Quantum enhanced imaging of nonuniform refractive profiles

Giuseppe Ortolano,Enrico Predazzi,Ivano Ruo-Berchera

doi:10.1142/s0219749919410107

Abstract

In this work, quantum metrology techniques are applied to the imaging of objects with a nonuniform refractive spatial profile. A sensible improvement on the classical accuracy is shown to be found when the “Twin Beam (TWB) State” is used. In particular, exploiting the multimode spatial correlation, naturally produced in the Parametric Down Conversion (PDC) process, allows a 2D reconstruction of complex spatial profiles, thus enabling an enhanced imaging. The idea is to use one of the spatially multimode beams to probe the sample and the other as a reference to reduce the noise. A similar model can also be used to describe wave front distortion measurements. The model is meant to be followed by a first experimental demonstration of such enhanced measurement scheme.

Highlights

A state often used in such schemes is the Twin Beam (TWB) state produced by the process of Parametric Down Conversion (PDC)[33,34] or four-wave mixing.[35,36]
This state is interesting because the use of quantum correlations allows a reduction of the uncertainty of an estimation below the Shot Noise Limit (SNL), and because of the spatial multimode nature of the PDC process, that automatically enables wideeld imaging, meaning that a 2D spatial prole can be imaged with a single exposure.[32]
It can be expected that the TWB state, as it is in the case of absorption imaging, can be used to achieve sub-SNL measurements of nonuniform refractive proles and aim of this work is, to investigate the improvements that the use of quantum correlations would bring to such measurements

Summary

Introduction

Quantum states of light have been proven successful in the enhancement of a variety of measurement schemes,[1,2] such as undetected photon imaging,[3] quantum illumination,[4,5,6] super resolution,[7,8] ghost imaging,[9,10,11,12,13,14] interferometry[15,16,17,18] and absorption imaging.[2,19,20,21] In particular, a fundamental limit in the accuracy of classical schemes is the Shot Noise Limit (SNL),[22,23] that bounds the uncertainty in the estimation of a parameter to scale as the inverse square root of. A state often used in such schemes is the Twin Beam (TWB) state produced by the process of Parametric Down Conversion (PDC)[33,34] or four-wave mixing.[35,36] In PDC, a laser pump interacts with a nonlinear crystal creating, as a result, a pair of photons correlated both in position and momentum This state is interesting because the use of quantum correlations allows a reduction of the uncertainty of an estimation below the SNL, and because of the spatial multimode nature of the PDC process, that automatically enables wideeld imaging, meaning that a 2D spatial prole can be imaged with a single exposure.[32] It can be expected that the TWB state, as it is in the case of absorption imaging, can be used to achieve sub-SNL measurements of nonuniform refractive proles and aim of this work is, to investigate the improvements that the use of quantum correlations would bring to such measurements. Interference e®ects are not considered here given the incoherent properties of the multimode source

The Model

Direct scheme and SNL

Correlation based scheme

Results and Discussion

Conclusions