Abstract
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 {{mathbb{Z}}}_{2} 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.
Highlights
Non-Hermitian systems exhibit markedly different phenomena than their conventional Hermitian counterparts
We show that non-Hermitian lattice dynamics does provide a unique means for constructing enhanced sensors; this advantage persists even when operating in truly quantum regimes
Somewhat surprisingly, that the nonHermitian skin effect does not provide any advantage over more traditional sensing protocols. We find another distinct non-Hermitian mechanism that enables a dramatic enhancement of measurement sensitivity: the quantum Fisher information per photon exhibits an exponential scaling with system size
Summary
Non-Hermitian systems exhibit markedly different phenomena than their conventional Hermitian counterparts. We show that certain asymmetric non-Hermitian tight-binding models with a Z2 symmetry yield a pronounced sensing advantage: the quantum Fisher information per photon increases exponentially with system size. The paradigmatic example is the so-called “non-Hermitian skin effect”[14,15,16,17], which occurs in several non-Hermitian tight-binding models[18,19,20,21,22] In these systems, all eigenvalues and wavefunctions of the Hamiltonian exhibit a dramatic sensitivity to a change of boundary conditions. Somewhat surprisingly, that the nonHermitian skin effect does not provide any advantage over more traditional sensing protocols Rather, we find another distinct non-Hermitian mechanism that enables a dramatic enhancement of measurement sensitivity: the quantum Fisher information per photon exhibits an exponential scaling with system size. The underlying mechanism makes use of both non-reciprocity and an unusual kind of symmetry breaking
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