1. On Quantum Imaging with Time-Resolving Detector Arrays
Manuel Unternährer
Quantum Optics Lab – The Stefanov Group
PhD Defense
April 26, 2018
Quantum imaging covers broad variety of research topics, among them is the improvement of image quality in microscopy. This is what I would like to talk about in the following.

2. Microscopy
1 mm
0.1 mm
0.1 mm
0.03 mm
Microscopy opens us the door into the world of the small.
It shows these beautiful structures otherswise not visible to the naked eye.
Eg. Snow flake, lily pollens, small animals, human cells.
Thereby, Microscoy allows us to study processes in phyiscs, biology and medicine and helps to improve the understanding of nature.
Lily pollens
Rotifer, rädertierechen
Hela cancer cells (coloured microtubule)
Source: Nikon Small World
Manuel Unternährer

3. Microscopy Image Resolution Limited by the Illumination Wavelength λ
But: Sensitivity of Biological Samples to Short Wavelengths
Super-Resolution Techniques based on Sample Fluorescence
Long Wavelength Illumination
Sub-Wavelength Image Resolution
Nobel Prize 2014 in Chemistry (Betzig, Hell, Moerner)
Drawback: Sample Preparation with Fluorophores
λ = 1000 nm
Infra-Red
λ = 300 nm
Ultra-Violet
λ = 500 nm
1 µm
Source: J. A. Galbraith, NIH
Fundamental limitations of microscopy
Red light long wavelength, blue light better due to shorter wavelength
Individual protein molecules visible
Track Individual Molecules
Show you the Origin of wavelength dependence and a possible alternative to these techniques relying on quantum effects.
Make sure we understand the limitation of optical microscopy.
(STED, PALM, STORM)
Manuel Unternährer

4. Optical Microscopy
Imprint Object Shape onto Light → Measure Magnified Image Remotely
Image Formation with Single Lens
Physical Model of Light
Ray Optics, Geometric Optics (Euclid 320 BC, Fermat 1662)
Wave Description of the Electromagnetic Field (Maxwell 1861)
Diffraction Limit of Image Resolution (Abbe 1873, Rayleigh 1896)
Rayleigh Resolution Limit
Point as Test Object
Microscopes complex lens systems: Single lens simplest system to study relevant phenomena
Planes, sharp image only plane to plane (photography)
Would like to get better resolution than possible according to this theory of light, so let’s have a look to the more refined theory, the quantum theory of light.
Object Plane
Lens
Image Plane
Manuel Unternährer

5. Quantum Theory of Light
Photon: Smallest Energy Quantum of Light, Fundamental Particle
Laser-Pointer Beam
Efficient Detection with Single Photon Counters
Quantum Theory: Double Slit Experiment
Source:
Source:
More refined, more accurate theory of light. Quantum Electrodynamics.
Smallest packet of energy, fundamental particle,
Weak sources of single photons: Very sensitive detector, using an amplification effect, -> electrical pulse
Mechanics not sufficient but quantum theory is the physical model which is needed to describe how photons behave
Manuel Unternährer

6. Quantum Theory of Light
Photon: Smallest Energy Quantum of Light
Laser-Pointer Beam
Efficient Detection with Single Photon Counters
Quantum Theory: Double Slit Experiment
Intensity of Light → Probability Distribution of Photon
Superposition Principle of Quantum Mechanics: “Photon takes both slits”
Entangled Photon Pair: “Entangled = Photons taking same slit”
λ = 800 nm, Entangled
Not only photon, but electron, atoms, molecules experimentally demonstrated. Cats to be done
QT tells us how to calculate, philosophers still struggling with interpretation.
Feynman: QT’s only paradoxon or mystery
Generalization to N photons, N times lower wavelength,
Exploit for image resolution resolution
λ = 800 nm, Classical ∞
M. D’Angelo et al., PRL 87, (2001).
Manuel Unternährer

7. SuperTwin Project
New Type of Microscope Exploiting Quantum Features of Light → Super-Resolution without Object Preparation
Adoption of Existing Sensor for Q. Imaging
Algorithm Development for Data Processing
Specification for Newly Developed Detector
Proof-Of-Principle Imaging Experiments
Optimization of Reconstruction Algorithm
Fondazione Bruno Kessler FBK (Italy)
A.P.E. Research srl (Italy)
Centre Suisse d'Electronique et Microtechnique CSEM (Switzerland)
III-V Lab (France)
Single Quantum (Netherlands)
University of Bern (Switzerland)
École Polytechnique Fédérale de Lausanne EPFL (Switzerland)
Institute of Physics, National Academy of Sciences of Belarus
LFoundry srl (Italy)
Staring point of supertwin, eu research project, our group is part of.
Goal: research new type of microscope exploiting quantum feature of light for resolution improvement.
We provide an existing well characterized source of entangled photon,
provide input to detector team using sensor test experiments
Provide measurement data to the theory group, test algorithm
Motivates the overview
Manuel Unternährer

8. Overview Time-Resolving Detector Arrays
What is to be measured in quantum imaging experiments?
Devices and Exemplary Experiments
Super-Resolution Quantum Imaging
Resolution in Multi-Photon Imaging
Reconstruction Algorithm
Results on Imaging and Object Reconstruction
Entanglement-Enhanced Quantum Imaging
Mechanism of Resolution Advantage
Experimental & Theoretical Results
First part allows for the experiments in the latter
Manuel Unternährer

9. Time-Resolving Detector Arrays
Part I
Test existing detector, possible in quantum optics application?
Devise specification for new sensors,
Time-Resolving Detector Arrays

10. Light Measurement Standard Imaging: Light Intensity (Photon Flux)
Camera Sensors with Pixels (e.g. CCD sensor)
Quantum Imaging: Field Correlation Functions (Glauber, 1963)
Scanning, Fiber-Coupled Single Photon Counters (SPCs)
Time-to-Digital Converters (TDCs), Sub-Nanosecond Time Resolution
N Detectors required for , Long Scanning Time!
CCD
???
SPCs
TDCs
What to measure
Imaging, photo camera or microscopy. Simple example here
Coordinate system explain, rho transverse plane position, z optical axis, direction of light propagation
→ Photon Counting without Time-Resolution within Exposure or Frame
Correlation function: standard quantities to characterize the electric field, quantum expectation value of measurement operators.
Positive negative frequency field operators at transverse position, represent the electric field in quantum formalism.
n photon flux density. : : Normal Ordering, Technicality.
Timing, when photons appear relevant, not only total number
Rate/Probability to have two photon, one detected at… the other at…
No off the shelf devices to measure
SPC: single pixels moving around, electric pulse
TDC: time of an electrical pulse
Nanosecond: billionth of a second, needed for the correlation time of light source
TDC big boxes z
Manuel Unternährer

11. Correlation Function Processing Measurement Data
General Formalism for Processing
Spatial & Temporal Discretization
Example: Temporally Coincident Correlation Function
Optimized Processing Algorithm
Sparsity of Summands
Symmetry of Resulting Correlation Function
Analytic Expression for V
Measurement Data
Averaging Region Selector
Detector “Blind Spots”
Not straightforward, My major contribution to the project in my opinion.
Not worked out in literature as far as I know.
Very technical, do not want to bore you but just give a short example
Perfect temporal spatial resolution not given, pixels -> discretization, Integer numbers
Example: to get an idea of the form and arising problems
Not time argument, implicit
Consider only photons arriving within a coincidence window Tc (source correlation time), selected by sampling function
Averaging over samples of measured data n
Sampling function: binary, how to average, how are samples of quantum state located in time and space
Detector blindness
Measurement window T,
More general result, adaptable to arbitrary light sources and sensors
A lot of data, an image with this number of pixels few kilobytes, here gigabytes for moderate correlation orders.
1-10k times per second for real-time data processing
Manuel Unternährer

12. Light Source
Frequency Degenerated, Type-0 Spontaneous Parametric Down-Conversion (SPDC)
Generation of Spatially Entangled Photon Pairs
Standard Camera Image
Non-Linear
Crystal
CCD
Filter
SPCs
TDCs
For test and characterization, well known source of correlated light
SPDC: nonlinear optical process in a NLC with momentum and Energy Conservation
Very low gain regime, only two photon
coincident emission of pairs of photon pairs
Narrowband, spatial and temporal degrees factorize
Thin nlc: Coherent superposition, biphoton
Lambda biphoton wave function given by process parameters
1D scan in one line z
Manuel Unternährer

