spectral weight of quasi-particles decreases as the system approaches superfluidity, indicating increased mobility.

## Abstract

We report on the investigation of the three-dimensional single-atom-resolved distributions of bosonic Mott insulators in momentum-space. Firstly, we measure the two-body and three-body correlations deep in the Mott regime, finding a perfectly contrasted bunching whose periodicity reproduces the reciprocal lattice. In addition, we show that the two-body correlation length is inversely proportional to the in-trap size of the Mott state with a pre-factor in agreement with the prediction for an incoherent state occupying a uniformly filled lattice. Our findings indicate that the momentum-space correlations of a Mott insulator at small tunnelling is that of a many-body ground-state with Gaussian statistics. Secondly, in the Mott insulating regime with increasing tunnelling, we extract the spectral weight of the quasi-particles from the momentum density profiles. On approaching the transition towards a superfluid, the momentum spread of the spectral weight is found to decrease as a result of the increased mobility of the quasi-particles in the lattice. While the shapes of the observed spectral weight agree with the ones predicted by perturbative many-body calculations, the fitted mobilities are larger than the theoretical ones. This discrepancy is similar to that previously reported on the time-of-flight visibility.