# Presentation: 035250

## Photon-number resolving detectors using conventional APDs

- Daryl Achilles
- Czarek Sliwa
- Christine Silberhorn
- Konrad Banaszek
- Ian A. Walmsley

- Funded by NSF and ARDA

## Outline

- • Photon detection
- 	Detection efficiency vs quantum efficiency
- 	Number-resolving detection

- •Engineering concepts

- Mode separation
- Multiple-vs-single detectors

- • Initial demonstration

- Photon statistics of a weak coherent state

## Nonlinear sign-shift gate

- Engineered source with K=1
- leads to optimum fidelity.

- Fidelity of
- gate operation

- Mode-matching

- If T1 T2 T3 fire simultaneously:
-    (3 photons input)
- and NS triggers i.e. C1=1 C2=0,
-    there cannot be D1 D2 coincidence

- D1-D2 Conditional visibility

**Sources should emit photon multiplets in appropriate modes**

## Conditional entanglement Preparation

- PDC – parametric down-conversion crystal
*a*, *b*, ... – spatial modes
- BS1, BS2 – beam-splitters
- HWP – half wave plate at 22.5°
- PBS1, PBS2 – polarisation analysers
*x*, *y* – polarisation modes

- the output is conditioned on four-fold coincidence in detection
-  coincidence is not possible in first order in photon generation
-  The second order vacuum term vanishes due to interference
-  the third order yields the maximal entanglement

- Appropriate use of correlated multiphoton state guarantees the output is a pure two-photon entangled state

- Sliwa and Banaszek, PRA, 2003

## Conditional entanglement Fidelity

## Multiple-photon discrimination

- • Statistics can be altered by conditional detection

- • Need for detectors that discriminate between multiple photons

- What can be done with existing technology?

## Mode-separation detector

- •	•	•	•

- •	•	•	•

- • Input light  in a single mode
- • Divide input among many modes
- • ensure that there are many more output modes than input photons
- • count “clicks” (I.e. presence or absence of photons) in the output modes

- Input light

- “click” counting detectors

- Unitary mode transformer

## Loop-detector

- Loop detector based on room-temperature APD and fiber technology

- S - switch
- C - few dB coupler (loss =      )
- APD - Avalanche photodiode
- Loop latency > APD dead time

- Input and output modes are time-slots

- Efficiency

## Loop-detector: Analysis

- = prob of *k* “clicks”

- = moment generating fn for click distribution with
-     input intensity *I*

- For coherent state input each round trip is independent:

- = Poisson dist. With effective detection efficiency

##  Efficiency up to that of the detector but with photon number resolution

-  Efficiency up to that of the detector but with photon number resolution

- Distribution can be inverted to get input photon statistics

- Photon number distribution at input

- Given the click-counting distribution for coherent state input:

- Then:

- But also:

- From which the                can be obtained

## Multiple-photon discrimination

- Count probability

- Photon #  probability

- Photon Number

## Simplified Loop-detector

- Passive mode splitter for up to eight modes (2 spatial, 4 temporal)

- 3 dB coupler

- Fiber loop
- (delay > APD latency)

- APDs

## Loop-detector output 

- Loop-detector output

- Classical light input for calibration

- Channel 1 output

- Channel 2 output

- Eight-fold loop constructed from single mode fiber-optical components @ 780 nm

- 44% coupling losses

**Notes:**
 it contains the two traces of the two outputs of the fiber measured by a photodiode, and one sample of a typical measurement shot. In the typical measurment channel 1 shows the trigger pulse, channel 2 shows the response of one APD with 2 photons measured in time slot 1&4, and channel 3 gives the response of the second APD measuring also two photons here for the time slots 1&3. The delays between the slots are between 1&2:108ns, between 2&3: 164ns and between 3&4: 110ns. The APDs have a response time of 34 ns, however the deadtime shoud be longer: the manufactuarer gives a "dead time of 50ns between pulses and single photon arrival can be measured."

In front of the loop the pulses have a distance from each other of 270μs, after the loop this corresponds to measured signals separated in time by 134μs. The wavelength of the pulses is 780 nm, and we used a single mode fiber for that wavelength. The pulse duration of the "mean" pulse is approximately 6.5ns, but the pulses have a long tail: for approximately 7 ns the power is not negligible, after that there is still some power in the tail for 15.5ns
  I measured the transmission through the loop by coupling into a second fiber and connect this then to the loop. Thus I determined a transmission of  56%. However the fiber connection to the loop seems not to be good. By measuring the connection by a third fiber I measured a loss of approximately 25% by the connection, however the variation by different times of connecting the fibers was quite big: approximately 6% deviation.

## Loop-detector output 

- Loop-detector output

- Classical light input - APD detection

- Channel 1 output

- Channel 2 output

## Loop-detector output 

- Loop-detector output

- 0.034

- 0.034

- 0.28

- 0.30

- Number of “clicks”

- “click” count distributions
- (10,000 runs)

- Frequency of “click” number

- 8

- 0

- Poissonian

## Loop-detector output 

- Loop-detector output

- 1.75

- 1.41

- 2.98

- 1.93

- 5.16

- 2.10

- Non-Poissonian

## Prospects

- • Photon-resolving detection
- 	Application to conditional state preparation
- 		Single and entangled photons
- 		Distillation of Gaussian states

- •Engineering concepts

- General approach
- Loss-limited
- Optimal design

## Slide 18