Exponentially-enhanced quantum sensing with non-Hermitian lattice dynamics

<jats:title>Abstract</jats:title><jats:p>Non-Hermitian systems exhibit markedly different phenomena than their conventional Hermitian counterparts. Several such features, such as the non-Hermitian skin effect, are only present in spatially extended systems. Potential applications of these effects in many-mode systems however remains largely unexplored. Here, we study how unique features of non-Hermitian lattice systems can be harnessed to improve Hamiltonian parameter estimation in a fully quantum setting. While the quintessential non-Hermitian skin effect does not provide any distinct advantage, alternate effects yield dramatic enhancements. We show that certain asymmetric non-Hermitian tight-binding models with a <jats:inline-formula><jats:alternatives><jats:tex-math>$${{\mathbb{Z}}}_{2}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mrow> <mml:mi>Z</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msub> </mml:math></jats:alternatives></jats:inline-formula> symmetry yield a pronounced sensing advantage: the quantum Fisher information per photon increases exponentially with system size. We find that these advantages persist in regimes where non-Markovian and non-perturbative effects become important. Our setup is directly compatible with a variety of quantum optical and superconducting circuit platforms, and already yields strong enhancements with as few as three lattice sites.</jats:p>