Unraveling Two-Photon Entanglement via the Squeezing Spectrum of Light Traveling through Nanofiber-Coupled Atoms

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Unraveling Two-Photon Entanglement via the Squeezing Spectrum of Light Traveling through Nanofiber-Coupled Atoms

Jakob Hinney, Adarsh S. Prasad, Sahand Mahmoodian, Klemens Hammerer, Arno Rauschenbeutel, Philipp Schneeweiss, Jürgen Volz, and Max Schemmer

Phys. Rev. Lett. 127, 123602 – Published 14 September 2021

Abstract

We observe that a weak guided light field transmitted through an ensemble of atoms coupled to an optical nanofiber exhibits quadrature squeezing. From the measured squeezing spectrum we gain direct access to the phase and amplitude of the energy-time entangled part of the two-photon wave function which arises from the strongly correlated transport of photons through the ensemble. For small atomic ensembles we observe a spectrum close to the line shape of the atomic transition, while sidebands are observed for sufficiently large ensembles, in agreement with our theoretical predictions. Furthermore, we vary the detuning of the probe light with respect to the atomic resonance and infer the phase of the entangled two-photon wave function. From the amplitude and the phase of the spectrum, we reconstruct the real and imaginary part of the time-domain wave function. Our characterization of the entangled two-photon component constitutes a diagnostic tool for quantum optics devices.

Received 20 November 2020
Accepted 22 July 2021

DOI:https://doi.org/10.1103/PhysRevLett.127.123602

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.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Light-matter interaction Nanophotonics Quantum description of light-matter interaction Quantum optics

Atomic, Molecular & Optical

Authors & Affiliations

Jakob Hinney^1,†, Adarsh S. Prasad¹, Sahand Mahmoodian ^2,*,‡, Klemens Hammerer ², Arno Rauschenbeutel^1,3, Philipp Schneeweiss ^1,3, Jürgen Volz^1,3, and Max Schemmer ^3,§

¹Vienna Center for Quantum Science and Technology, TU Wien-Atominstitut, Stadionallee 2, 1020 Vienna, Austria
²Institute for Theoretical Physics, Institute for Gravitational Physics (Albert Einstein Institute), Leibniz University Hannover, Appelstraße 2, 30167 Hannover, Germany
³Department of Physics, Humboldt-Universität zu Berlin, 10099 Berlin, Germany

^*sahand.mahmoodian@sydney.edu.au
^†Present address: Department of Electrical Engineering, Columbia University, New York, New York 10027, USA.
^‡Present address: Centre for Engineered Quantum Systems, School of Physics, The University of Sydney, Sydney New South Wales 2006, Australia.
^§maximilian.schemmer@hu-berlin.de

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Issue

Vol. 127, Iss. 12 — 17 September 2021

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Images

Figure 1
(a) Atom-mediated photon interaction: two photons interact with a two-level atom and exchange energy such that they become red detuned and blue detuned with respect to the incident light. (b) The scattered light exhibits a Lorentzian shaped spectrum. (c) As the generated photon pairs propagate through the ensemble, absorption around the atomic resonance $ω_{0}$ attenuates the central part of the spectrum, leaving red- and blue-detuned sidebands. (d) Schematic setup: probe light exiting the nanofiber interferes with a local oscillator at phase $θ$ on a 50:50 beam splitter and is analyzed on balanced photodetectors. Atoms are trapped in the evanescent field of the nanofiber waist of a tapered optical fiber by a combination of red-detuned standing-wave light field at a wavelength of 935 nm (solid gray line) and blue-detuned running-wave light field (dashed gray line) at 685 nm.
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Figure 2
The observed output noise as a function of the phase $θ$ . The noise is normalized to the vacuum reference and deduced from the frequency range $f_{\min} = 1.5 MHz$ to $f_{\max} = 23 MHz$ . The signal obtained with trapped atoms (shown in circles) is compared to the measurement without atoms (shown in triangles). We fit the experimental data with trapped atoms using the function $- A \cos (2 θ + φ) + c$ (black line) which reveals the expected $\cos (2 θ)$ modulation. Squeezing occurs for $θ$ around 0 and $π$ while antisqueezing occurs around $π / 2$ and $3 π / 2$ . The resonant input power is $P_{in} / P_{sat} = 0.51 \pm 0.04$ .
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Figure 3
The first row of panels, (a)–(c), shows the squeezing spectrum $S_{θ} (ω)$ for three different atom numbers at input powers $s = (0.15 \pm 0.01, 0.67 \pm 0.05, 0.29 \pm 0.02)$ (from left to right) at the angle of largest squeezing, $θ = (0, π)$ in orange (bright), and largest antisqueezing, $θ = (π / 2, 3 π / 2)$ in blue (dark). The corresponding theoretical predictions are shown as solid lines. The second row of panels, (d)–(f) shows the entangled photon spectrum $| ϕ_{N} (ω) |$ which is deduced from the upper row with the corresponding theoretical prediction (solid line). All theoretical curves are predictions based on the independently measured parameters $β$ and $N$ , without any free fit parameter taking into account the effect of independently estimated photon loss and detection efficiency in our setup [34, 43, 44].
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Figure 4
The phase of the entangled part of the two-photon wave function $φ_{N}$ for $N = 140$ together with the corresponding theoretical predictions in solid lines. (a) The integrated phase $φ_{N} (τ = 0) = Arg {ϕ_{N} (τ = 0)}$ for different detunings $Δ$ . (b) The phase $φ (ω)$ as a function of frequency. The detunings from top to bottom are $Δ / Γ_{tot} = 1.9$ , 0.8, 0, $- 1$ , $- 1.9$ and share the same color code as in (a). (c) The reconstructed real and imaginary part of the entangled two-photon time-domain wave function $ϕ_{N} (τ)$ . The solid lines show the corresponding theoretical predictions based on the independently measured values of $β$ and $N$ , without any free fit parameter.
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