Exponentially-enhanced quantum sensing with non-Hermitian lattice dynamics

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 $${{\mathbb{Z}}}_{2}$$ 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.

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DISORDER INDUCED ORDER IN AN ARRAY OF CHAOTIC DUFFING OSCILLATORS

International Journal of Modern Physics C ◽

10.1142/s0129183112500714 ◽

2012 ◽

Vol 23 (10) ◽

pp. 1250071 ◽

Cited By ~ 3

Author(s):

YOUMING LEI ◽

FULI GUAN

Keyword(s):

Intermediate Phase ◽

Duffing Oscillator ◽

Random Phase ◽

Practical Method ◽

Spatially Extended ◽

Potential Applications ◽

Spatially Extended Systems ◽

The Common ◽

Spatio Temporal ◽

Control And Synchronization

This paper addresses the issue of disorder induced order in an array of coupled chaotic Duffing oscillators which are excited by harmonic parametric excitations. In order to investigate the effect of phase disorder on dynamics of the array, we take into account that individual uncoupled Duffing oscillator with a parametric excitation is chaotic no matter what the initial phase of the excitation is. It is shown that phase disorder by randomly choosing the initial phases of excitations can suppress spatio-temporal chaos in the system coupled by chaotic Duffing oscillators. When all the phases are the same and deterministic, the oscillators remain chaotic and asynchronous no matter what the common phase is. When driven asynchronously by introducing phase disorder, the oscillators coupled in the array appear more regular with increase of the amplitude of random phase, and the highest level of synchrony between them is induced by intermediate phase disorder, displaying a resonance like phenomenon caused from the transition of the coupled oscillators from chaos to periodic motion. Since varying the initial phases of excitations is more feasible than altering parameters intrinsic to the oscillators coupled in an array, this study provides a practical method for control and synchronization of chaotic dynamics in high-dimensional, spatially extended systems, which might have potential applications in engineering, neuroscience and biology.

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Critical non-Hermitian skin effect

Nature Communications ◽

10.1038/s41467-020-18917-4 ◽

2020 ◽

Vol 11 (1) ◽

Cited By ~ 6

Author(s):

Linhu Li ◽

Ching Hua Lee ◽

Sen Mu ◽

Jiangbin Gong

Keyword(s):

Thermodynamic Limit ◽

Skin Effect ◽

Finite Size ◽

System Size ◽

Critical Systems ◽

Anomalous Scaling ◽

Lattice Systems ◽

New Class ◽

Rlc Circuit ◽

Zero Coupling

Abstract Critical systems represent physical boundaries between different phases of matter and have been intensely studied for their universality and rich physics. Yet, with the rise of non-Hermitian studies, fundamental concepts underpinning critical systems - like band gaps and locality - are increasingly called into question. This work uncovers a new class of criticality where eigenenergies and eigenstates of non-Hermitian lattice systems jump discontinuously across a critical point in the thermodynamic limit, unlike established critical scenarios with spectrum remaining continuous across a transition. Such critical behavior, dubbed the “critical non-Hermitian skin effect”, arises whenever subsystems with dissimilar non-reciprocal accumulations are coupled, however weakly. This indicates, as elaborated with the generalized Brillouin zone approach, that the thermodynamic and zero-coupling limits are not exchangeable, and that even a large system can be qualitatively different from its thermodynamic limit. Examples with anomalous scaling behavior are presented as manifestations of the critical non-Hermitian skin effect in finite-size systems. More spectacularly, topological in-gap modes can even be induced by changing the system size. We provide an explicit proposal for detecting the critical non-Hermitian skin effect in an RLC circuit setup, which also directly carries over to established setups in non-Hermitian optics and mechanics.

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