Quantum non-Hermitian topological sensors

Florian Koch,Jan Carl Budich

doi:10.1103/physrevresearch.4.013113

Abstract

We investigate in the framework of quantum noise theory how the striking boundary sensitivity recently discovered in the context of non-Hermitian (NH) topological phases may be harnessed to devise novel quantum sensors. Specifically, we study a quantum-optical setting of coupled modes arranged in an array with broken ring geometry that would realize a NH topological phase in the classical limit. Using methods from quantum-information theory of Gaussian states, we show that a small coupling induced between the ends of the broken ring may be detected with a precision that increases exponentially in the number of coupled modes, e.g., by heterodyne detection of two output modes. While this robust effect only relies on reaching a NH topological regime, we identify a resonance phenomenon without direct classical counterpart that provides an experimental knob for drastically enhancing the aforementioned exponential growth. Our findings pave the way towards designing quantum NH topological sensors that may observe with high precision any physical observable that couples to the boundary conditions of the device.

Highlights

The quest for novel sensors that push the fundamental quantum-mechanical precision limits represents a promising direction towards widely applicable quantum technology [1–3]
In closed systems described by a Hermitian Hamiltonian, such energy shifts are always continuous towards perturbations, which may limit the achievable sensitivity of a given setting
Inspired by the classical analysis of Ref. [23], we have presented a quantum theory for a quantum non-Hermitian topological sensor (QUANTOS), the precision of which grows exponentially in system size N in a wide parameter range, provided that the underlying coupled mode model is brought into a NH topological phase

Summary

INTRODUCTION

The quest for novel sensors that push the fundamental quantum-mechanical precision limits represents a promising direction towards widely applicable quantum technology [1–3]. Combining NH sensing with the notion of topological matter [26–29], an enhancement in sensitivity that scales exponentially with system size is promoted to a stable phenomenon independent of fine-tuning [23] Such non-Hermitian topological sensors are based on the energy shift of a topological edge mode in response to small changes in the boundary conditions [11,12,15,23] of a chain in broken ring geometry (cf Fig. 1). The uncertainty in assessing the value of is limited by the Fisher information I[p ] [35] via the Cramér-Rao bound [36–38] The latter equality [Eq (1)], where N denotes the number of modes (system size) of the QUANTOS and κ, α > 0, may be seen as a quantum-mechanical counterpart of the exponentially enhanced sensitivity reported in a classical context in Ref. We reveal a resonance phenomenon that provides an experimental knob for tuning the value of α [see Eq (1)] so as to drastically increase the exponential growth rate of the precision

NON-HERMITIAN TOPOLOGY BY QUANTUM DISSIPATION

INPUT-OUTPUT THEORY OF THE QUANTOS

FISHER INFORMATION AND CRAMÉR-RAO BOUND

EXPONENTIALLY ENHANCED PRECISION

CONCLUDING DISCUSSION