13. Light Source
Frequency Degenerated, Type-0 Spontaneous Parametric Down-Conversion (SPDC)
Generation of Spatially Entangled Photon Pairs
1-D Correlation Function
Non-Linear
Crystal
Filter
SPCs
TDCs
G2: Photon spatially correlated, are «born» together in same position in crystal, at same time
Very accurate model of process vierified z
Manuel Unternährer

14. SPADnet-I Sensor
Time-Resolving Single Photon Detector Array (FBK, Trento)
Developed for Medial Applications (PET)
Suitable Technology for Quantum Imaging?
8 x 16 Pixels
Pixel = Single Photon Avalanche Diode
Per-Pixel TDC: Photon Detection Time Measurement with Resolution of ns
10 mm
5 mm
We know how to process data, start
FBK collaboration partner within Supertwin
Tenth ob a billionth of a second. Time light flies 2cm.
Testing of existing sensor prototype, evaluate for quantum optics applications, define requirements for next generation sensor
Pixel provides time information, photon arrival time
Time resolution, see demonstration later for next generation sensor
Leonardo Gasparini
L. H. C. Braga et al., IEEE Journal of Solid-State Circuits 49, (2013).
Manuel Unternährer

15. Measurement Results Frame / Picture (Exposed for 50ns) Intensity:
Filter
Crystal
Beam
Splitter
Frame / Picture (Exposed for 50ns)
Intensity:
Detection Events
5 Million Frames
Correlation Function:
128*128 = 16’384 Simultaneous Measurements
Two-lens instead of single lens image,
Beamsplitter separates photon pairs
5 Million Frames in 16s, 1.3GB
Fixed measuement time
4D object, as if one line of pixels, 128x128 = 16k mesaurements
Full 2D scan in 16s, before 1D dozens of minutes
Detection Events
Manuel Unternährer

16. Measurement Results Spatial Correlations in Different Crystal Planes:
“Observing Two-photon State Propagation”
z = 0 mm
z = 5 mm
z = 10 mm
Experiment:
Theory:
Photon pair separates while propagating -> FF anticorrelated
Point-to-point correspondence vanishes
Only left to right coinc: for removal of crosstalk
Residual xtalk
45s measurement time
M. Unternährer, B. Bessire, L. Gasparini, D. Stoppa, and A. Stefanov, Opt. Express 24, (2016).
Manuel Unternährer

17. SuperEllen Sensor
Time-Resolving Single Photon Detector Array (FBK, Trento)
New Design Based on SPADnet-I Experiments
32 x 32 Pixels
Pixel = Single Photon Avalanche Diode
Per-Pixel TDC: Photon Detection Time Measurement with Resolution of 0.2 ns
Now Needed: Data Compression Designed for Quantum Imaging
1.7 mm
These successful experiments motivated fo the next step
Built according our wishlist and the experiences from the prior experiments. Custom built camera
More and smaller pixels,
Fill factor more than ten times better than competitor, state-of-the art
500Mbit/s data stream
Leonardo Gasparini
L. Gasparini, M. Zarghami, H. Xu, L. Parmesan, M. M. Garcia, M. Unternährer, B. Bessire, A. Stefanov, D. Stoppa, and M. Perenzoni, IEEE-ISSCC, (2018).
Manuel Unternährer

18. SuperEllen Sensor Demonstration of Time Resolution with Sensor Array
Super-Continuum Generation in Photonic Crystal Fiber, 5 GHz Frame Rate
5 billion frames per second
100MHz Pulse rate, leaded light out of fiber
Supercontinuum generation in photonic crystal fiber.
Change of bandpasses: delay between red and blue components -> calculation of wavelength dependent group velocity
R. Warburton et al., Sci. Rep. 7 (2017).
Manuel Unternährer

19. SuperEllen Experiment
Far-Field Imaging of Photon Pairs
Crystal
Filters
Intensity:
Correlation Function:
1 Million Simultaneous Measurements
60s measurement time, 26MFrames
Intensity, what a normal camera sees
G2: 1M measurement points, scanning 1M positions
statistically analyze correlation properties:
Only temporally correlated signal extracted -> nice beam shape!
Realtime software
Source of Photon Pairs
Centroid Position:
Manuel Unternährer

20. Detector Arrays Measurement of Spatial Correlations of Photon Pairs
Development of a New Sensor + Software for Quantum Imaging
Considerable Speed Improvements in Comparison to Scanning Detectors
Processing Software for Real-Time G(2) Monitoring
Capability to Measure Higher-Order Correlations (up to G(4))
Pseudo-Thermal Light Source
Entangled Four-Photon Source
M. Unternährer, B. Bessire, L. Gasparini, D. Stoppa, and A. Stefanov, Opt. Express 24, (2016).
L. Gasparini, M. Zarghami, H. Xu, L. Parmesan, M. Moreno Garcia, M. Unternährer,
B. Bessire, A. Stefanov, D. Stoppa, and M. Perenzoni, IEEE-ISSCC, (2018).
Real-time: Setup alignment
4photon, succeeded in realization, but too weak signal on too strong background for current detector efficiencies.
Manuel Unternährer

21. Super-Resolution Quantum Imaging
Part II
Detectors: ready for microscopy but Light source not yet available, use of our two-photon and thermal light source for illumination
Provide experimental data to theory group in Belarus developing the algorithms
Proof concept experiments, later to be applied
Super-Resolution Quantum Imaging

22. Multi-Photon Imaging Classical Light Illumination Imaging
Object Transmission Function , Magnification m
Point-Spread-Function PSF at Illumination Wavelength λ
Two-Photon Illumination Imaging
Single Lens image, s
Not intended as real microscope in this form which have several lenses, but shows same limitation due to wavelength. Diffraction limit.
Allow to study resolution and wavelength dependence.
Object aperture A
Convolutoin, replaces every image point by disk
PSF, wavelength depndance the smaller lambda, the better the resolution
Paraxial approximation
Possible to beat this diffraction limit ->Super-resolution
with special light source
SuperEllen z
Manuel Unternährer

23. Imaging Results 1D Measurement: 0.6 x 0.6 mm
Low Numerical Aperture lens
G2 diagonal, two photons incident on same pixel
Less blurred, noise not present due to temporal coincidence acts as filter for uncorrelated events
Also possible application for noise measurement
Thermal light possible: G4, four photons incident on same pixel. No direct further improvement visible, but expected in reconstruction
G4 even larger space than G2. Only show single-pixel coincidences, much large space
G2 1D object example.
G2 diagonal, photon are detected in same position.
Intuition of improvement: Slits get more separated, isolated in this space as they are on diagonal
Theory agrees well to measurement within statistical noise, relevant for reconstruction
31um slit
Manuel Unternährer

24. Object Reconstruction Algorithm
Reconstruct Object from Measured Data
Formulated as Non-Linear Optimization Problem
Generalization to Nth-Order
Measured Correlation Function
Model Prediction depending on A
Estimated Measurement Error
Theory group in Belarus, collaborator in SuperTwin. developing algorithm.
More information in correlation function, 1 million data points
Thermal light, Nth order measurement possible.
A. Mikhalychev, A. Sakovich, I. Karuseichyk, B. Bessire,
M. Unternährer, A. Stefanov, and D. Mogilevtsev, in preparation.
Manuel Unternährer

25. Object Reconstruction Results
1D Measurement: 15 30 45 60 75 90
Reconstruction
Original Object
Rayleigh Limit
Preliminary results, still ongoing work
More quantitive comparison: 1D cut through image:
Reconstruction of object discretized into pixels
Up to 8x higher resolution than Rayleigh allows, full visibility
Thermal light upper, Photon pairs lower
15um slits 30 45
A. Mikhalychev et al., in preparation.
Manuel Unternährer

26. Super-Resolution Quantum Imaging
Super-Resolution Demonstrated
Far-Field Imaging and Object Reconstruction
Ongoing Research
Quantification of Effective Resolution Improvement
Advantage over Standard Methods
Resolution Scaling with Correlation Order N
Under investigation how resolution improvement scales with correlation order
Far-field: diffraction pattern (phase retrieval)
Fisher information: statistical measure of amount of information
Calculations show: Classically correlated photons same advantage
Qunatum effects
Manuel Unternährer

27. Entanglement-Enhanced Super-Resolution Quantum Imaging
Part III
Entanglement-Enhanced Super-Resolution Quantum Imaging
In literature no experimental results with images of objects.

