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Young Scientists Forum 2017

Toward performing angular rotating measure of Heisenberg scaling by using the four-photon Holland-Burnett state

Jiandong Zhang, Zijing Zhang, Longzhu Cen, Shuo Li, Feng Wang, Yuan Zhe Zhao

Published Mar 5, 2018• 0 citations
Publisher

Abstract

Quantum process tomography, as an advanced means of metrology, has a capacious range of applications for estimating numerous meaningful parameters. The parameter estimate precision of using coherent state and single photon state as probe are limited by the shot noise limit. Here we demonstrate a quantum enhanced rotating angle measure scheme based on the four-photon Holland-Burnett state can achieve the Heisenberg scaling by the coincidence counting technology. At the same time, the output signal of our scheme has an 8-fold super-resolution compared to the Malus law. In addition, the accuracy achieved by four photons is consistent with using 12 photons of single photon probe. That has incomparable preponderance in a situation in which only weak light can be exploited, like the measure of frangible biological specimens and photosensitive crystals. Moreover, the four-photon Holland-Burnett state can be generated by a polarization-entangled light source. These ensure that our scheme has a champaign application prospect.

DOI
10.1117/12.2303474

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Quantum process tomography, as an advanced means of metrology, has a capacious range of applications for estimating numerous meaningful parameters. The parameter estimate precision of using coherent state and single photon state as probe are limited by the shot noise limit. Here we demonstrate a quantum enhanced rotating angle measure scheme based on the four-photon Holland-Burnett state can achieve the Heisenberg scaling by the coincidence counting technology. At the same time, the output signal of our scheme has an 8-fold super-resolution compared to the Malus law. In addition, the accuracy achieved by four photons is consistent with using 12 photons of single photon probe. That has incomparable preponderance in a situation in which only weak light can be exploited, like the measure of frangible biological specimens and photosensitive crystals. Moreover, the four-photon Holland-Burnett state can be generated by a polarization-entangled light source. These ensure that our scheme has a champaign application prospect.
A fundamental task in photonics is to characterise an unknown optical process, defined by properties such as birefringence, spectral response, thickness and flatness. Amongst many ways to achieve this, single-photon probes can be used in a method called quantum process tomography (QPT). Furthermore, QPT is an essential method in determining how a process acts on quantum mechanical states. For example for quantum technology, QPT is used to characterise multi-qubit processors and quantum communication channels; across quantum physics QPT of some form is often the first experimental investigation of a new physical process, as shown in the recent research into coherent transport in biological mechanisms. However, the precision of QPT is limited by the fact that measurements with single-particle probes are subject to unavoidable shot noise---this holds for both single photon and laser probes. In situations where measurement resources are limited, for example, where the process is rapidly changing or the time bandwidth is constrained, it becomes essential to overcome this precision limit. Here we devise and demonstrate a scheme for tomography which exploits non-classical input states and quantum interferences; unlike previous QPT methods our scheme capitalises upon the possibility to use simultaneously multiple photons per mode. The efficiency---quantified by precision per photon used---scales with larger photon number input states. Our demonstration uses four-photon states and our results show a substantial reduction of statistical fluctuations compared to traditional QPT methods---in the ideal case one four-photon probe state yields the same amount of statistical information as twelve single probe photons.
Quantum metrology bears a great promise in enhancing measurement precision, but is unlikely to become practical in the near future. Its concepts can nevertheless inspire classical or hybrid methods of immediate value. Here we demonstrate NOON-like photonic states of m quanta of angular momentum up to m=100, in a setup that acts as a ‘photonic gear’, converting, for each photon, a mechanical rotation of an angle θ into an amplified rotation of the optical polarization by mθ, corresponding to a ‘super-resolving’ Malus’ law. We show that this effect leads to single-photon angular measurements with the same precision of polarization-only quantum strategies with m photons, but robust to photon losses. Moreover, we combine the gear effect with the quantum enhancement due to entanglement, thus exploiting the advantages of both approaches. The high ‘gear ratio’ m boosts the current state of the art of optical non-contact angular measurements by almost two orders of magnitude. Beating the standard measurement limits is a goal of metrology, as it would allow for more precise estimation of physical quantities. Borrowing concepts from NOON-state quantum metrology, this work presents a single-photon scheme to measure rotation angles of light with super-resolution precision.
Circular polarization-entangled photons can be used to obtain an enhancement of the precision in a rotation measurement. In this paper, the method of entanglement transformation is used to produce NOON states in circular polarization from a readily generated linear polarization-entangled photon source. Detection of NNN-fold coincidences serves as the postselection and NNN-fold superoscillating fringes are obtained simultaneously. A parity strategy and conditional probabilistic statistics contribute to a better fringe, saturating the angle sensitivity to the Heisenberg limit. The impact of imperfect state preparation and detection is discussed both separately and jointly. For the separated case, the influence of each system imperfection is pronounced. For the joint case, the feasibility region for surpassing the standard quantum limit is given. Our work pushes the state preparation of circular polarization-entangled photons to the same level as that in the case of linear polarization. It is also confirmed that entanglement can be transformed into different frames for specific applications, serving as a useful scheme for using entangled sources.
Quantum metrology leverages quantum correlations for enhanced parameter estimation. Recently, structured light enabled increased resolution and sensitivity in quantum metrology systems. However, lossy and complex setups impacting photon flux hinder true quantum advantage while using high dimensional structured light. We introduce a straightforward mechanical rotation quantum sensing mechanism, employing high-dimensional structured light and use it with a high-flux (45 000 coincidence counts per second) N00N state source with N = 2. The system utilizes two opposite spiral phase plates with topological charge of up to ℓ = 16 that converts mechanical rotation into wavefront phase shifts and exhibit a 16-fold enhanced super-resolution and 25-fold enhanced sensitivity between different topological charges, while retaining the acquisition times, and with negligible change in coincidence count. Furthermore, the high efficiency together with the high photon flux enables detection of mechanical angular acceleration in real-time. Our approach paves the way for highly sensitive quantum measurements, applicable to various interferometric schemes.
We propose a quantum process tomography scheme that utilizes two-mode squeezed vacuum to realize the parameter estimation with Heisenberg scaling. The objective is to estimate a rotating angle of polarization and parity detection is used as the detection strategy. With the help of symplectic matrix theory, we discuss the estimation visibility and sensitivity of output signal in lossless situation, the quantum Fisher information is also given via calculation. Finally, the impacts of two realistic factors on both visibility and sensitivity are also considered, including photon loss during the input generation, and photon loss along with thermal noise during the output detection.
Quantum metrology leverages quantum correlations for enhanced parameter estimation. Recently, structured light enabled increased resolution and sensitivity in quantum metrology systems. However, lossy and complex setups impacting photon flux, hinder true quantum advantage while using high dimensional structured light. We introduce a straightforward mechanical rotation quantum sensing mechanism, employing high-dimensional structured light and a compact high-flux (45,000 coincidence counts per second) N00N state source with N=2. The system utilizes two opposite spiral phase plates with topological charge of up to l=16 that convert mechanical rotation into wavefront phase shifts, and exhibit a 16-fold enhanced super-resolution and 25-fold enhanced sensitivity between different topological charges, while retaining the acquisition times and with negligible change in coincidence count. Furthermore, the high photon flux enables to detect mechanical angular acceleration in real-time. Our approach paves the way for highly sensitive quantum measurements, applicable to various interferometric schemes.