  We observe dynamical fermionization, where the momentum distribution of a
Tonks-Girardeau (T-G) gas of strongly interacting bosons in 1D evolves from
bosonic to fermionic after its axial confinement is removed. The asymptotic
momentum distribution after expansion in 1D is the distribution of rapidities,
which are the conserved quantities associated with many-body integrable
systems. Rapidities have not previously been measured in any interacting
many-body quantum system. Our measurements agree well with T-G gas theory. We
also study momentum evolution after the trap depth is suddenly changed to a new
non-zero value. We observe the predicted bosonic-fermionic oscillations and see
deviations from the theory outside of the T-G gas limit.
