First Detailed Study of the Quantum Decoherence of Entangled Gamma Photons
Abstract: Constraints on the quantum decoherence of entangled $\gamma$ quanta at the mega-electron-volt scale, such as those produced following positron annihilation, have remained elusive for many decades. We present the first statistically and kinematically precise experimental data for triple Compton scattering of such entangled $\gamma$. An entanglement witness ($R$), relating to the enhancement of the azimuthal correlation between the final scattering planes, is obtained where one of the $\gamma$ underwent intermediate Compton scattering. The measured $R$, deconvolved from multiple scattering backgrounds, are found to exceed the classical limit for intermediate scatter angles up to $\sim$60${\circ}$ and diminish at larger angles. The data are consistent with predictions from a first quantum theory of entangled triple Compton scattering as well as a simple model based approach. The results are crucial to future study and utilisation of entangled mega-electron-volt $\gamma$ in fundamental physics and PET imaging.
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- QEG4-FD is consistent with standard Geant4 (γ1,2subscript𝛾12\gamma_{1,2}italic_γ start_POSTSUBSCRIPT 1 , 2 end_POSTSUBSCRIPT separable) to ≤\leq≤5% over data range.
- The current development version of QEG4 (v11.1) requires a filter on event ordering such that the polarization vectors are correctly assigned for all events.
- Approach is supported by [11], where CS visibility is factored from the DCS cross section.
- ϵ^γ2′subscript^italic-ϵsuperscriptsubscript𝛾2′\hat{\epsilon}_{\gamma_{2}^{\prime}}over^ start_ARG italic_ϵ end_ARG start_POSTSUBSCRIPT italic_γ start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT end_POSTSUBSCRIPT lies in the plane formed by the polarization of the incoming γ𝛾\gammaitalic_γ, ϵ^γ2subscript^italic-ϵsubscript𝛾2\hat{\epsilon}_{\gamma_{2}}over^ start_ARG italic_ϵ end_ARG start_POSTSUBSCRIPT italic_γ start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT end_POSTSUBSCRIPT and γ^2′superscriptsubscript^𝛾2′\hat{\gamma}_{2}^{\prime}over^ start_ARG italic_γ end_ARG start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT and is perpendicular to γ^2′superscriptsubscript^𝛾2′\hat{\gamma}_{2}^{\prime}over^ start_ARG italic_γ end_ARG start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT.
- Derived from the difference in CS cross sections for orthogonally polarised 511511511511 keV γ𝛾\gammaitalic_γ from polarised KN formula: VCS=sin2(θ)12−cos(θ)+sin2(θ)−cos(θ)subscript𝑉𝐶𝑆𝑠𝑖superscript𝑛2𝜃12𝑐𝑜𝑠𝜃𝑠𝑖superscript𝑛2𝜃𝑐𝑜𝑠𝜃V_{CS}=\frac{sin^{2}(\theta)}{\frac{1}{2-cos(\theta)}+sin^{2}(\theta)-cos(% \theta)}italic_V start_POSTSUBSCRIPT italic_C italic_S end_POSTSUBSCRIPT = divide start_ARG italic_s italic_i italic_n start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT ( italic_θ ) end_ARG start_ARG divide start_ARG 1 end_ARG start_ARG 2 - italic_c italic_o italic_s ( italic_θ ) end_ARG + italic_s italic_i italic_n start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT ( italic_θ ) - italic_c italic_o italic_s ( italic_θ ) end_ARG.
- Small difference attributable to light collection for crystal entry points of CS γ𝛾\gammaitalic_γ c.f. calibration data and non-linearities in energy calibration .
- For θ1′,2′=81.7∘subscript𝜃superscript1′superscript2′superscript81.7\theta_{1^{\prime},2^{\prime}=81.7^{\circ}}italic_θ start_POSTSUBSCRIPT 1 start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT , 2 start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT = 81.7 start_POSTSUPERSCRIPT ∘ end_POSTSUPERSCRIPT end_POSTSUBSCRIPT R=1.63𝑅1.63R=1.63italic_R = 1.63 from [13]. Current data for 81.7±∘2∘{}^{\circ}\pm 2^{\circ}start_FLOATSUPERSCRIPT ∘ end_FLOATSUPERSCRIPT ± 2 start_POSTSUPERSCRIPT ∘ end_POSTSUPERSCRIPT.
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