28. Mechanism of Resolution Advantage
Double Slit Experiment
Imaging of a Point
N-Photon Illumination: Standard Quantum Limit
Full Exploitation of Entanglement: Heisenberg Limit → de Broglie Wavelength
PSF: Interference of Probability Amplitudes (Electric Fields)
De bröii
Measurement classical light intensity with their theoretical curves. campirson to entangled photons, correlated measurement.
Width proportional to wavelength, double
Two-Photon interference, deBroglie wavelength relevant, 810nm behave like 405nm photons.
Good qualitative agreement.
Feynman diagrams, of very simple form:
1 diagram corresponds a probability amplitude for transition of initial state O to final state x, complex number
According to quantum theory: add up all possible amplitudes how a process can happen, feynman: all possible histories
never seen in any quantum optics publication, but powerful tool to get intutition
Analyze situation with two-photon illumination with these diagrams +
+ …
Manuel Unternährer

29. Mechanism of Resolution Advantage
Double Slit Experiment +
Imaging of a Point +
+ …
Imaging with a “Two-Photon Transmitter”
Two-photon transmitter not existing yet, but in principle possible
Conclusion: photon have to be “kept together”, to form a unity, de Broglie wavelength relevant
This intuitive picture allowed me to devise an experiment which exploits this mechanism +
+ …
Manuel Unternährer

30. Experiment + + … Object illuminated at 405 nm
4-f Image
Single Lens Image
Crystal
Lens
SuperEllen
Laser
Object
Object illuminated at 405 nm
Spatial information transferred to 810 nm
Resolution of 405 nm still present!
Imaging of quantum state:
Imaging Quality under Investigation
Preparation of quantum state
Formal calculations how +
+ …
M. Unternährer, B. Bessire, L. Gasparini, M. Perenzoni, and A. Stefanov, arXiv: [quant-ph] (2018).
Manuel Unternährer

31. Imaging Results 1D Measurement: Light Source: 810 nm, Classical
0.6 x 0.6 mm
Light Source:
810 nm, Classical
405 nm, Classical
810 nm, Entangled
1D Measurement:
70um slits
M. Unternährer, B. Bessire, L. Gasparini, M. Perenzoni, and A. Stefanov, arXiv: [quant-ph] (2018).
Manuel Unternährer

32. Entanglement-Enhanced Imaging
Theoretical Results
Generalization to N-Photons, Each at Wavelength λ
Resolution Improvement at the Heisenberg Limit → True Quantum Effect
Demonstration of Fundamental Principle
Electric field can carry finer spatial structure in quantum correlations than classically possible in intensity distributions.
No need of evanescent fields for sub-wavelength structures imprinted in light.
Potentially Lithographic Applications
M. Unternährer, B. Bessire, L. Gasparini, M. Perenzoni, and A. Stefanov, arXiv: [quant-ph] (2018).
PSF tiild
Physics was so nice to allow for a simple formula (if the right assumptions are made and you push it a little)
Lithographic: expose film with small structures like computer chips
Manuel Unternährer

33. Conclusion and Outlook
Detectors for Measurement of Sub-Nanosecond Correlation Functions
Allows Fast High-Order Measurements in Quantum Imaging
Tool for Light Characterization (Setup Alignment)
Next Generation Sensor in Development
Quantum Imaging with Object Reconstruction
Promising Preliminary Results, Proof-of-Principle
Ongoing Statistical Analysis
Light Source for Microscopy Applications to be Developed
Entanglement-Enhanced Imaging
First Images with Spatial Resolution Improvement Exploiting Entanglement
Unifies Understanding of Alternative Schemes Proposed in Literature
More efficient detection method, opens way for experiment in higher-order correlations
Up to now not off-the-shelf buyable
Find its way into quantum optics labs
OCM: cute experiment, proof-of-concept, at least pedagogical, might stimulate further research.
Manuel Unternährer

34. Acknowledgments Sensor Arrays Reconstruction Algorithm
André Stefanov, Bänz Bessire
Sensor Arrays
Leonardo Gasparini, Matteo Perenzoni, David Stoppa
(Fondazione Bruno Kessler, Trento, Italy)
Reconstruction Algorithm
Alexander Mikhalychev, Ilya Karuseichyk, Dmitri Mogilevtsev
(Institute of Physics of the Belarus National Academy of Science)
Andre supervision of thesis and qo group leader giving me the chance to dive into these interesting topics
Special thanks to Bänz, involved in all projects leading to the presented results
Many more people made my time here wonderful:
Thomas Feurer, and All people from laser dvision,
people from the institute, secretary and workshop who many times helped me,
Friends, class mates became friends,
my family and especially Laura
Manuel Unternährer

35. Backup slides

36. References
M. Unternährer, B. Bessire, L. Gasparini, D. Stoppa, and A. Stefanov, ”Coincidence detection of spatially correlated photon pairs with a monolithic time-resolving detector array”, Optics Express 24, (2016).
L. Gasparini, B. Bessire, M. Unternährer, A. Stefanov, D. Boiko, M. Perenzoni, and D. Stoppa (2017), ”SUPERTWIN: towards 100kpixel CMOS quantum image sensors for quantum optics applications”, in Proc. of SPIE, Vol (2017),
L. Gasparini, M. Zarghami, H. Xu, L. Parmesan, M. Moreno Garcia, M. Unternährer, B. Bessire, A. Stefanov, D. Stoppa and M. Perenzoni, ”A 32x32-pixels time-resolved single-photon image sensor with mm pitch and 19.48% fill-factor with on-chip row/frame skipping features reaching 800 kHz observation rate for quantum physics applications”, in International Solid-State Circuits Conference, ISSCC’18 (IEEE, 2018, in press).
Under submission:
M. Unternährer, B. Bessire, L. Gasparini, M. Perenzoni, and A. Stefanov, ”Super-Resolution Quantum Imaging at the Heisenberg Limit”, arXiv: [quantph], (2018).
In preparation:
M. Unternährer and A. Stefanov, ”Self-Calibrating Optical Low-Coherence Reflectometry using Energy-Time Entangled Photons”, in preparation.
A. Mikhalychev, A. Sakovich, I. Karuseichyk, B. Bessire, M. Unternährer, A. Stefanov, and D. Mogilevtsev, ”Piecewise Tomography: Optimizing Reconstruction of Multi-Parameter Systems”, in preparation.
Manuel Unternährer

37. Correlation Functions
Field Characterization (Glauber, 1963)
For narrow bandwidth and low intensity → photon counting
Spatial & Temporal Discretization by Detector Pixel Array
Measurement: Sample Averaging
Needed: Copies of same quantum state / symmetries of correlation function
Correlation function: standard quantities to characterize the electric field, quantum expectation value of measurement operators.
Positive negative frequency field operators at transverse position, represent the electric field in quantum formalism.
n photon flux density. : : Normal Ordering, Technicality.
Correlated expectation value, theoretical prediction exists. How to measure?
Perfect temporal spatial resolution not given -> discretization
Photon number, actually measurable quantity
Quantum expectation value results from statistical averaging of the same measurement. No hat, measured photon number.
Manuel Unternährer

38. Correlation Functions
Example: Time-Stationary Field
Measurement of
Detector provides → Single statistical sample of
Fix two arbitrary pixels :
Averaging over “equal” regions
Sampling Function
Sampling Space Volume 1 2 T …
Example symmetry, time stationarity. See it in a moment illustrated. Other examples: pulsed sources, pulse to pulse same correlation function
Goal, measure G2(dt), fully characterizes field.
Photon numbers n at every pixel and time interval, repeated measurements for average needed.
“Equality” due to symmetry of correlation function
Measurement window “Frame” of length T
Detail: Theta_meas: avoid non-measrable regions (pixel self-correlation not possible at zero time separation)
Sampling Function, defines symmetry, or “how to average over measurement data”
Sampling Space Volume: number of measurements present in average at certain coordinate (p1,p2,dt)
Manuel Unternährer

