Interference of Single Photons Emitted by Entangled Atoms in Free Space

G. Araneda, D. B. Higginbottom, L. Slodička, Y. Colombe, and R. Blatt

Phys. Rev. Lett. 120, 193603 – Published 11 May 2018

Abstract

The generation and manipulation of entanglement between isolated particles has precipitated rapid progress in quantum information processing. Entanglement is also known to play an essential role in the optical properties of atomic ensembles, but fundamental effects in the controlled emission and absorption from small, well-defined numbers of entangled emitters in free space have remained unobserved. Here we present the control of the emission rate of a single photon from a pair of distant, entangled atoms into a free-space optical mode. Changing the length of the optical path connecting the atoms modulates the single-photon emission rate in the selected mode with a visibility $V = 0.27 \pm 0.03$ determined by the degree of entanglement shared between the atoms, corresponding directly to the concurrence $C_{ρ} = 0.31 \pm 0.10$ of the prepared state. This scheme, together with population measurements, provides a fully optical determination of the amount of entanglement. Furthermore, large sensitivity of the interference phase evolution points to applications of the presented scheme in high-precision gradient sensing.

Received 30 November 2017

DOI:https://doi.org/10.1103/PhysRevLett.120.193603

Physics Subject Headings (PhySH)

Entanglement detection Quantum information processing Quantum metrology Quantum optics Superradiance & subradiance

Trapped ions

Optical interferometry

Atomic, Molecular & Optical

Authors & Affiliations

G. Araneda^1,*, D. B. Higginbottom^1,2, L. Slodička³, Y. Colombe^1,†, and R. Blatt^1,4

¹Institut für Experimentalphysik, Universität Innsbruck, Technikerstraße 25, 6020 Innsbruck, Austria
²Centre for Quantum Computation and Communication Technology, Research School of Physics and Engineering, The Australian National University, Canberra ACT 2601, Australia
³Department of Optics Palacký University, 17. Listopadu 12, 77146 Olomouc, Czech Republic
⁴Institut für Quantenoptik und Quanteninformation, Österreichische Akademie der Wissenschaften, Technikerstraße 21a, 6020 Innsbruck, Austria

^*gabriel.araneda-machuca@uibk.ac.at
^†yves.colombe@uibk.ac.at

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Vol. 120, Iss. 19 — 11 May 2018

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Images

Figure 1
(a) Electronic levels of ${}^{138}{Ba}^{+}$ . (b) Excitation of the short-lived intermediate state $| i ⟩$ by a $σ^{+}$ beam at 493 nm. Detecting a $π$ -polarized herald photon during a weak excitation pulse prepares a two-atom entangled state. A further, stronger excitation scatters a $π$ -polarized witness photon from the entangled state in the common mode with a probability that depends on the phase difference $Δ ϕ$ . (c) Two ${}^{138}{Ba}^{+}$ ions, $A$ and $B$ , are trapped and cooled in a linear Paul trap, separated by a distance $z ≃ 5.2 μ m$ . The radiation fields are collimated using two identical in-vacuum high numerical aperture lenses ( $L 1$ and $L 2$ ). A mirror ( $M$ ) at a distance $d / 2 ≃ 30 cm$ superimposes emissions from the ions so that they are coupled to a common spatial mode. The mirror is mounted on piezotransducers (PZT) that allow fast subwavelength control of the atom-atom distance in the common optical mode. A polarizing beam splitter (PBS) selects $π$ -polarized photons, which are coupled to a single-mode fiber (SMF) and detected by an avalanche photodiode (APD). A Michelson interferometer enabled by a flip mirror (FM) is used to calibrate the PZT-mirror voltage-displacement response.
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Figure 2
Absolute ( $P$ ) and relative ( $R$ ) witness photon probability from the atom pair as a function of the phase difference $Δ ϕ$ for the entangled state $| ψ ⟩$ (blue circles) and the separable state $| ζ ⟩$ (orange squares). Error bars correspond to the Poissonian error from photon counting. The blue solid curve is the amplitude and offset fitted scattering model for the entangled state, while the black dashed curve shows the expected probability from the independent estimation of its concurrence. The gray dashed line is the average of the fitted curve. The witness photon detection probability for $| ψ ⟩$ is maximally enhanced at $Δ ϕ = 0$ , $2 π$ and maximally suppressed at $Δ ϕ = π$ . The photon detection probability for $| ζ ⟩$ is constant within the measurement uncertainty.
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Figure 3
Absolute ( $P$ ) and relative ( $R$ ) witness photon probability when $Δ ϕ = 0$ (blue circles) and $Δ ϕ = π / 2$ (orange squares) for delay times $τ$ in the presence of a magnetic field gradient compared to the same measure in the absence of a magnetic field gradient (purple diamonds) with $Δ ϕ = 0$ . The blue curve is amplitude and period fitted to the measured data for $Δ ϕ = 0$ (blue points), while the orange dashed curve is a $π / 2$ phase shifted version of this fit, showing with the $Δ ϕ = π / 2$ measured data. The dashed purple line shows constant enhancement in the absence of magnetic field gradient.
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