Two-beam light with simultaneous anticorrelations in photon-number fluctuations and sub-Poissonian statistics

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

Phys. Rev. A 104, 013712 – Published 12 July 2021

Abstract

Two twin beams with a shared signal beam and separated idler beams are used together with the photon-number-resolving postselection in the signal beam to arrive at two coupled beams with anticorrelations in photon-number fluctuations. Moreover, the beams exhibit the sub-Poissonian photon-number statistics in their marginal distributions under suitable conditions. The postselected fields with the increasing mean photon numbers are reconstructed from the experimental photocount histograms by the maximum likelihood approach. Also a suitable Gaussian fit of both original twin beams and simulation of the postselection process are applied to arrive at the corresponding photon-number distributions. Their nonclassical properties are analyzed by suitable nonclassicality criteria and quantified by the corresponding nonclassicality depths. Determining the appropriate quasidistributions of integrated intensities with negative values, the performance of different non-classicality criteria is judged. Properties of the postselected fields reached both by the used and ideal photon-number-resolved detectors are mutually compared.

Received 20 October 2020
Accepted 30 June 2021

DOI:https://doi.org/10.1103/PhysRevA.104.013712

Physics Subject Headings (PhySH)

Nonlinear optics Optical coherence Quantum entanglement Quantum metrology Quantum optics

Quantum Information, Science & TechnologyAtomic, Molecular & Optical

Authors & Affiliations

Jan Peřina, Jr.^1,*, Václav Michálek¹, Radek Machulka ², and Ondřej Haderka ²

¹Joint Laboratory of Optics of Palacký University and Institute of Physics of the Czech Academy of Sciences, Faculty of Science, Palacký University, 17. listopadu 12, 77146 Olomouc, Czech Republic
²Institute of Physics of the Czech Academy of Sciences, Joint Laboratory of Optics of Palacký University and Institute of Physics of CAS, 17. listopadu 50a, 772 07 Olomouc, Czech Republic

^*jan.perina.jr@upol.cz

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Issue

Vol. 104, Iss. 1 — July 2021

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Images

Figure 1
(a) Scheme of the experimental setup: Laser: frequency-tripled pump laser with power stabilizer; HWP: half-wave plate; BBO: two thin optically contacted BBO crystals; BD: polarizing beam displacer; iCCD: intensified CCD camera. (b) Images acquired by the detector, in turn: typical single-shot image, accumulated image from multiple single-shot exposures forming one signal (left) and two idler (right) intense strips, and cumulative frame formed by individual detection events identified by signal processing within regions defined by one signal, one narrow noise (formed solely by the dark, ambient and readout noise) and two idler beams.
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Figure 2
(a) Mean number of photons $〈 n_{i_{1}} 〉$ (photocounts $〈 c_{i_{1}} 〉$ ) and (b) Fano factor $F_{n, i_{1}}$ ( $F_{c, i_{1}}$ ) of the first idler field, (c) modified noise-reduction-parameter $R_{n, +}$ ( $R_{c, +}$ ), (d) covariance $C_{n, Δ}$ ( $C_{c, Δ}$ ), and nonclassicality depths (e) $τ_{C_{W}}$ and (f) $τ_{M_{W}}$ of the 2D idler fields observed after postselection as they depend on the signal-field postselecting photocount number $c_{s}$ . Isolated symbols are drawn for the experimental photocount histograms (red $*$ ) and fields reconstructed by 2D maximum-likelihood approach (green $▵$ ); solid blue curves originate in the 3D Gaussian model. The horizontal dashed lines indicate the borders of anticorrelation ( $C_{Δ} = 0$ ) and nonclassicality ( $F_{i_{1}} = 1$ , $R_{+} = 1$ ) regions.
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Figure 3
(a) Mean number of photons ${〈 n_{i_{1}} 〉}^{id}$ and (b) Fano factor $F_{n, i_{1}}^{id}$ of the first idler field, (c) modified noise-reduction-parameter $R_{n, +}^{id}$ , (d) covariance $C_{n, Δ}^{id}$ , and nonclassicality depths (e) $τ_{C_{W}}^{id}$ and (f) $τ_{M_{W}}^{id}$ of the 2D idler fields reached by the ideal photon-number-resolving postselection as they depend on the signal-field post-selecting photon number $n_{s}$ . Isolated symbols are drawn for the field reconstructed by 3D maximum-likelihood approach (dark green $⋄$ ); solid dark blue curves originate in the 3D Gaussian model. The horizontal dashed lines indicate the borders of anticorrelation ( $C_{Δ}^{id} = 0$ ) and nonclassicality ( $F_{i_{1}}^{id} = 1$ , $R_{+}^{id} = 1$ ) regions.
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Figure 4
(a), (b) Photon-number distribution $p_{ii} (n_{i_{1}}, n_{i_{2}})$ with (c), (d) the corresponding quasidistribution $P_{ii, s} (W_{i_{1}}, W_{i_{2}})$ of integrated intensities and nonclassicality depths $\bar{τ}$ of the NCCa (e), (f) ${\bar{C}}_{p} (n_{i_{1}}, n_{i_{2}})$ , (g), (h) ${\bar{M}}_{p} (n_{i_{1}}, n_{i_{2}})$ , and (i), (j) $L_{W p} (n_{i_{1}})$ drawn as they depend on the numbers $n_{i_{1}}$ and $n_{i_{2}}$ of photons in the idler fields. The fields postselected by $c_{s} = 5$ signal photocounts (a), (c), (e), (g), (i) and $n_{s} = 10$ signal photons (b), (d), (f), (h), (j) are analyzed. In (c) [(d)], $s = 0.1$ $[s = - 0.15]$ and the integrated intensities are expressed in the units of photon numbers. In (e), (g) [(f), (h)], only the NCCa for which the mean value of the used probabilities is greater than 0.01 [0.02] are considered. In (i) [(j)], isolated symbols (green $▵$ ) [dark green $⋄$ ] originate in 2D [3D] maximum-likelihood method.
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