Three-body contact of the unitary Fermi gas

The unitary Fermi gas is a notable example of strongly correlated system realized with cold atoms. Tan's contact is a universal physical quantity that characterizes two-body correlations, such as the number of pairs at short distance, the momentum distribution, and the variation of energy. While various experimental and theoretical works have successfully determined accurate values of the two-body contact, much less is known about the three-body contact which characterizes three-body correlations: the number of the triplets at short distance, and the three-body recombination rate [1,2].

Here, we determine the three-body contact for the unitary Fermi gas and its temperature dependence. First, we calculate the three-body contact for three trapped fermions at zero temperature by solving the three-body problem, and validate the result through comparison between several different methods. We then use this value to extract the three-body contact density of many-body fermions from measurements of the three-body loss rates for three and many fermions. The obtained three-body contact agrees with the virial expansion at high temperature, whereas it is significantly suppressed at low temperatures, unveiling non-trivial three-body correlations in the strongly correlated quantum many-body system.