  We use fidelity susceptibility to calculate quantum critical scaling
exponents for a system consisting of $N$ identical bosons interacting with a
single impurity atom in a double well potential (bosonic Josephson junction).
Above a critical value of the boson-impurity interaction energy there is a
spontaneous breaking of $\mathbb{Z}_2$ symmetry corresponding to a second order
quantum phase transition from a balanced to an imbalanced number of particles
in either the left or right hand well. We show that the exponents match those
in the Lipkin-Meshkov-Glick and Dicke models suggesting that the impurity model
is in the same universality class. The phase transition can be interpreted as a
measurement of the position of the impurity by the bosons.