39. Correlation Functions
Example: Temporally Coincident Nth-Order Correlations
Abbreviations
Sampling Function: Coincidence Window
Averaging (Data Processing)
Computationally expensive! Optimized algorithm uses
Sparsity of detection events and sampling function
Symmetry of resulting correlation function
Analytic expression for sampling space volume 1 2 T 3 …
Consider only photons arriving within a coincidence window (source correlation time)
Higher-Order Correlations
Sampling function: maximal temporal separation of N photons,
Example: for N=2 and Tc=2, two fixed pixels.
Note: no time argument in GN, implicit temporal coincidence assumed
Expensive, T=100, pixels=1000, frames per second 500k. N=4
Algorithm, implemented in C, nearly real-time analysis possible up to N=4
Manuel Unternährer

40. Correlation Functions
More general results derived
General formalism for measurement data processing of Nth-order intensity correlation functions
Ready for general light source modalities (Pulsed, Time-Stationary, …)
Worked out special cases (above examples), extensively used in imaging experiments
Fast Algorithm for High-Order Coincidence Measurement
Experimentally verified in thermal light experiments up to N=4
Manuel Unternährer

41. Correlation Functions
Discretization
Manuel Unternährer

42. SPADnet-I Sensor
A time resolving single photon detector array (FBK, Trento) developed for PET and adapted for quantum experiments within SUPERTWIN
Sensor
Process technology
CMOS
Array size
8 x 16 pixels
Pixel pitch
0.61 x 0.57 mm2
In-pixel photodetectors
720 SPADs
Chip size
5.4 x 9.8 mm2
Pixel fill factor FF
43 %
Max. frame rate
500 kfps
10 mm
5 mm
Per Pixel Time-to-Digital Converter (TDC)
Range (12 bit)
260 ns
Resolution
(65 ± 1.9) ps
Single Photon Avalanche Diodes (SPADs)
Size
Ø 16.2 µm
Jitter
171 ps
Avg. dark count rate
42 kHz
Detection efficiency
450nm,
810 nm
Testing of existing sensor prototype, evaluate for quantum optics applications, define requirements for next generation sensor
SPAD = ?
90k SPADs in total
SPDADnet-I
L. H. C. Braga et al.,
IEEE Journal of solid-state circuits 49, (2013)
Manuel Unternährer

43. Experiment - SuperEllen
A time resolving single photon detector array in CMOS technology (FBK, Trento)
Sensor
Process technology
CMOS (150 nm)
Array size
32 x 32 pixels
Pixel pitch
44.64 µm
In-pixel photodetectors
1 SPAD per pixel
Chip size
1.69 x 1.88 mm2
Pixel fill factor FF
19.48%
Max. frame rate
800kHz
Per Pixel Time-to-Digital Converter (TDC)
Range (8bit)
52 ns
Resolution
(204.5± 2.7) ps
Single Photon Avalanche Diodes (SPADs)
Avg. dark count rate
<1 kHz
Detection efficiency
400 nm
810 nm
L. Gasparini et al., IEEE-ISSCC, (2018)
Manuel Unternährer

44. SPDC Light Source
Frequency degenerate, type-0 spontaneous parametric down-conversion (SPDC)
Generation of spatially entangled photon pairs
Near-Field
Far-Field 1-D, Correlation Function
Schmidt Number
Non-Linear
Crystal
SPADnet-I
Filter
SPCs
TDCs
Far-field: anticorrelated, or fixed center of gravity
Characteristic of entanglement: correlation and anti-correlation
near vs. far-field: Violates Heisenberg-like uncertainty imposed by assumption of classical correlation:
Schmidt number: 38 different position (orthogonal states) of birth which are coherently superposed
1D measurement, dozens of minutes need to scan space -> detector array parallel
Well characterized light source -> we know what we should measure.
??? z
Manuel Unternährer

45. SPDC Source
Frequency degenerate, type-0 spontaneous parametric down-conversion (SPDC)
idler (i)
signal (s)
CW pump (p)
PPKTP
Temporal correlation: simultaneous emission (100 fs)
Transverse position correlation:
Entangled two-photon state at output plane of crystal spatial second-order correlation function:
SPDC: nonlinear optical process in a NLC with momentum and Energy Conservation
Coincident emission of pairs of photons
Lambda biphoton wave function given by process parameters (poling period, pump wavelength)
Rho: transversal part of 3dim position vector
G1: Transversal Intensity Distribution (=pump beam cross section), as seen on a camera
G2: Glauber 2nd order corr. function., what we will measure in the following, coincident photon, spatial correlation. positions difference as argument! How far apart they will be emitted. Illustration
Schmidt number prop to ratio of areas G2 / I
Manuel Unternährer

46. SPDC Source
Frequency degenerate, type-0 spontaneous parametric down-conversion (SPDC)
Thin Crystal
idler (i)
signal (s)
CW pump (p)
PPKTP
NLC end surface: spatially entangled two-photon state
Thin crystal & plane wave pump approximation
SPDC: nonlinear optical process in a NLC with momentum and Energy Conservation
Very low gain regime, coincident emission of pairs of photons
Perturbation theory, kappa interaction and pump field strength.
Contrast to sacha, jos: narrowband, single temporal mode here.
Thin nlc: Coherent superposition, biphoton
Lambda biphoton wave function given by process parameters (poling period, pump wavelength)
Rho: transversal part of 3dim position vector
Manuel Unternährer

47. SPDC Measurement with SuperEllen
Manuel Unternährer

48. G2 Maps Two-lens instead of single lens image,
Beamsplitter separates photon pairs
5 Million Frames in 16s, 1.3GB
Fixed measuement time
4D object, as if one line of pixels, 128x128 = 16k mesaurements
Full 2D scan in 16s, before 1D dozens of minutes

49. Model Experiment Imaging with Classical Light Illumination
Object with transmission function , magnification m
Point-Spread-Function (PSF) → Image Resolution Lens Diameter D, Illumination Wavelength λ
Diffraction Limit, Rayleigh Resolution Limit
Single Lens image, s
Not intended as real microscope in this form which have several lenses, but shows same limitation due to wavelength. Diffraction limit.
Allow to study resolution and wavelength dependence.
Object aperture A
Convolutoin, replaces every image point by disk
PSF, wavelength depndance the smaller lambda, the better the resolution
Paraxial approximation
Possible to beat this diffraction limit ->Super-resolution
with special light source z
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50. Model Experiment Imaging with Two-Photon Illumination
Spatial two-photon coincidences
In addition: More image information in full correlation function
1024
data points
1 million data points
Spatial coincidence: distribution of two photon in same location
For reconstruction algorithm, more information
SuperEllen z
Manuel Unternährer

51. Object Reconstruction Algorithm
Idea: Image information content larger in than
Reconstruct object from measured data
Formulated as non-linear optimization problem
Generalization to Nth-order
Measured Correlation Function
Model Prediction depending on A
Estimated Measurement Error
Theory group in Belarus, collaborator in SuperTwin. developing algorithm.
More information in correlation function, 1 million data points
Thermal light, Nth order measurement possible.
A. Mikhalychev et al., ''Piecewise Tomography: Optimizing Reconstruction of Multi-Parameter Systems'', in preparation.
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52. Thermal Light Source
Isserli’s (Wick’s) Theorem for Moments of Multivariate Gaussian Distribution:
Manuel Unternährer

53. Thermal-Light Measurements
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54. 4-Photon Source Testing of new sensors & imaging
NLC for
SHG
NLC for
SPDC
Fourier lens
395 nm
Testing of new sensors & imaging
Source characterization
Far-field correlation measurement
Second-order correlation sufficient
Pulsed Tiger fs, 500 mW
Fourier lens, fiber on motorized stages, SPD
G2 measurement sufficient, detect just 2 of 4 photons: we know two-photon state, don‘t expect new. Only double-pair correlation interesting
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55. 4-Photon State
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56. 4-Photon Source - Characterization
Far-field correlation measurement
Stimulated double-pair emission (2nd order PT)
Single-pair events (1st order PT)
Generation of correlated 4-photon states verified
Soon ready for use with new sensor array and imaging → Visit of Leonardo Gasparini (FBK, Trento)
Coincidence between consecutive pulses: belong to two different pairs. Assume same probability of two consecutive emission as two within same pulse
But stimulated emission increases probability within same pulse having two -> visible!
Manuel Unternährer

