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A key observable in investigations into quantum systems are the $n$-bodycorrelation functions, which provide a powerful tool for experimentallydetermining coherence and directly probing the many-body wavefunction. Whilethe (bosonic) correlations of photonic systems are well explored, thecorrelations present in matter-wave systems, particularly for fermionic atoms,are still an emerging field. In this work, we use the unique single-atomdetection properties of $^3$He* atoms to perform simultaneous measurements ofthe $n$-body quantum correlations, up to the fifth-order, of a degenerate Fermigas. In a direct demonstration of the Pauli exclusion principle, we observeclear anti-bunching at all orders and find good agreement with predictedcorrelation volumes. Our results pave the way for using correlation functionsto probe some of the rich physics associated with fermionic systems, such asd-wave pairing in superconductors.

$n$-body anti-bunching in a degenerate Fermi gas of $^3$He* atoms