Quantum
Ghost Imaging
BY WATHAN PRATUMWAN
Imaging
Bob
Alice
| ↕ +| ↔
| ↕ +| ↔
| ↕ 𝐴| ↕ 𝐵+| ↔ 𝐴| ↔ 𝐵
Entangled pair
“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
coincidence circuit
Laserpump
BBO
prism polarizingbeam splitter
lens
filteraperture
collection lens
filter
X-Y scanningfibre
D1
D2
Experiment
signal
idler
Result
Aperture
Coincident counts as a function of the fiber tip’s coordinates
BBO
beam splitter
lens
aperture
X-Y scanningfibre
1
𝑆+1
𝑆′=1
𝑓Gaussian thin lens
| Ψ =
𝑠,𝑖
𝛿 𝜔𝑠 + 𝜔𝑖 − 𝜔𝑝 𝛿 𝐤𝑠 + 𝐤𝑖 − 𝐤𝑝 | 𝐤𝑠 ⊗ | 𝐤𝑖
Phase-matching wavefunction
Entangled state wavefunction
Two-photon geometrical optics
signal
idler
pump
BBO
𝛽𝑠
𝛽𝑖
𝛼𝑠
𝛼𝑖
𝑘𝑠 sin 𝛼𝑠 = 𝑘𝑖 sin 𝛼𝑖
𝜔𝑠 sin 𝛽𝑠 = 𝜔𝑖 sin 𝛽𝑖𝜔𝑠 ≃ 𝜔𝑖 ≃ 𝜔𝑝 2
Two-photon geometrical optics
signal
idler
𝑓 = 400 mm
𝑆 = 600 mm 𝑆′ = 1200 mm
Two-photon geometrical optics
collectionlens
lensfiber
tip plane
BBO
D1
Summary The entanglement is nonlocal correlation of multi-particle system.
The ghost imaging experiment demonstrates the entanglement between a pair of photons.
Geometrical optics can apply to quantum optics.
“We cannot make the mystery go
away by explaining how it works.
We will just tell you how it works.”
─ Richard P. Feynman
ReferencesPittman, 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
The End