# Engineering First-Order Quantum Phase Transitions for Weak Signal Detection

## TL;DR

This paper demonstrates that first-order quantum phase transitions enable high sensitivity for weak signal detection, offering a new approach for quantum amplification and detector design.

## Contribution

It introduces a detailed analysis of first-order QPTs in quantum detectors, including new order parameters and the use of Husimi Q-functions to characterize ground-state changes.

## Key findings

- First-order QPTs exhibit giant sensitivity for weak signals.
- Husimi Q-functions reveal fundamental ground-state changes during QPTs.
- Quantum gain and signal-to-noise ratio are significantly enhanced in first-order QPT-based detectors.

## Abstract

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.