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Advanced Optical Microscopy
lecture
4. February 2013
Kai Wicker
Exam:
written exam
26 February 2013
exact time and place will be announced by email
Today:
The quantum world in microscopy
1. Photon anti-bunching
2. Interaction-free measurements
3. Entangled photons, parametric down-conversion
4. Beating shot-noise
5. Entangled two-photon microscopy
1. Photon anti-bunching
Normal fluorescence
Jablonski diagram
Absorption…
… and spontaneous emission
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)
b) + d)
c) + e)
Pulsed excitation and synchronised detection
Two-pixel correlations
Three-pixel correlations
Super resolution imaging exploiting sub-Poissonian statistics
a) + d)
b) + e)
c) + f)
Conventional fluorescence image
Second order anti-bunching
Third order anti-bunching
2. Interaction-free measurements
Seeing without light
Fabry-Perot resonator
Mirror
Transmitted light
Reflected light
Fabry-Perot resonator
Mirror
Transmitted light
Reflected light
Transmitted light
Reflected light
Transmitted light
Fabry-Perot resonator
Mirror
Fabry-Perot resonator
Mirror
opposite phase  cancellation
Fabry-Perot resonator
Case 1
One mirror
Case 2
Two mirrors, resonator
Case 3
Two mirrors with obstacle
Interaction-free
measurement
Experiment:
Imaging photographic film without exposing it to light
„sample“-film
scan area
„detector“-film
Experiment:
Imaging photographic film without exposing it to light
3. Entangled photons, parametric downconversion
Coherent super-positions of states:
𝑏
𝑎
𝜓 = 𝑎
1
𝜓 =
𝐴 + 𝐵
2
𝐴
𝐵
“click”
parametric down-conversion
𝜓 =
𝜓 =
1
3
𝑟𝑒𝑑
1
𝑏𝑙𝑢𝑒
1
𝑟
1
𝑟𝑒𝑑
1
𝑑3𝑟
2
+ 𝑔𝑟𝑒𝑒𝑛
−𝑟 2 𝑑 3 𝑟
𝑔𝑟𝑒𝑒𝑛
𝑏𝑙𝑢𝑒
1
𝑔𝑟𝑒𝑒𝑛
2
+ 𝑏𝑙𝑢𝑒
1
𝑟𝑒𝑑
Position entanglement!
1
1
𝑟1
Image:
European Space Agency
𝑔𝑟𝑒𝑒𝑛
𝑏𝑙𝑢𝑒
2
2
−𝑟
𝑟𝑒𝑑
2
2
2
4. Beating shot-noise
Beating shot-noise
𝜓 =
1
𝑑3𝑟
𝑟
1
−𝑟 2 𝑑 3 𝑟
Position entanglement!
Intensity distributions are correlated, even down to Poisson noise!!
Image: Alessandra Gatti, Enrico Brambilla, and Luigi Lugiato, “Quantum Imaging,” 2007
Beating shot-noise
Illumination
Quantum
Classical image:
image:
𝐷1 𝑟 = 𝐼 𝑟 ±
𝐼 𝑟
Not
Identical!
correlated!
𝐷2 𝑟 = 𝐷
𝑟
𝐼 1𝑟 −𝑆𝑟𝑟𝑆 ±
Weakly absorbing object
𝐼 𝑟 𝑆 𝑟
Beating shot-noise
imaging a weakly absorbing object
Beating shot-noise
imaging a weakly absorbing object
Simulation
Sample
Classical image: SNR 1.2
Quantum image: SNR 3.3
Beating shot-noise
imaging 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
Normal fluorescence
Jablonski diagram
NO absorption…
2-photon fluorescence
Jablonski diagram
2-photon absorption…
… and spontaneous emission
2-photon fluorescence
Classical:
- 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