57. SuperEllen Experiment
Far-Field Imaging of Photon Pairs
Crystal
Filters
Intensity:
Correlation Function:
1 Million Simultaneous Measurements
60s measurement time, 26MFrames
Intensity, what a normal camera sees
G2: 1M measurement points, scanning 1M positions
statistically analyze correlation properties:
Only temporally correlated signal extracted -> nice beam shape!
Realtime software
Centroid Position:
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58. Mechanism of Quantum Advantage
Double Slit Experiment +
Imaging of a Point +
+ …
Imaging with a N-Photon Transmitter
Photon pair propagates as a unity: interference effect +
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59. Optical Centroid Measurement
N-Photon OCM Image State
Change of Variables
Propagated through General Optical System
Single Lens Imaging: Effective PSF
In Far-Field Basis
M. Tsang, PRL 102, (2009)
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60. OCM State Generation SPDC Generated State OCM Image State
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61. OCM Results
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62. Multi-Photon Imaging Classical Light Illumination Imaging
Two-Photon Illumination Imaging
Single Lens image, s
Not intended as real microscope in this form which have several lenses, but shows same limitation due to wavelength. Diffraction limit.
Allow to study resolution and wavelength dependence.
Object aperture A
Convolutoin, replaces every image point by disk
PSF, wavelength depndance the smaller lambda, the better the resolution
Paraxial approximation
Possible to beat this diffraction limit ->Super-resolution
with special light source
SuperEllen z
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63. Acknowledgments Andre, Co-Referee Prof. Marco Genovese,
Feurer head of laser division,
QO my doctoral brothers, especially Bänz,
Long-time Office mates
Laser Group and the whole IAP,
With secretariat, mechanical workshop electronics and chemistry
Friends,
my “physicist” friends
Master class mates and friends
Family, and especially
Prof. André Stefanov, Dr. Marco Genovese
Prof. Thomas Feurer
Prof. Thomas Becher
QO Group: Bänz, Jos, Stefan, Sacha
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64. J. C. Maxwell ( )
P. de Fermat ( )
Diffraction
Interference pattern: regions of constructive/destructive interference: canceling regions
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65. : Measurement time and equipment considerable
SPCs
TDCs
CCD
: Measurement time and equipment considerable
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66. PPKTP Crystal 400 nm 800 nm pump (p) signal (s) idler (i)
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67. Model Experiment Imaging with Classical Light Illumination
Object with transmission function A, magnification m
Point-Spread-Function (PSF), circular lens of diameter D
400 nm
800 nm
800 nm
400 nm
At fixed D and wavelength λ,
photon pairs for illumination?
Not intended as real microscope in this form, but mimicks the limitation due to wavelength in microscopes qu
Object aperture A
Convolutoin, replaces every image point by disk
PSF, wavelength depndance
Pollen, electron microscopy
At fixed D and wavelength λ, photon pairs for illumination give advantage? D z
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68. Object Reconstruction Results
Reconstruction Original Object Rayleigh Limit
Lens of large Diameter changed, fixed wavelength
More quantitive comparison: 1D cut through image:
Reconstruction of object discretized into pixels
Up to 8x higher resolution than Rayleigh allows, full visibility
Thermal light upper, Photon pairs lower 15 30 45 60 75 90 15 30 45 60 75 90 30 45
A. Mikhalychev et al., manuscript in preparation.
Manuel Unternährer

69. Overview Quantum Imaging Supertwin Project
Classical Light: Imaging, Resolution Limit
Quantum Advantage?
Biphoton Optics: Light Source, Super-Resolution Imaging
Supertwin Project
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70. Classical Light – Imaging
Goal: “Measure shape of an object remotely”
Imprint shape of object onto electric field
Manipulate electric field
Measure field (intensity) & reconstruct shape
Transverse position coordinate
Recepie
Prototype imaging setup
Simplest case of imprint: measure transmission through object. Represented by a aperture function.
Pixelated/scanning detection device, squared modulus of electric field
??? z z1 z2
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71. Classical Light – Imaging
Monochromatic light source
Linear optical setup, response function
Get rid of any temporal dependences
A little heavy formal machinery, later for quantum multi-mode light source
H: relates two planes, if field source at rho1, distribution at rho2
Sum over all field sources at rho1, coherently add up them on rho2 H z z1 z2
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72. Classical Light – Imaging
Monochromatic light source
Linear optical setup, response function
Near-field imaging with single lens, magnification m, object transmission A
NF: object to image plane trafo,
PSF: object point to image spot -> delta function in ideal case -> upside down replication of A in image plane
PSF, FT of aperture function
In case of plane wave illumination -> convolved z z1 z2
Manuel Unternährer

73. Classical Light – Imaging
Monochromatic light source
Linear optical setup, response function
Near-field imaging with single lens, magnification m, object transmission A
Far-field imaging, distance L
Far-field: paraxial approximation used. Spherical wave from rho1 point to rho2, tilt from exponential
FT of object, Lambda determines scale of diffraction pattern
Destructive interference if path length difference half a wavelength z z1 z2
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74. Classical Light – Imaging
Far Field Measurement
Object: Double slit, line width 111 μm
Halfed diffraction angles at 400 nm “Denser image information”
Fourier lens f = 500 mm
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75. Classical Light – Imaging
Near Field Imaging
Circular aperture diameter D, Airy disk
Resolution limit (Rayleigh) D
For circular aperture, Airy disk / pattern, Bessel function
Scales with parameters.
Smaller psf for larger D, or lower lambda z z1 z2
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76. Classical Light – Imaging
Near Field Measurement, CCD
Object line width: μm, lens diameter D
D = 12 mm
D = 1.5 mm
405 nm
f = 60mm, 12x magnification,
810 nm
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77. Quantum Advantage?
de Broglie wavelength of a composite system of n photons
Quantum metrology, e.g. phase estimation
Probe with n photons
Independent photons / classical light Standard Quantum limit
Entangled photons (NOON state) Heisenberg limit
Why to think that quantum light better resolution?
Phase estimation, eg. Ellipsometry
Heisenberg limit, best quantum improvement. Equally to n-fold wavelength
Quantum light source, Independant fiber detectors H z z1 z2
Manuel Unternährer

