Tripartite quantum correlations obtained by post-selection from twin beams

TL;DR

This work demonstrates the generation of tripartite quantum correlations by post-selecting three idler beams from a triple twin-beam configuration, conditioned on a fixed signal photocounts $c_s$. The authors reconstruct the joint photon-number distribution $p(n_s, n_{i1}, n_{i2}, n_{i3})$ using maximum-likelihood and a multi-mode Gaussian model, and quantify nonclassicality with moment-based NCCa, their nonclassicality depths $\tau$, and quasi-distributions of integrated intensities. Real detectors reveal nonclassicality dominated by quantum correlations, while ideal post-selection enhances marginal sub-Poissonianity and anti-correlations, as shown by larger $\tau$ values (e.g., $\tau_C \approx 0.56$, $\tau_M \approx 0.65$ for probability NCCa) and stronger negativity in the corresponding quasi-distributions. The methodology paves the way for applications in quantum metrology and secure communications by enabling controllable tripartite nonclassical states via post-selection on a shared signal beam.

Abstract

Spatially-resolved photon counting of a twin beam performed by an iCCD camera allows for versatile tailoring the properties of the beams formed by parts of the original twin beam. Dividing the idler beam of the twin beam into three equally-intense parts and post-selecting by detecting a given number of photocounts in the whole signal beam we arrive at the idler fields exhibiting high degrees of nonclassicality and being endowed with tripartite quantum correlations. Nonclassicality is analyzed with the help of suitable nonclassicality witnesses and their corresponding nonclassicality depths. Suitable parameters are introduced to quantify quantum correlations. These parameters are analyzed as they depend on the field intensity. The experimental photocount histograms are reconstructed by the maximum-likelihood approach and the obtained photon-number distributions are compared with a suitable model in which the original twin beam is approximated by an appropriate multi-mode Gaussian field and undergoes the corresponding beams' transformations.

Figures (8)

• Figure 1: (a) Schematic of the experimental setup composed of laser, tripler, half-wave-plate HWP, polarizing beam splitter PBS, BBO crystal, highly-reflected mirror HR, laser-light detector D, frequency filter F, and iCCD camera. (b) Multiple exposition of an image acquired by the detector - (left) signal strip monitored by detector D$_\mathrm{s}$, (right) idler strip divided into three parts detected by detectors D$_{\mathrm{i}_1}$, D$_{\mathrm{i}_2}$, and D$_{\mathrm{i}_3}$.
• Figure 2: Graphical representation of diagonal and triangular planes in the space ($n_{\mathrm{i}_1}$, $n_{\mathrm{i}_2}$, $n_{\mathrm{i}_3}$): (a) diagonal plane, (b) triangular plane, (c) both planes.
• Figure 3: (a) Mean photon (photocount) number $\langle n_{\mathrm{i}_1} \rangle$ ($\langle c_{\mathrm{i}_1} \rangle$) of idler beam 1, (b) its Fano factor $F_{n, \mathrm{i}_1}$ ($F_{c, \mathrm{i}_1}$), and (c) correlation function $C_{\Delta n, \mathrm{i}_2\, {\rm i}_3}$ [$C_{\Delta c, \mathrm{i}_2\, {\rm i}_3}$] of photon-number fluctuations in idler beams 2 and 3 as they depend on the post-selecting signal photocount number $c_\mathrm{s}$. Symbols $\ast$ belong to the experimental photocount histogram, symbols $\triangle$ to ML reconstruction, and solid curves to Gaussian reconstruction.
• Figure 4: Photon-number distribution $p_{\rm i}^\mathrm{ML}(n_{\mathrm{i}_1}, n_{\mathrm{i}_2}, n_{\mathrm{i}_3})$ drawn in its (a) diagonal and (b) triangular planes and quasi-distribution $P_{\mathrm{i}}^\mathrm{ML}(W_{\mathrm{i}_1}, W_{\mathrm{i}_2}, W_{\mathrm{i}_3})$ of integrated intensities drawn in its (c) diagonal and (d) triangular planes for the field reached by real post-selection with $c_\mathrm{s}=5$.
• Figure 5: Nonclassicality depth $\bar{\tau}_\mathrm{C}$ [$\bar{\tau}_\mathrm{M}$] for the probability Cauchy--Schwarz [matrix] NCCa drawn in its (a) [(c)] diagonal and (b) [(d)] triangular planes for the field reached by real post-selection assuming $c_s=5$.