Experimental Quantification of the Entanglement of Noisy Twin Beams

Václav Michálek, Jan Peřina, Jr., and Ondřej Haderka

Phys. Rev. Applied 14, 024003 – Published 3 August 2020

Abstract

Gradual loss of the entanglement of a twin beam containing around 25 photon pairs with the increasing external noise is experimentally investigated. The entanglement is quantified by the nonclassicality depths and the nonclassicality counting parameters related to several nonclassicality criteria. The reduction of intensity moments of the analyzed multimode twin beams to single-mode ones allows determination of the negativity as another quantifier of the entanglement. Both the raw photocount histograms and the reconstructed photon-number distributions are analyzed in parallel.

Received 6 April 2020
Revised 4 June 2020
Accepted 15 July 2020

DOI:https://doi.org/10.1103/PhysRevApplied.14.024003

Physics Subject Headings (PhySH)

Beam optics Entanglement measures Optical quantum information processing Photon pairs & parametric down-conversion Photon statistics Quantum entanglement Quantum metrology Quantum states of light

Atomic, Molecular & OpticalQuantum Information, Science & Technology

Authors & Affiliations

Václav Michálek ^1,*, Jan Peřina, Jr.^1,†, and Ondřej Haderka ²

¹Joint Laboratory of Optics of Palacký University and Institute of Physics of CAS, Faculty of Science, Palacký University, 17. listopadu 50a, 771 46 Olomouc, Czech Republic
²Institute of Physics of Academy of Sciences of the Czech Republic, Joint Laboratory of Optics of Palacký University and Institute of Physics of CAS, 17. listopadu 12, 772 07 Olomouc, Czech Republic

^*vaclav.michalek@upol.cz
^†jan.perina.jr@upol.cz

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Vol. 14, Iss. 2 — August 2020

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Images

Figure 1
(a) Scheme of the experimental setup: nonlinear crystal BBO producing a TWB; mirror HR reflecting the idler beam; light bulb (LB) emitting the noisy field with defined intensity uniform over the ICCD; bandpass interference filter (IF); intensified CCD camera (ICCD); detector D used for pump-beam stabilization. (b) Normalized experimental photocount histogram $f (c_{s}, c_{i})$ giving the number of realizations with $c_{s}$ and $c_{i}$ registered electrons (photocounts) and (c) the corresponding reconstructed photon-number distribution $p (n_{s}, n_{i})$ of the least-noisy TWB.
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Figure 2
(a) Mean experimental photocount numbers $⟨ c_{s} ⟩$ (blue $△$ ), $⟨ c_{i} ⟩$ (red $\circ$ ), and $⟨ c ⟩_{n}$ ( $*$ ) in, in turn, signal-beam, idler-beam, and noise-detection region versus the number $i$ identifying a TWB. (b) Noise-reduction-factors $R_{c}$ ( $*$ ) and $R_{n}$ (blue $△$ ) determined for the experimental photocount histograms and reconstructed photon-number distributions of TWBs, respectively, as they depend on mean noise photocount number $⟨ c ⟩_{n}$ . Experimental data are plotted as isolated symbols with error bars derived from the number of measurement repetitions. Relative errors in (b) estimated from the data scattering are better than 3%. In (a), experimental errors are smaller than the plotted symbols. In (b), theoretical solid curves with appropriate symbols originate in the model, dashed line $R = 1$ indicates the nonclassicality border.
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Figure 3
Nonclassicality depths $τ$ (a),(b) and nonclassicality counting parameters $ν$ (c),(d) for NIs $M$ (black $*$ ), $E_{2}$ (blue $△$ ), and $E_{3}$ (red $\circ$ ) for photocount histograms (a),(c) and photon-number distributions (b),(d) as they depend on mean noise photocount number $⟨ c ⟩_{n}$ . Experimental data are plotted as isolated symbols with error bars derived from the number of measurement repetitions, solid curves with appropriate symbols come from the model. Relative errors in (a),(b) [(c),(d)] estimated from the data scattering are better than 10% [5%].
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Figure 4
Negativity $E_{N}$ (a),(b) and nonclassicality depth $τ$ (c),(d) for NIs $M$ (black $*$ ), $E_{2}$ (blue $△$ ), and $E_{N}$ (red $\circ$ ) for photocount histograms (a),(c) and photon-number distributions (b),(d) “reduced” to a single-mode along Eq. (12) as they depend on mean noise photocount number $⟨ c ⟩_{n}$ . Experimental data are plotted as isolated symbols with error bars derived from the number of measurement repetitions, solid curves with appropriate symbols come from the model. Relative errors estimated from the data scattering are better than 10% for all plotted quantities.
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