78. Biphoton Optics – SPDC Source
Frequency degenerate, type-0 spontaneous parametric down-conversion (SPDC)
Thin Crystal
idler (i)
signal (s)
CW pump (p)
PPKTP
NLC end surface: spatially entangled two-photon state
Thin crystal & plane wave pump approximation
SPDC: nonlinear optical process in a NLC with momentum and Energy Conservation
Very low gain regime, coincident emission of pairs of photons
Perturbation theory, kappa interaction and pump field strength.
Contrast to sacha, jos: narrowband, single temporal mode here.
Thin nlc: Coherent superposition, biphoton
Lambda biphoton wave function given by process parameters (poling period, pump wavelength)
Rho: transversal part of 3dim position vector
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79. Biphoton Optics – Measurements
Second order correlation measurements
Rate of coincident photon pairs measured by single photon counters
Measuring a two-photon state
Example: SPDC, 1D x-scan
Intensity correlation, expectation
Omit delta t = 0, always the case.
SPC, 0 or 1 output
Two photon absorbing film -> diagonal of G2
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80. Biphoton Optics – Imaging
Two-photon state propagation (source → detectors)
Near-field imaging
Ideal SPDC light source
Two-photon absorbing film
General: Effective PSF narrowed by factor Standard Quantum Limit
Quantum Theory tells us:
Lambda transforms like product of two independent electric fields. Both photons independently transformed in linear system
From crystal to detector
Blue: crossection of PSF of a circular aperture vs higher powers
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81. Biphoton Optics – Imaging
Near-field imaging
Double slit object: d = μm
1D scanning fiber coincidence measurement
Statistical and geometrical interpretation of resolution enhancement d
D = 12 mm
D = 1.5 mm
f = 60mm, magnification 12x
12x magnification
Blurred due to increased PSF, resolution advantage by diagonal separation
Statistical: two photon emerge from same slit, both spread by PSF = their random distribution, take average position -> spread sqrt2
geometrical: in G2 space, slits effectively separated by sqrt(2) longer distance, circular symmetric less extended
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82. Biphoton Optics – Imaging
Far-field imaging
Response function, source to detectors distance L
Ideal SPDC light source
Two-photon absorbing film
General: Effective wavelength enhanced by entangled photon number Heisenberg limit
Heisenberg limit, largest possible quantum advantage.
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83. Biphoton Optics – Imaging
Far Field Measurement
Object: Double slit, line width 111 μm
Near-field
Far-field
No fitting
Devition from perfect Gaussian beam, as assumed in theory
Object features recoverable by reconstruction
Fourier lens f = 500 mm
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84. Biphoton Optics - Intuition
“Feynman Diagrams”
Far-Field
NOON state like situation
Biphoton effectively “bound”, enforced by detection
De Broglie wavelength of bound, composite system
Near-Field
Contributions from paths where biphoton separates
No bound state, photons propagate independently
TPA
TPA
Difference of resolution advantage.
Sum amplitudes of all paths that lead to same final state = detected state
Two photon transmitter
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85. Overview Quantum Imaging Supertwin Project
Project Partners and Objectives
Our experimental work within Supertwin
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86. Supertwin Project www.supertwin.eu H2020: FET Open section
Fondazione Bruno Kessler (Italy)
A.P.E. Research srl (Italy)
Centre Suisse d'Electronique et Microtechnique (Switzerland)
III-V Lab (France)
Single Quantum (The Netherlands)
University of Bern (Switzerland)
École Polytechnique Fédérale de Lausanne (Switzerland)
Institute of Physics, National Academy of Sciences of Belarus LFoundry S.r.l. (Italy)
Who is involved?
Fet section of h2020 program
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87. Objectives of Supertwin
Beyond Rayleigh resolution microscopy with entangled photons: System concept, architecture and processing algorithms
Efficient solid-state source of entangled photons based on superradiant pulse emission
Development of imaging sensor for fast photon correlation measurement
Demonstrator breadboard as proof-of-concept for super-resolution microscopy
Workpackage, Leader
Source: High risk high reward
Fiber scanning, very long measurement time, rises exponentially with photon number.
SPAD array, fast correlation measurements in parallel.
CCD. Made for longtime exposure, no single photon correlation efficiently possible
Resolution: 41 nm (factor 5 improvement over classical light)
Acquisition time: 10 min
Image: 256x256 pixels
Sample type: organic or inorganic, without preparation
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88. Our Work within Supertwin
Quantum Imaging Experiments
Proof-of-principle
Test of image reconstruction algorithms
Imaging sensor characterization
Generate data for
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89. Quantum Imaging – Setup
CW pump power: 32 mW
(Spec. bandwidth: <2 MHz)
Superradiant not available yet, so stick SPDC two-photon source
Max. SPDC power of 2.1 nW Flux 8 x 109 ph/s
Imaging parameters: L1, L2: f = 50 mm (=> m=1),
L3: f = 60 mm (=> m=sI/sO=12)
variable aperture, diameter D
USAF 1951
Near- and Far-Field imaging possible, depending on focal length of L3
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90. Quantum Imaging – Near Field
Double slit object: d = μm
1D scanning fiber coincidence measurement d
D = 12 mm
D = 1.5 mm
12x magnification
Blurred due to increased PSF, resolution advantage by diagonal separation
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91. Quantum Imaging – Near-Field
Data pattern based reconstruction algorithm (IPNASB)
G1 (intensity) image
Expected object shape
Reconstructed image
Group 5, element 1, slit width = μm,
ws = 16.8 μm, R = 2.5 mm, pixel size = 4.35 μm
Classical resolution (Rayleigh limit)
Or deconvolution
Discretization of object: Pixels
optimization problem „what object would produce measurement with lowest error“,
4x, 6x and 5x superresolution, achieved through „statistical superresolution“ = deconvolution
W_s = rayleigh resolution
Group 5, element 1, slit width = μm,
ws = 28.0 μm, R = 1.5 mm, pixel size = 4.35 μm
Group 4, element 1, slit width = μm, ws = 41.9 μm, R = 1.0 mm, pixel size = 8.51 μm
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92. Our Work within Supertwin
Quantum imaging experiments
Imaging sensor characterization
Test existing prototype device with SPDC
Future: Test new devices with higher photon-number correlations
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93. SPADnet-I Sensor
A time resolving single photon detector array (FBK, Trento) developed for PET and adapted for quantum experiments within SUPERTWIN
Sensor
Process technology
CMOS
Array size
8 x 16 pixels
Pixel pitch
0.61 x 0.57 mm2
In-pixel photodetectors
720 SPADs
Chip size
5.4 x 9.8 mm2
Pixel fill factor FF
43 %
Max. frame rate
500 kfps
10 mm
5 mm
Per Pixel Time-to-Digital Converter (TDC)
Range (12 bit)
260 ns
Resolution
(65 ± 1.9) ps
Single Photon Avalanche Diodes (SPADs)
Size
Ø 16.2 µm
Jitter
171 ps
Avg. dark count rate
42 kHz
Detection efficiency
450nm,
810 nm
Testing of existing sensor prototype, evaluate for quantum optics applications, define requirements for next generation sensor
SPAD = ?
90k SPADs in total
SPDADnet-I
L. H. C. Braga et al.,
IEEE Journal of solid-state circuits 49, (2013)
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94. Non-linear crystal in object plane
SPADnet-I Experiment
Non-linear crystal in object plane
Telescope
1:8
Sensor in image plane
2nW 10^10 ph/s
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95. SPADnet-I Results Coincidence detection between two pixels i, j
Frame data evaluation, accidental removal
Visualize spatial correlations
Coincidence Window
t=-80
1 TDC unit = 65 ps
Accidental background
Our source emits photon of a pair simultaneously. Delta t = 0
Coincidence window, non zero due to electronic jitter
Accidental = events between two different photon pairs, or dark count and
16s measurement time
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96. SPADnet-I Results SPDC spatial correlations at different object planes
“Observing two-photon state propagation”
z = 0 mm
z = 5 mm
z = 10 mm
Experiment:
Theory:
Photon pair separates while propagating -> FF anticorrelated
Only left to right coinc for removal of crosstalk
45s measurement time
M. U., B. Bessire, L. Gasparini, D. Stoppa, and A. Stefanov, Opt. Express 24, (2016).
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97. SPADnet-I Results
The results helped us identifying the following requirement for the next sensors:
Reduce the cross-talk
Enhance the rather low duty cycle of 0.33 %
Better photon detection efficiency
Smaller pixels to obtain better resolution
But technology is promising for performing fast quantum imaging experiments!
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98. 4-Photon Source Testing of new sensors & imaging
NLC for
SHG
NLC for
SPDC
Fourier lens
395 nm
Testing of new sensors & imaging
Source characterization
Far-field correlation measurement
Second-order correlation sufficient
Pulsed Tiger fs, 500 mW
Fourier lens, fiber on motorized stages, SPD
G2 measurement sufficient, detect just 2 of 4 photons: we know two-photon state, don‘t expect new. Only double-pair correlation interesting
Manuel Unternährer

99. 4-Photon Source - Characterization
Far-field correlation measurement
Stimulated double-pair emission (2nd order PT)
Single-pair events (1st order PT)
Generation of correlated 4-photon states verified
Soon ready for use with new sensor array and imaging → Visit of Leonardo Gasparini (FBK, Trento)
Coincidence between consecutive pulses: belong to two different pairs. Assume same probability of two consecutive emission as two within same pulse
But stimulated emission increases probability within same pulse having two -> visible!
Manuel Unternährer

