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arXiv:2006.12114 · Quantum

Weakly invasive metrology: quantum advantage and physical implementations

Martí Perarnau-Llobet, Daniel Malz, J. I. Cirac

Published Apr 28, 2021• 9 citations
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Abstract

We consider the estimation of a Hamiltonian parameter of a set of highly photosensitive samples, which are damaged after a few photons Nabs are absorbed, for a total time T . The samples are modelled as a two mode photonic system, where photons simultaneously acquire information on the unknown parameter and are absorbed at a fixed rate. We show that arbitrarily intense coherent states can obtain information at a rate that scales at most linearly with Nabs and T , whereas quantum states with finite intensity can overcome this bound. We characterise the quantum advantage as a function of Nabs and T , as well as its robustness to imperfections (non-ideal detectors, finite preparation and measurement rates for quantum photonic states). We discuss an implementation in cavity QED, where Fock states are both prepared and measured by coupling atomic ensembles to the cavities. We show that superradiance, arising due to a collective coupling between the cavities and the atoms, can be exploited for improving the speed and efficiency of the measurement.

DOI
10.22331/q-2021-04-28-446

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We consider the estimation of a Hamiltonian parameter of a set of highly photosensitive samples, which are damaged after a few photons Nabs are absorbed, for a total time T . The samples are modelled as a two mode photonic system, where photons simultaneously acquire information on the unknown parameter and are absorbed at a fixed rate. We show that arbitrarily intense coherent states can obtain information at a rate that scales at most linearly with Nabs and T , whereas quantum states with finite intensity can overcome this bound. We characterise the quantum advantage as a function of Nabs and T , as well as its robustness to imperfections (non-ideal detectors, finite preparation and measurement rates for quantum photonic states). We discuss an implementation in cavity QED, where Fock states are both prepared and measured by coupling atomic ensembles to the cavities. We show that superradiance, arising due to a collective coupling between the cavities and the atoms, can be exploited for improving the speed and efficiency of the measurement.
Quantum estimation of parameters defining open-system dynamics may be enhanced by using ancillas that are entangled with the probe but are not submitted to the dynamics. Here we consider the important problem of estimation of transmission of light by a sample, with losses due to absorption and scattering. We show, through the determination of the quantum Fisher information, that the ancilla strategy leads to the best possible precision in single-mode estimation—the one obtained for a Fock-state input—through joint photon counting of probe and ancilla, which are modes of a bimodal squeezed state produced by an optical parametric amplifier. This proposal overcomes the challenge of producing and detecting high-photon-number Fock states, and it is quite robust in the presence of additional noise: We show that it is immune to phase noise and the precision does not change if the incoming state gets disentangled. Furthermore, the quantum gain is still present under moderate photon losses of the input beams. We also discuss an alternative to joint photon counting, which is readily implementable with present technology and approaches the quantum Fisher information result for weak absorption, even with moderate photon losses of the input beams before the sample is probed: a time-reversal procedure, placing the sample between two optical parametric amplifiers, with the second undoing the squeezing produced by the first one. The precision of estimation of the loss parameter is obtained from the average outgoing total photon number and its variance. In both procedures, the state of the probe and the detection procedure are independent of the value of the parameter. Published by the American Physical Society 2024
Abstract Two-photon absorption (TPA) is a nonlinear optical process with wide-ranging applications from spectroscopy to super-resolution imaging. Despite this, the precise measurement and characterisation of TPA parameters are challenging due to their inherently weak nature. We study the potential of single-mode quantum light to enhance TPA parameter estimation through the quantum Fisher information (QFI). Discrete variable quantum states (defined to be a finite superposition of Fock states) are optimised to maximise the QFI for given absorption, revealing a quantum advantage compared to both the coherent state (classical) benchmark and the single-mode squeezed vacuum state. For fixed average energy n ¯ ∈ 2 N , the Fock state is shown to be optimal for large TPA parameters, while a superposition of vacuum and a particular Fock state is optimal for small absorption for all n ¯ . This differs from single-photon absorption where the Fock state is always optimal. Notably, photon counting is demonstrated to offer optimal or nearly optimal performance compared to the QFI bound for all levels of TPA parameters for the optimised quantum probes, and their quantum advantage is shown to be robust to single-photon loss. Our findings provide insight into known limiting behaviours of Gaussian probes and their different FI scalings under photon counting ( ∝ n ¯ 2 for squeezed vacuum states versus n ¯ 3 for coherent states). The squeezed state outperforms coherent states for small TPA parameters but underperforms in the intermediate regime, becoming comparable in the large absorption limit. This can be explained through fundamental differences between behaviours of even and odd number Fock states: the former’s QFI diverges in both large and small absorption limits, while the latter diverges only in the small absorption limit, dominating at intermediate scales.
