Designer photons and detectors

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Designer photons and detectors

• Brian J. Smith1,2, O. Cohen2, N. Thomas-Peter2,
  H. Coldenstrodt-Ronge2, P. J. Mosley2, P. Mahou2,
  J. S. Lundeen2, G. Puentes2, Ch. Silberhorn3, A.
  Feito4,5, K. L. Pregnell4,5, J. Eisert5,6, T. C.
  Ralph7, M. B. Plenio4,5, and I. A. Walmsley1
• 1Centre for Quantum Technologies, National
  University of Singapore, 3 Science Drive 2,
  117543 Singapore, Singapore
• 2University of Oxford, Clarendon Laboratory,
  Parks Road, Oxford OX1 3PU, United Kingdom
• 3Max-Planck-Institute for the Science of Light,
  Gunther-Scharowsky-Str. 1/Building24, 91058
  Erlangen, Germany
• 4Institute for Mathematical Sciences, Imperial
  College London, Princes Gardens, London SW7 2PG,
  United Kingdom
• 5QOLS, Blackett Laboratory, Imperial College
  London, Prince Consort Road, London SW7 2BW,
  United Kingdom
• 6Institute for Physics and Astronomy, University
  of Potsdam, 14476 Potsdam, Germany
• 7Department of Physics, University of Queensland,
  Brisbane, QLD 4072, Australia

Quantum Optics VII Zakopane, Poland Wednesday, 10
June 2009
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Roadmap for the next 25 minutes

• Motivation Sources and detectors for quantum
  applications
• Sources
• Spontaneous parametric downconversion
• Spontaneous four-wave mixing in PCF
• Spontaneous four-wave mixing in standard fiber
• Configurable detector From photon counting to
  quadrature measurements
• Detector tomography Whats in that black box?

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MotivationSources and detectors for photonic
quantum technologies

• Quantum technologies
• Quantum information (computation / cryptography)
• Quantum sensing (increased precision)
• Quantum simulation
• Control of non-classical systems
• Fundamental tests of quantum theory
• The ability to create, manipulate and measure
  quantum states of light enables testing of
  quantum theory
• Macroscopic superposition collapse via
  measurements

These require a range of light sources, from
highly entangled to completely unentangled states
and configurable detectors capable of changing
their measurement basis
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Spontaneous parametric downconversion
Nonlinear Optical Crystal
Signal
Energy Conservation
Pump
Idler

• One pump photon is spontaneously converted into
  two daughter photons in a material.

• Momentum conservation is typically obtained by
  utilizing birefringence on nonlinear crystals.

Momentum Conservation
Goal Create heralded single photons in pure
spatio-temporal states
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Why pure state single photons?
Many quantum technologies rely on high-visibility
Hong-Ou-Mandel (HOM) interference between
heralded photons

s
Pump
A click at this detector indicates (heralds)
there is a photon in this beam.
i
A Quantum Gate

• The visibility of HOM interference is bounded
  below by the purity of the photons

• Photonic quantum-computing requires high-quality
  heralded photons

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Two-photon joint spectrum
The two-photon state produced is generally
correlated in both frequency and transverse
momentum due to energy and momentum conservation
Correlations lead to mixed states when heralding
single photons if the detectors used are too slow
and too big.
Joint Spectum
Joint temporal function
Fourier Transform
Spectral anticorrelations
Temporal correlations
This leads to a fundamental problem Temporal and
spectral jitter with slow detectors!
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Timing jitter
Space-time entanglement between signal and idler
photons leads to time / frequency jitter between
photons from different sources, even when using
an ultrashort pump pulse.

• Timing and frequency jitter introduces errors
  into quantum computer gates.

