advanced optical microscopy lecture 4. february 2013 kai wicker

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