Photonic states with large and fixed photon numbers, such as Fock states, enable quantum-enhanced metrology but remain an experimentally elusive resource. A potentially simple, deterministic, and scalable way to generate these states consists of fully exciting NNN quantum emitters equally coupled to a common photonic reservoir, which leads to a collective decay known as Dicke superradiance. The emitted NNN-photon state turns out to be a highly entangled multimode state, and to characterize its metrological properties in this work we (i) develop theoretical tools to compute the quantum Fisher information of general multimode photonic states, (ii) use it to show that Dicke superradiant photons in one-dimensional waveguides achieve Heisenberg scaling, which can be saturated by a parity measurement, and (iii) study the robustness of these states to experimental limitations in state-of-the-art atom-waveguide QED setups.
Absorption and gain processes are fundamental to any light-matter interaction and a precise measurement of these parameters is important for various scientific and technological applications. Quantum probes, specifically the squeezed states, have proved very successful, particularly in the applications that deal with phase shift and force measurements. In this paper, we focus on improving the sensitivity of the estimation of the photon-loss coefficient of a weakly absorbing medium as well as the estimation of the gain parameter using a two-mode bright squeezed state. The generation of this state combines the advantage of a coherent beam for its large photon number with the quantum properties of the two-mode squeezing operation in an optical parametric amplifier. We present two measurement schemes: balanced photodetection and time-reversed metrology, both utilizing two-mode bright squeezed light. The maximum quantum advantage we can achieve using two-mode bright squeezed light is 3.7 times for the absorption parameter $\ensuremath{\alpha}=0.05$ and 8.4 times for $\ensuremath{\alpha}=0.01$ as compared to using only the coherent state. Similarly, the maximum quantum advantage for the estimation of optical gain is found around 2.95 times for the gain coefficient G=1.05G=1.05G=1.05 and around 6.35 times for G=1.01G=1.01G=1.01. We discuss the significance of using one measurement scheme over the other under different squeezing conditions. We compare our results with the Cram\'er-Rao bound for a two-mode bright squeezed state to assess the quality of the proposed methodologies.
In conventional measurement, to reach the greatest accuracy of parameter estimation, all samples must be measured since each independent sample contains the same quantum Fisher information. In postselected metrology, postselection can concentrate the quantum Fisher information of the initial samples into a tiny post-selected sub-ensemble. It has been proven that this quantum advantage can not be realized in any classically commuting theory. In this work, we present that the advantage of postselection in weak value amplification (WVA) can not be achieved without quantum coherence. The quantum coherence of the initial system is closely related to the preparation costs and measurement costs in parameter estimation. With the increase of initial quantum coherence, the joint values of preparation costs and measurement costs can be optimized to smaller. Moreover, we derive an analytical tradeoff relation between the preparation, measurement and the quantum coherence. We further experimentally test the tradeoff relation in a linear optical setup. The experimental and theoretical results are in good agreement and show that the quantum coherence plays a key role in bounding the resource costs in the postselected metrology process.
Optical quantum metrology uses specially-prepared states of light to probe sensitive samples. Choosing a suitable probe state allows one to extract more information per probe photon about an unknown parameter than is possible using any classical technique. In effect, these techniques improve the sensitivity of the measurement whenever the number of probe photons is constrained in some way. This thesis presents experimental and theoretical results on the use of pairs of time-frequency entangled photons in precision measurements. It begins with an overview of necessary background knowledge about quantum optics and quantum information. This is followed by a theoretical discussion on the estimation of a single delay using two-photon interference. We show that constraints on the probe photon's bandwidth complicate the measurement problem, requiring suitable optimization of the two-photon quantum state to avoid losing precision. We then consider the use of two-photon interference for linear spectroscopic measurements. Linear spectroscopy relates the absorption and phase spectrum of a sample to unknown electronic parameters. We describe a proof-of-principle experiment demonstrating that two-photon interferometric spectroscopy can be used for simultaneously measurement of both absorption and phase. This is followed by an information-theoretic discussion of the precision of this technique. For low losses, we show that the method provides phase sensitivity similar to classical interferometry while approaching the optimal absorption precision of any possible measurement. If the absorption and phase values are both related to a single unknown parameter, then our technique provides improved sensitivity to this parameter compared to both classical measurements and other quantum techniques in the presence of realistic levels of loss. We conclude with a discussion of quantum-optical coherence tomography, which is a two-photon interferometric method for determining the material structure of a sample. We present an ongoing experiment which aims to apply the method to tissue-like samples, where the quantum measurement is limited by a poor signal-to-noise ratio. Preliminary results demonstrate that this noise can be largely reduced by suitable frequency-domain filtering. This allows us to precisely determine the position of a scattering center using a few hundred detected photon pairs despite the presence of large amounts of noise. We follow this with a theoretical discussion of signal artifacts which are known to complicate the measured interferogram. We show these artifacts are due to a distinct interferometric effect, which can be distinguished from the signal of interest using the relative time delay between detected photons. We conclude with a brief discussion on possible techniques for artifact removal.