100. Conclusion Spatially entangled photons can enhance image resolution
Far-field imaging fully exploits quantum advantage
Near-field imaging needs more investigation
For practical application needed:
Source of high number of spatially entangled photons
Fast, specialized detectors
Take Home Message
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101. SUPERTWIN All Solid-State Super-Twinning Photon Microscope PROJECT ID: 686731
Chip design team IRIS, head david stoppa.
funded by the EU within future and emerging technologies section of horizon2020 program
Participating many institutions and companies
Thank to andré for opportunity to work in this project, and Bänz for very pleasant collaboration and
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102. Thank you for your attention!
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103. SPADnet-I Results SPDC measurement in far-field
Telescope replaced by Fourier lens L1
Single counts
Spatial anti-correlations f
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104. Entangled 4-Photon Source
Strong pulsed pump → Second order PT: Four photon state
spontaneous emission
Test a next generation sensor with 4-photon correlations, maybe imaging experiments
Photon number ket, number per mode
Here formulated in far-field, FT to get to NF
At what angles are photon emitted
Factor 2 -> double probability to have coincidence in same mode. (because
Spontanueous: two independent pairs, no correlation!
Stimulated: factor two, increased probability to detect in same q-mode
Only spatial modes treated here.
Single temporal mode: DC photons temporally indistinguishable, coherence time spdc >> pulse
Visibility inversely proportional with temporal mode number
No too short: walk off between pump and in NLC
spontaneous + stimulated emission
Single temporal mode needed:
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105. Pulsed laser induced SPDC
What is the optimal length of the crystals? v tc
Δtp=2 ps
...
tphc
Spatially mono-mode (e.g. collinear configuration of photons)
Coherence time of an SPDC photon tphc =100 fs
N->1 in the limit of tph≈Δtp.
Additional spectral filtering of the SPDC
photons to make N as small as possible.=>Genuine 4-photon states are dominating.
Assume photon number
resolving detector scheme:
Distinguish between 0,2 and genuine 4-photon states
Able to directly measure photon number statistics
Statistics will be of thermal nature
For CW pump case the statistics is Poissonian
N≈1:
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106. WP1.5 Image reconstruction algorithms
Possible approaches to reconstruction problem
Deconvolution.
Applicable to linear problems.
Image decomposition in terms of orthogonal functions.
Phase information is required.
Convergence of iterative phase retrieval approaches breaks for “super-resolution” regime.
“Data pattern” approach.
Quantum tomography:
Data-pattern tomography of entangled states,
V. Reut, A. Mikhalychev, and D. Mogilevtsev PRA 95, (2017)
Manuel Unternährer

107. WP1.2 Quantum imaging - SPDC
Entangled 2-photon state by SPDC
2-photon wave function in momentum/frequency space
Why entangled?
Not yet a quantification of entanglement only the definition
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108. Super-Resolution Techniques
SOA: super-resolution techniques that make use of fluorescence staining of the samples
SOA
SUPERTWIN
Super-resolution
~20nm-100nm (SNOM, STED)
42 nm
Acquisition time (depends on area and resolution)
few min
10 nm
Sample preparation and compatibility
Yes No
Manuel Unternährer

109. WP1 SPADnet-I Results Single photon detection
Data acquisition during 5.4 M frames (45 s effective measurement time)
Distribution of the detected photon number N
Total of 3.07 M registered events (dark counts: 427 k):
PDE = 810 nm (36% SPADs active)
55% of the frames contain no event
0.57 events per frame
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110. WP1 SPADnet-I Results
Coincidence detection in the time domain (second-order correlation)
Frames with N ≥ 2 : Histogram of detection time difference in from 5.4 M frames (blue)
Accidental events: Dark counts and photons from different pairs
Central coincidence peak with |t| < 390 ps (6 TDC units) consists of real coincidence events (two-photons from same pair) and pixel- crosstalk
Accidental events
t=30
t=-80
1 TDC unit = 65 ps
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111. Histogram in pixel position differences
WP1 SPADnet-I Results
Coincidence detection in the spatial domain
For each two-pixel combination: 300 ps coincidence window
Linear indexing to visualize spatially resolved two-pixel correlations 1 2 3 4 9 17
128
Histogram in pixel position differences
Long ranging optical crosstalk between pixels
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112. WP1 SPADnet-I Results Spatial 2nd order correlations in far-field
Telescope replaced by Fourier lens L1 f
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113. Frame
(Map of timestamps)
Per external trigger event (up to 250kHz): two frames each of 10 ns exposure time
Time-stamp of the first photon detected within pixel
1 TDC unit = 65 ps
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114. Classical Light – Imaging
Near Field Imaging
Circular aperture PSF
Resolution (Rayleigh)
Minimal feature size by max. transverse wave vector
For circular aperture, Airy disk / pattern, Bessel function
Scales with parameters.
Smaller psf for larger D, or lower lambda z zO zD
Manuel Unternährer

115. Introduction Detection of transverse photon correlations
Application in experiments in
Fundamental tests of quantum theory (e.g. Einstein-Podolsky-Rosen original formulation)
Quantum information in high dimensional Hilbert spaces
Quantum imaging (e.g. ghost imaging, lithography, super-resolution)
These correlations can be explored by scanning detectors, or more efficiently by multi-pixel arrays
EMCCD
ICCD
On-pixel time resolution
F. Just et al., Opt. Express 22, (2014)
Hybrid photon detector
- 256 x 256 pixels
- Single pixel time
resolution: ≈10 ns
Variety of exp: fundamental test, applications like quantum imaging.
No temporal Resolution within frame -> low exposure time/low photon flux needed for coincidence detection
Low Frame Rates -> long measurement time
Very high dimensional Hilbert spaces
CCD: single photon sensitive, but readout noise does not allow SP operation
EMCCD: amplify photoelectron prior to readout (electron multiplying)
ICCD: use image intensifier in front of CCD
Complex systems
Hybrid:
Per pixel in chip TDC, time of arrival per pixel, 10ns.
Relies on image intensifier
Very low frame rate, Bulky
Hybrid = signal processing and photosensitive area separately produced, then bonded
We present
Detector with higher temporal resolution,
fully produced in standard CMOS semiconductor manufacturing process.
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116. SPADnet-I Sensor
Time resolving Single Photon Avalanche Diode array, fully digital and integrated (FBK, Trento)
10 mm
5 mm
Sensor
Process technology
CMOS
Array size
8 x 16 pixels
In-pixel photodetectors
720 SPADs
Chip size
5.4 x 9.8 mm2
Pixel fill factor
43 %
Max. frame rate
500 kfps
SPDADnet-I
Single Photon Avalanche Diodes (SPADs)
Size
Ø 16.2 µm
Avg. dark count rate
42 kHz
Detection efficiency
450nm,
810 nm
SPAD =
Developed for PET, adapted for quantum photonics in this work
Integrated, all in chip, board only for data extraction
Fully digital, signal digitalized, counted and timed within pixel
Pixel size large, developed for medical Imaging applications in medicine, PET
Record fill factor in comparison to similar sensors with on chip TDCs
digital signal handling, in pixel tdc+counters
Frame, being explained
Rather low PDE, not optimized for our experiment, semiconductor bandgap…
Dark count produce uncorrelated events, can be filtered in postprocessing step, see later.
Ethernet link for data read out, 500Mbit/s on a commercial FPGA board.
PDE including Fill Factor
Effective temporal resolution 260ps
Per Pixel Time-to-Digital Converter (TDC)
Resolution
(65 ± 1.9) ps
L. H. C. Braga et al., IEEE Journal of solid-state circuits 49, (2013)
Manuel Unternährer

