Nonlinear Interferometry for Quantum-Enhanced Measurements of Multiphoton Absorption

Open Access

Nonlinear Interferometry for Quantum-Enhanced Measurements of Multiphoton Absorption

Shahram Panahiyan, Carlos Sánchez Muñoz, Maria V. Chekhova, and Frank Schlawin

Phys. Rev. Lett. 130, 203604 – Published 19 May 2023

Abstract

Multiphoton absorption is of vital importance in many spectroscopic, microscopic, or lithographic applications. However, given that it is an inherently weak process, the detection of multiphoton absorption signals typically requires large field intensities, hindering its applicability in many practical situations. In this Letter, we show that placing a multiphoton absorbent inside an imbalanced nonlinear interferometer can enhance the precision of multiphoton cross section estimation with respect to strategies based on photon-number measurements using coherent or even squeezed light directly transmitted through the medium. In particular, the power scaling of the sensitivity with photon flux can be increased by 1 order compared with transmission measurements of the sample with coherent light, such that the measurement precision at any given intensity can be greatly enhanced. Furthermore, we show that this enhanced measurement precision is robust against experimental imperfections leading to photon losses, which usually tend to degrade the detection sensitivity. We trace the origin of this enhancement to an optimal degree of squeezing which has to be generated in a nonlinear SU(1,1) interferometer.

Received 6 October 2022
Revised 30 March 2023
Accepted 25 April 2023

DOI:https://doi.org/10.1103/PhysRevLett.130.203604

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Open access publication funded by the Max Planck Society.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Light propagation, transmission & absorption Nonclassical interferometry Photon statistics Quantum metrology Squeezing of quantum noise

Atomic, Molecular & OpticalCondensed Matter, Materials & Applied PhysicsFluid DynamicsGravitation, Cosmology & AstrophysicsNetworksNuclear PhysicsPhysics Education ResearchPolymers & Soft MatterStatistical Physics & ThermodynamicsQuantum Information, Science & TechnologyPlasma PhysicsParticles & FieldsNonlinear DynamicsInterdisciplinary PhysicsGeneral PhysicsEnergy Science & TechnologyPhysics of Living SystemsAccelerators & Beams

Authors & Affiliations

Shahram Panahiyan ^1,2,3,*, Carlos Sánchez Muñoz ⁴, Maria V. Chekhova^5,6, and Frank Schlawin ^1,2,3,†

¹Max Planck Institute for the Structure and Dynamics of Matter, Luruper Chaussee 149, 22761 Hamburg, Germany
²The Hamburg Centre for Ultrafast Imaging, Luruper Chaussee 149, Hamburg D-22761, Germany
³University of Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
⁴Departamento de Física Teórica de la Materia Condensada and Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid, 28049 Madrid, Spain
⁵Max-Planck Institute for the Science of Light, Staudtstraße 2, Erlangen D-91058, Germany
⁶University of Erlangen-Nuremberg, Staudtstraße 7/B2, Erlangen D-91058, Germany

^*shahram.panahiyan@mpsd.mpg.de
^†frank.schlawin@mpsd.mpg.de

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Issue

Vol. 130, Iss. 20 — 19 May 2023

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Images

Figure 1
(a) The setup considered in this manuscript. A coherent seed pulse passes through a first degenerate OPA on the left which prepares a squeezed state. It is focused on an $m$ -photon absorption sample, where a part of the light field is lost due to single-photon scattering. The transmitted light field is then focused on a second degenerate OPA. The light field finally reaches the detection device on the right where imperfect detection gives rise to another loss source. (b) Variance $Δ ϵ_{2, SU (1, 1)}^{2}$ for two-photon absorption ( $m = 2$ ) with $η_{In} = η_{Ex} = 1$ , and $n_{S} = 15$ , as a function of interferometer and laser phases (upper panel with $r_{1} = 0.939$ and $r_{2} = 1.447$ ) and also as a function of squeezing parameters (lower panel with $ϕ_{Las} = π / 2$ and $ϕ_{Int} = π$ ). The sensitivity becomes independent of the second squeezing parameter for a sufficiently large second squeezing parameter $r_{2}$ . The light blue line maps optimal regimes of squeezing parameters. (c) $Δ ϵ_{m, SU (1, 1)}^{2}$ (dotted-dashed lines) and Eq. (7) (solid lines) as a function of second squeezing parameter for different photon numbers at the sample ( $n_{S}$ ). We observe that for sufficiently large second squeezing parameter $r_{2}$ , $Δ ϵ_{m, SU (1, 1)}^{2}$ converges to the scaling behavior reported in Eq. (7) (for sufficiently high $n_{S}$ ).
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Figure 2
(a) Optimum $Δ ϵ_{m}^{2}$ as a function of the photon number interacting with the sample, $n_{S}$ . We observe that squeezing inside the SU(1,1) interferometer enhances the best achievable sensitivity compared with a classical interferometer. (b) Eq. (5) is shown in the limit of very large $r_{2}$ as a function of external losses for optimized SU(1,1) measurements (solid lines) and coherent states (dashed lines) in the case of one-, two-, three-, and four-photon absorption. By adjusting the squeezing parameters, the effects of external loss can be completely compensated in the SU(1,1) case. (c) Scaling exponent $γ$ of the sensitivity (i.e., $Δ ϵ_{m}^{2} \sim n_{S}^{- γ}$ ) as a function of the internal loss. SU(1,1) interferometric measurements show superior precision scaling compared with coherent state measurements even in the presence of strong internal loss, up to $\sim 10 %$ . (d) The optimal squeezing parameter $r_{1}$ as a function of photon number for three different levels of internal loss. Overall, we observe that higher-order nonlinear processes have better sensitivity indicating that the measurement of the cross section in samples with higher-order nonlinear processes has better precision.
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