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The solution Vacuum engineering
The goal is a factorable joint spectral amplitude
Pump function
Phasematching function
Joint spectrum
Fixed at 45
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Pure photons in SPDC
With careful choice of dispersion in a
nonlinear crystal (KDP) we have been able to
engineer the modes into which SPDC can occur.
Measured joint spectrum
Hong-Ou-Mandel Interference
Quality gt 98

• Heralding efficiency up to 44
• High four-fould count rates (60 /sec with 300 mW
  pump power per crystal)
• High-quality quantum interference with no
  filters
• Broadest bandwidth heralded photons
• Drawbacks
• Bulk source Difficult to couple efficiently
  into single-mode fibers
• Limited to natural dispersion of nonlinear
  materials

P. J. Mosley et. al. Phys. Rev. Lett. 100, 133601
(2008)
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Spontaneous four-wave mixing
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Spontaneous Four-Wave Mixing
Optical Fiber
Pump
Energy Conservation
Idler

• Two pump photons are spontaneously converted
  into two sideband photons in a material.

• Small core size and long interaction length
  compensate for small coupling, compared to
  of nonlinear crystals.

Momentum Conservation

• J. E. Sharping, M. Fiorentino, and P. Kumar,
  Opt. Lett. 26, 367 (2001).
• H. Takesue and K. Inoue, Phys. Rev. A 70,
  031802R (2004).
• J. Rarity, J. Fulconis, J. Duligall, W.
  Wadsworth, and P. Russell, Opt. Express 13, 534
  (2005).
• J. Fan and A. Migdall, Opt. Express 13, 5777
  (2005).
• O. Cohen et al, Phys. Rev. Lett. 102, 123603,
  (2009).

DSF
PCF
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Two-photon state from SFWM
The two-photon state produced is given by
For a single pump laser the joint-spectral
amplitude, , can be expressed as
Pump function
Phasematching function
Joint spectrum
Central frequencies set by birefringence
Fixed at 45
K. Garay-Palmett et al, Opt. Express 15,
14870-14886 (2007).
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Photonic crystal fiber source
By finding the photonic crystal fiber (PCF) with
appropriate dispersion we have been able to
engineer the modes into which SFWM can occur.
Polarization Hong-Ou-Mandel type interference
Quality gt 86
Utilizes birefringent phasematching pump along
one axis and create photon pairs along the other.
O. Cohen et al, Phys. Rev. Lett. 102, 123603,
(2009).
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Photonic crystal fiber source
By finding the photonic crystal fiber (PCF) with
appropriate dispersion we have been able to
engineer the modes into which SFWM can occur.
Polarization Hong-Ou-Mandel type interference

• High four-fould count rates (3 /sec with 0.7 mW
  pump power per crystal)
• High-quality quantum interference with no
  filters
• Broad bandwidth heralded photons
• Drawbacks
• PCF spatial mode Difficult to couple
  efficiently into single-mode fibers
• Relatively new technology High cost and low
  uniformity of fiber parameters

Quality gt 86
Utilizes birefringent phasematching pump along
one axis and create photon pairs along the other.
O. Cohen et al, Phys. Rev. Lett. 102, 123603,
(2009).
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Spontaneous four-wave mixing in a different medium
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Standard fiber source Phasematching
The phasematching function (up to an overall
phase) is given by a sinc function
Modeling the fiber dispersion by bulk-silica
refractive index along one axes and add a
constant birefringence, , for the other axis
Leads to a wave-vector mismatch
Plotting the frequencies that satisfy energy
conservation and solves gives the
phasematching plot (points where SFWM is most
likely to occur)
Detuning
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Standard fiber source
Map out the phasematching plot by scanning the
pump central wavelength
Fibercore HB800G
4-f spectral filter
SMF
Spectrometer
Grating
BIF
aHWP
TiSapphire
5050
PBS
PBS
DM
SMF
Bi-SMF
LPF
HWP
Photon Counting Rates
g(2)(0) lt 1 implies non-classical
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Measured phasematching
Measured signal (red square ) and idler (blue
cross ) central wavelengths as a function of
the pump central wavelength.
Lines predicted phasematching curves using
simple model discussed.
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SFWM joint spectrum
Joint spectrum is dominated by phasematching
Fibercore HB800G
Count Rate / 10 sec
Count Rate A.U.
Joint spectrum is not yet factorable Requires
either shorter fiber or narrower pump.
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Quantum measurement
A general quantum detector can be represented
mathematically by a positive operator-value
measurement (POVM) set
labels the measurement outcomes
labels the measurement settings
Positive
Probability
The probability to obtain outcome , when the
detector is in configuration , and the input
state is known to be , is given by the
generalized Born rule
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Examples
Photon number projectors (Arises in photon
counting detectors APDs, etc.)
Wigner representation of measurement
Outcome probabilities can be seen as overlap
between state and measurement Wigner functions
Quadrature projectors (Arises in standard
homodyne detection)
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Phase-sensitive photon-counting detector
Combine photon-number resolving detection with
weak homodyne (i.e. a phase-reference with
uncertain photon number) to bridge the gap
between photon number and quadrature measurements.
Ideally photon number projectors
Measurements POVM