117. SPADnet-I Sensor Features
Chip allows to individually disable single SPADs within a pixel
64% of SPADs disabled (black regions)
Mute SPADs with high dark count rates
Disable boarders between pixels to avoid crosstalk
Frame
(Map of timestamps)
Per external trigger event (up to 250kHz): two frames each of 10 ns exposure time
Time-stamp of the first photon detected within pixel
1 TDC unit = 65 ps
Map, white enabled, dark disabled
High dark count due to fabrication variation. 50% disabled
Crosstalk = spurious detection events. electrically avoided due to fully digital signal handling. Only optical expected (detection/dark diode avalanche produce secondary photons)
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118. Experiment Light Source
Frequency degenerate, type-0 spontaneous parametric down-conversion (SPDC)
idler (i)
signal (s)
CW pump (p)
PPKTP
Temporal correlation: simultaneous emission (100 fs)
Transverse position correlation:
Entangled two-photon state at output plane of crystal spatial second-order correlation function:
SPDC: nonlinear optical process in a NLC with momentum and Energy Conservation
Coincident emission of pairs of photons
Lambda biphoton wave function given by process parameters (poling period, pump wavelength)
Rho: transversal part of 3dim position vector
G1: Transversal Intensity Distribution (=pump beam cross section), as seen on a camera
G2: Glauber 2nd order corr. function., what we will measure in the following, coincident photon, spatial correlation. positions difference as argument! How far apart they will be emitted. Illustration
Schmidt number prop to ratio of areas G2 / I
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119. Experiment Optical Setup
Non-linear crystal in object plane
Pump spectral filter,
(810 ± 5) nm
Telescope magnification 8x
Sensor in image plane
Photon pair separation on two separate sensor regions
Avoid both photons being incident on same pixel
Suppression of crosstalk
NLC, filters to remove pump
Telescope images central plane onto detector
Pixel goes blind after detection, second photon would be lost.
Correlation length smaller than pixel size.
Pair correlation time of ≈ 100 fs, not resolvable by sensor
2 nW SPDC power incident onto sensor (photon flux ≈ 1010 ph/s = 100 ph/frame)
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120. Results Single photon detection
Data acquisition of 5.4 M frames (16s measurement time, 1.3 GB binary data)
Total of 3.07 M registered events (dark counts: 427 k)
PDE = 810 nm (36% SPADs active)
Distribution of the detected photon number N
55% of the frames contain no event
Average: 0.57 events per frame (57 Mcps)
Manuel Unternährer

121. Results Spatial second-order correlations measurement evaluation
Coincidences between pixel pair i, j
t=-80
1 TDC unit = 65 ps
Accidental events
Accidental (i.e. uncorrelated) events: Dark counts and photons from different pairs
Linear fit and extrapolation: Estimate and subtract accidental events around Δt=0
Crosstalk is coincident, no accidental
Central peak: real coincidence events (red), i.e. photons from same pair and pixel-crosstalk
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122. Histogram in pixel position differences
Results
Spatial second-order correlations of SPDC 1 2 3 4 9 17
128
Linear indexing to visualize 4D correlation function
Histogram in pixel position differences
Long ranging optical crosstalk between pixels
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123. Results Spatial second-order correlations of SPDC
Various crystal positions = measurement in different object planes, observing biphoton propagating
z = 0 mm
z = 5 mm
z = 10 mm
Experiment:
Theory:
Different positions along optical axis z.
Varying NLC temperature
Consider only correlations between left and right side of the sensor to suppress crosstalk
M. U., B. Bessire, L. Gasparini, D. Stoppa, and A. Stefanov, Opt. Express 24, (2016).
Manuel Unternährer

124. Conclusions and Outlook
Fast and easy spatial second-order correlation measurement
Reconstruction of spatial correlations in the presence of a high amount of noise
Fully digital, integrated sensor technology in standard manufacturing process allows cost-effective production for use in future devices
Outlook
Next generation sensor under development at FBK
256 x 256 pixels
Mfps
Crosstalk reduction
>5% photon detection efficiency at 800 nm
4-photon coincidence measurements, quantum imaging experiments
SUPERTWIN project:
Develop a new type of microscope with super-resolving capabilities based on quantum states of light
Fast: within seconds or at most minues, no scanning needed, simple as a camera
Higher fps, by in-chip data reduction, coincidence preprocessing in hardware
no separation of pairs needed
Fast < 3min
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125. SUPERTWIN All Solid-State Super-Twinning Photon Microscope PROJECT ID: 686731
Chip design team IRIS, head david stoppa.
funded by the EU within future and emerging technologies section of horizon2020 program
Participating many institutions and companies
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126. Results Spatial 2nd order correlations in far-field
Telescope replaced by Fourier lens L1
Direction of emission, Well known emission cones
Momentum conservation -> anticorrelation
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127. Results Isolate pixel crosstalk in the time domain
Increase the optical path delay between the two beams from 20 mm to 300 mm (1 ns delay)
Signal peak expected at (accidentals removed):
Crosstalk (4 x 104 events) masks the coincidence signal (blue curve)
Consider only coincident events between pixels on the right side and the left side of the sensor (red curve). Still a bit of crosstalk included in the signal.
Manuel Unternährer

128. Results
Coincidence detection in the spatial domain (second-order correlation)
Theory (z=0 mm, T = 25°C) versus measurement (correlation width 0.3 mm < pixel size 0.6 mm)
Reason for beam-splitting: Resolve correlation function and separate cross-talk
Add additional beam delay (20 mm to 300 mm)
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129. Results
Coincidence detection in the spatial domain (second-order correlation)
Spatial correlations as a function of various crystal temperatures T
Minimize crosstalk: Consider only inter-beam correlations
z = 5 mm
T = 25°C
T = 24°C
T = 23°C
Experiment:
Theory:
M. Unternährer et al., Opt. Express 24, (2016)
Manuel Unternährer

130. Accidentals
Uncorrelated events lead to accidental coincidence detections
Dark counts and photons from different pairs have uniform detection time distribution within measurement window
Detection probability density
10ns t
0ns
Distribution of difference in detection time of two uncorrelated events is the convolution of
the two uniform distributions
10ns Δt
-10ns
Detection probability density
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131. Accidental Subtraction
Uncorrected vs. corrected for accidentals
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132. Sensor operating mode Timing diagram of the SPADnet-I sensor
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133. SPDC State
Degenerate, Collinear, Type-0 Spontaneous Parametric Down-Conversion (SPDC)
idler (i)
signal (s)
Monochromatic Pump, 405nm
≙ 810 nm
Undepleted pump approximation, 1st order perturbation theory yields
Two slides ago: Experiment we performed to test this sensor using entangled photon pairs.
Nonlinear optical process. Inverse spontaneous process as SHG,
Degenerate =, Collinear = , Type-0 =
Chi2, second order susceptibility, material property.
Signal/idler: labels, indistinguishable in this case
Conservation of energy. Monochromatic, not pulsed. Biphoton large uncertainty of detection, but time difference between photons very short, 100fs
Wavevector k, or Momentum. Direction of propagation
Transverse momentum, plane orthogonal to optical axis. Sufficient to define state given wavelength. Paraxial approximation: K_z constant
First order perturbation in low gain regime, only spontaneous process. Momentum conservation explicit.
Phase mismatch function, which directions interfere constructively along to crystal
Thermal dependence of index of refraction. Thermal Expansion, only minor contribution
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134. Determine the Poling Period G
Use experimental data to fit the poling period of the NLC
Make near-field correlation measurement
Fit theory to measurement to obtain G = μm
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135. Free space transfer function
Free space transfer function in paraxial approximation
Shift the NLC in z-direction (i.e. z ≠ 0 mm) leads to non-collinear correlation pattern
Corresponding free space propagation transfer function (paraxial approximation)
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136. Imaging Resolution Object A Sensor Homogenous light source
Standard quantum limit here, sqrt(n) advantage in resolution, limited number of spatial modes transmitted to
Two photon absorber.
Heisenberg limit, n advantage: mimicking with biphoton a photon of double energy
Classical g^n: split and measure, signal reduction.
Noise: I^n -> n*I^(n-1)*sqrt(I) -> S/N = sqrt(I)/n
→ Smaller effective PSF by averaging positions
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137. CCD Cameras CCD devices to detect transverse correlations
Conventional CCD cameras are limited by read-out noise introduced by output amplifier
Do not work in single photon counting regime
Electron-multiplying CCD (EMCCD)
Amplifies collected photo electrons in a gain register before readout
Can work in single photon counting regime (one photon/pixel regime)
Exposure time of the order of μs (not usable for a coincidence gate)
(Flux of SPDC photons must be reduced to distinguish between independent pairs)
Cooling needed to suppress dark counts
Intensified CCD (ICCD)
Amplifies collected photo electrons in a gain register before readout
Can work in single photon counting regime (one photon/pixel regime)
Exposure time of the order of μs (not usable for a coincidence gate)
Manuel Unternährer

138. Sensor in PET application
Time resolution of coincident event gives special resolution of 3cm
Classical tomography only considers projection, time information gives additional information, allows to
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