  The quantum critical detector (QCD), recently introduced for weak-signal
amplification [Opt. Express 27, 10482 (2019)], functions by exploiting high
sensitivity near the phase transition point of first-order quantum phase
transitions. We contrast the behavior of the first-order as well as the
second-order quantum phase transitions (QPTs) in the detector. We find that the
giant sensitivity to a weak input signal, which can be utilized for quantum
amplification, only exists in first-order QPTs. We define two new magnetic
order parameters to quantitatively characterize the first-order QPT of the
interacting spins in the detector. We also introduce the Husimi $Q$-functions
as a powerful tool to show the fundamental change in the ground-state wave
function of the detector during the QPTs and especially, the intrinsic
dynamical change within the detector during a quantum critical amplification.
We explicitly show the high figures of merit of the QCD via the quantum gain
and signal-to-quantum noise ratio. Specifically, we predict the existence of a
universal first-order QPT in the interacting spin system resulting from two
competing ferromagnetic orders. Our results motivate new designs of weak signal
detectors by engineering first-order QPTs, which are of fundamental
significance in the search for new particles, quantum metrology, and
information science.
