Quantum squeezing and sensing with pseudo anti-parity-time symmetry

The emergence of parity-time ($\mathcal{PT}$) symmetry has greatly enriched our study of symmetry-enabled non-Hermitian physics, but the realization of quantum $\mathcal{PT}$-symmetry faces an intrinsic issue of unavoidable symmetry-breaking Langevin noises. Here we construct a quantum pseudo-anti-$\mathcal{PT}$ (pseudo-$\mathcal{APT}$) symmetry in a two-mode bosonic system without involving Langevin noises. We show that the spontaneous pseudo-$\mathcal{APT}$ symmetry breaking leads to an exceptional point, across which there is a transition between different types of quantum squeezing dynamics, i.e., the squeezing factor increases exponentially (oscillates periodically) with time in the pseudo-$\mathcal{APT}$ symmetric (broken) region. Such dramatic changes of squeezing factors and quantum dynamics near the exceptional point are utilized for ultra-precision quantum sensing. These exotic quantum phenomena and sensing applications can be experimentally observed in two physical systems: spontaneous wave mixing nonlinear optics and atomic Bose-Einstein condensates. Our work offers a physical platform for investigating exciting $\mathcal{APT}$ symmetry physics in the quantum realm, paving the way for exploring fundamental quantum non-Hermitian effects and their quantum technological applications.