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