1. Quantum
Ghost Imaging
BY WATHAN PRATUMWAN

2. Imaging

4. Alice
|↕ +|↔
Entangled pair
|↕ 𝐴 |↕ 𝐵 +|↔ 𝐴 |↔ 𝐵
Bob |↕ +|↔

5. “I cannot seriously believe in quantum
theory because it cannot be reconciled with
the idea that physics should represent a
reality in time and space, free from
spooky actions at a distance.”
─ Albert Einstein

7. Experiment
D1
collection lens
Laser
pump
aperture
filter
coincidence
circuit
lens
BBO
filter
signal
prism
polarizing
beam splitter
D2
idler
X-Y scanning
fibre

8. Result
Coincident counts as a
function of the fiber tip’s
coordinates
Aperture

9. aperture
lens
BBO
beam splitter
X-Y scanning
fibre
Gaussian thin lens
1 1 1
+ =
𝑆 𝑆′
𝑓

10. Entangled state wavefunction
Phase-matching wavefunction
|Ψ =
𝛿 𝜔𝑠 + 𝜔𝑖 − 𝜔 𝑝 𝛿 𝐤 𝑠 + 𝐤 𝑖 − 𝐤 𝑝 | 𝐤 𝑠 ⊗ | 𝐤 𝑖
𝑠,𝑖

11. Two-photon geometrical optics
signal
𝛽𝑠
𝛼𝑠
𝛼𝑖
pump
𝛽𝑖
BBO
idler
𝜔𝑠 ≃ 𝜔𝑖 ≃ 𝜔 𝑝 2
𝑘 𝑠 sin 𝛼 𝑠 = 𝑘 𝑖 sin 𝛼 𝑖
𝜔 𝑠 sin 𝛽 𝑠 = 𝜔 𝑖 sin 𝛽 𝑖

12. Two-photon geometrical optics
signal
idler

13. Two-photon geometrical optics
collection
lens
lens 𝑓 = 400 mm
D1
BBO
𝑆 = 600 mm
𝑆 ′ = 1200 mm
fiber
tip plane

14. Summary
 The entanglement is nonlocal correlation of multiparticle system.
 The ghost imaging experiment demonstrates the
entanglement between a pair of photons.
 Geometrical optics can apply to quantum optics.

15. “We cannot make the mystery go
away by explaining how it works.
We will just tell you how it works.”
─ Richard P. Feynman

16. References
Pittman, T., Shih, Y., Strekalov, D., & Sergienko, A. (1995). Optical imaging by
means of two-photon quantum entanglement. Physical Review A, 52(5),
R3429–R3432.
Shih, Y. (2008). The Physics of Ghost Imaging. Quantum Physics. Retrieved from
http://arxiv.org/abs/0805.1166

17. The End