Measurements setting
PSPC
signal
R
Measurements outcomes
Local Oscillator
Joint click statistics
G. Puentes et al, Phys. Rev. Lett. 102, 080404
(2009).
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Wigner representation of PSPC
Projections onto
(a) Fock state (b) Displaced Fock state (c)
Schrödinger Kitten (d) Squeezed state
for h1,290
Typical fidelity with target state
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Realistically we use time-multiplexed detectors
for PC
Time-multiplexed detector (TMD)
Input state is assumed to be contained in one
spatial-temporal pulsed mode
Click statistics
Photon number distribution
8 temporal modes
C L matrices describe how photons end up in
different bins (C) and get lost (L).
D. Achilles, C. Silberhorn, C. Sliwa, K.
Banaszek, I. Walmsley , Opt.. Lett. 28, 2387
(2003).
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PSPC with TMDs
Replace the ideal photon counters, with
realistic TMDs
Ideally photon number projectors
Measurements POVM
m

Measurements setting
TMD
PSPC
signal
TMD
R
n
Measurements outcomes
Local Oscillator
Joint click statistics
G. Puentes et al, Phys. Rev. Lett. 102, 080404
(2009).
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An application State tomography
Phase averaged coherent states
Experimental set-up
Weak coherent states
Typical fidelities F gt0.95
Could also be used in heralding non-classical
states or quantum metrology
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But really, whats in that black box? (or
detector tomography)
A quantum experiment in general can be described
in three stages
D.T. Smithey, et al., PRL 70, p.1244 J. Fiurásek,
PRA 64, 024102
D.T. Smithey, et al., PRL 70, p.1244
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Detector Tomography
State Tomography
IN

With well characterised states, we can
reconstruct the POVM
?
State Density matrix
Utilize maximum likelihood to obtain most likely
POVM element
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Detectors

• Avalanche Photodiode

• Time multiplexed detector

click
no click

• Both detectors are measuring in the photon
  number space of a mode
• Suitable probe states are coherent states

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Experimental Setup

• Use the half-wave plate to create a series of
  coherent states with different intensities
• For each intensity measure the rates of each
  detector outcome
• These correspond to different POVM elements
• Measure the intensities of the coherent states
  with the power meter in the monitor arm

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Results for the APD
Binary Detector just two outcomes
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Wigner-Function for TMD
Reconstructed Wigner function for the TMD 1-click
event
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Conclusion and Outlook

• Experimental demonstrations for engineering the
  mode structure of light in spontaneous nonlinear
  optical processes
• Photodetection that bridges the particle and wave
  sensitivity of photon counting and quadrature
  (homodyne) detectors
• Detector tomography is a means to determine the
  POVM of a given detector off the shelf
• Future directions
• Heralding pure state single photons with standard
  fibers
• Utilizing two phase-sensitive photon counting
  detectors as an entanglement witness
• Preparing non-classical states from entangled
  sources and PSPC
• Any suggestions?

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Thanks!
Hendrik Coldenstrodt-Ronge
N. Thomas-Peter
Graciana Puentes
Pete Mosley
Uwe Dorner
Ian Walmsley
Jeff Lundeen
Offir Cohen