advanced optical microscopy lecture 4. february 2013 kai wicker
TRANSCRIPT
Advanced Optical Microscopylecture
4. February 2013Kai Wicker
Exam:
written exam26 February 2013exact time and place will be announced by email
Today:
The quantum world in microscopy
1. Photon anti-bunching2. Interaction-free measurements3. Entangled photons, parametric down-conversion4. Beating shot-noise5. Entangled two-photon microscopy
1. Photon anti-bunching
Jablonski diagram
Absorption…
… and spontaneous emission
Normal fluorescence
Photon anti-bunching:
- only 1 photon per emitter and excitation pulse - sub-Poissonian (!) statistics
1.0
anti-bunching
Possible applications of photon anti-bunching:
- single molecule localisation: is it really just one single molecule?
- super resolution imaging exploiting sub-Poissonian statistics
Super resolution imaging exploiting sub-Poissonian statistics
a) Pulsed excitation and synchronised detectionb) + d) Two-pixel correlationsc) + e) Three-pixel correlations
Super resolution imaging exploiting sub-Poissonian statistics
a) + d) Conventional fluorescence imageb) + e) Second order anti-bunchingc) + f) Third order anti-bunching
2. Interaction-free measurements
Seeing without light
Mirror
Transmitted light
Reflected light
Fabry-Perot resonator
Reflected light
Transmitted light Transmitted light
Reflected lightTransmitted light
Mirror
Fabry-Perot resonator
Mirror
Fabry-Perot resonator
opposite phase cancellation
Mirror
Fabry-Perot resonator
Case 1One mirror
Case 2Two mirrors, resonator
Case 3Two mirrors with obstacle
Fabry-Perot resonator
Interaction-freemeasurement
Experiment:Imaging photographic film without exposing it to light
„sample“-film „detector“-film
scan area
Experiment:Imaging photographic film without exposing it to light
3. Entangled photons, parametric down-conversion
Coherent super-positions of states:
|𝑎 ⟩
|𝑏 ⟩
|𝐵 ⟩
|𝐴 ⟩
|𝜓 ⟩ =|𝑎 ⟩
|𝜓 ⟩ = 1
√2 (|𝐴 ⟩ +|𝐵 ⟩ )
“click”
Image: European Space Agency
parametric down-conversion
|𝜓 ⟩ = 1
√3 (|𝑟𝑒𝑑 ⟩1|𝑏𝑙𝑢𝑒 ⟩2+|𝑔𝑟𝑒𝑒𝑛 ⟩1|𝑔𝑟𝑒𝑒𝑛 ⟩2+|𝑏𝑙𝑢𝑒 ⟩1|𝑟𝑒𝑑 ⟩ 2 )
|𝑟𝑒𝑑 ⟩1 |𝑏𝑙𝑢𝑒 ⟩2|𝑔𝑟𝑒𝑒𝑛 ⟩1 |𝑔𝑟𝑒𝑒𝑛 ⟩2
|𝑏𝑙𝑢𝑒 ⟩1 |𝑟𝑒𝑑 ⟩2
|𝑟 ⟩1
|−𝑟 ⟩2
|𝜓 ⟩ = 1
√∫𝑑3𝑟∫|𝑟 ⟩1|− �⃑� ⟩ 2𝑑3𝑟 Position entanglement!
4. Beating shot-noise
Beating shot-noise
|𝜓 ⟩ = 1
√∫𝑑3𝑟∫|𝑟 ⟩1|− �⃑� ⟩ 2𝑑3𝑟 Position entanglement!
Image: Alessandra Gatti, Enrico Brambilla, and Luigi Lugiato, “Quantum Imaging,” 2007
Intensity distributions are correlated, even down to Poisson noise!!
𝐷1 ( �⃗� )=𝐼 (𝑟 )±√ 𝐼 (𝑟 )
𝐷2 (𝑟 )=𝐷1 (−𝑟 )𝑆 (𝑟 )
Identical!
Quantum image:
Weakly absorbing object
Illumination
𝐷1 ( �⃗� )=𝐼 (𝑟 )±√ 𝐼 (𝑟 )
𝐷2 (𝑟 )=𝐼 (𝑟 )𝑆 (𝑟 )±√ 𝐼 (𝑟 )𝑆 (𝑟 )
Not correlated!
Classical image:
Beating shot-noise
Beating shot-noiseimaging a weakly absorbing object
Beating shot-noiseimaging a weakly absorbing object
Simulation
Sample Classical image: SNR 1.2 Quantum image: SNR 3.3
Beating shot-noiseimaging a weakly absorbing object
Experiment
Sample: π-shaped titanium deposition
Classical image: SNR 1.2 Quantum image: SNR 1.7
5. Entangled two-photon microscopy
Jablonski diagram
NO absorption…
Normal fluorescence
Jablonski diagram
2-photon absorption…
… and spontaneous emission
2-photon fluorescence
2-photon fluorescenceClassical:
- 2-photon absorption requires two photons to be present simultaneously.
- The probability for this grows quadratically with intensity.
- It will only occur where the local intensity is high.
Quantum:
- 2-photon absorption requires two photons to be present simultaneously.
- This is achieved through temporal coincidence of entangled photons.
Entangled two-photon microscopy
Comparisson of different imaging modalities:
Entangled two-photon microscopy
End of lecture