Photon pair generation via spontaneous fourwave mixing in birefringent optical fibers

1
Photon pair generation via spontaneous four-wave
mixing in birefringent optical fibers

• Brian J. Smith1,2, Pierre Mahou1, Offir Cohen1,
• J. S. Lundeen1, and I. A. Walmsley1
• 1Clarendon Laboratory, University of Oxford,
  Parks Road, Oxford OX1 3PU, UK
• 2Centre for Quantum Technologies, National
  University of Singapore, 117543 Singapore

IQEC ITuE2 Tuesday, 2 June 2009
2
Motivation / Background

• Non-classical light for quantum technologies
• Quantum information (computing and
  communications)
• Precision sensing / metrology
• Nonlinear sources of non-classical light
• Spontaneous Parametric Downconversion (SPDC) in
  second-order nonlinear materials
• Spontaneous four-wave mixing (SFWM) in optical
  fibers
• Advantages of fiber sources
• Large effective interaction strength with low
  pump power
• Single spatial mode operation
• Controllable dispersion properties (in principle)
• Why regular birefringent fiber over PCF and DSF?
• Mode matching
• Mature manufacturing (low cost, better
  uniformity, matched to current technology)
• Tunability does not depend significantly on
  dispersion

3
Basics of SFWM
Signal
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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Dispersion Model and 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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SFWM Experimental Setup
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
7
SFWM Spectrum
Raman background
Residual Pump
Map out the phase matching function of the fiber
by scanning the pump wavelength
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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, neglecting self- and
cross-phase modulation.
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g(2)(0) measurement
Use idler photon to trigger signal photon
g(2)(0) is a measure of the non-classicality of
the single-photon state
Fibercore HB800G
4-f spectral filter
a
SMF
5050
Grating
BIF
aHWP
TiSapphire
b
PBS
PBS
DM
CC
Bi-SMF
LPF
SMF
c
HWP
g(2)(0) lt 1 implies non-classical
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Joint Spectrum Experimental Setup
Connect SMFs to monochromators (MCs) Scan MCs and
count coincidences to map out the joint spectrum
4-f spectral filter
SMF
CC
MC
Grating
BIF
aHWP
TiSapphire
MC
PBS
PBS
DM
Bi-SMF
SMF
LPF
HWP
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Measured Joint Spectrum
Joint spectrum is dominated by phasematching
Fibercore HB800G
Count Rate / 10 sec
Count Rate A.U.
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Summary

• Demonstrated the ability to generate bright,
  photon pair source via SFWM using birefringent
  phasematching in standard fibers
• Standard fibers have unique advantages over other
  approaches (PCF, DSF, PDC)
• SFWM in optical fibers enables great control over
  the photonic state produced
• Next step is to produce factorable photons

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Heralding leads to mixed states (usually)

• The joint two-photon state in SPDC and SFWM is
  generally correlated in both frequency and
  transverse momentum due to energy and momentum
  conservation.
• Correlations lead to mixed states when heralding
  a single-photon state if our detectors are not
  fast enough or have significant spectral
  resolution
• This is due to in-principle information about
  the heralded (signal) photon that could have been
  determined from the detection of the herald
  (idler) photon

Joint Spectum
Joint temporal function
Fourier Transform
Spectral anticorrelations
Temporal correlations
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Timing jitter and HOM interference
Reduced visibility HOM dip
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Pure photons in SPDC
95
Peter Mosley et. al. Phys. Rev. Lett. 100, 133601
(2008)

• Drawbacks
• bulk source (difficult to couple into fibers)
• limited to natural dispersion of nonlinear
  crystals

16
Factorable photons in SFWM
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Finding the right fiber
Idler wavelength (nm)
Signal wavelength (nm)
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Essential ingredients

• Photonic crystal fiber
• Fiber
• Crystal Fiber NL-1.8-750
• Length 40 cm
• Core diameter 1.75 ?m
• Fill fraction 50
• Pump
• 0.7 mW per pass
• ?p 785 nm
• ??p 8 nm
• 80 MHz rep. rate
• Photon Pairs
• ??i 860 nm
• ??i 2 nm
• ?s 720 nm
• ???s 8 nm
• 2-fold rate 15,000 /s
• 4-fold rate 3 /s
• Accidentals / coinc. lt 1/25

• Birefringent SMF fiber
• Fiber
• Fibercore HB800G
• Length 10 cm
• Birefringence 4 x 10-4
• Pump
• 15 mW per pass
• ?p 704 nm
• ??p 2.5 nm
• 80 MHz rep. rate
• Photon Pairs
• ??i 830 nm
• ??i 8 nm
• ?s 610 nm
• ???s 3 nm
• 2-fold rate 30,000 /s
• 4-fold rate NA
• Accidentals / coinc. lt 1/200

• SPDC - Nonlinear Crystal
• Crystal
• Potassium Di-phosphate
• Length 5 cm
• Pump
• 300 mW per crystal
• ?p 415 nm
• ??p 3 nm
• 80 MHz rep. rate
• Photon Pairs
• ??i 830 nm
• ??i 3 nm
• ?s 830 nm
• ???s 10 nm
• 2-fold rate 500,000 /s
• 4-fold rate 60 /s
• Accidentals / coinc. lt 1/100

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References

• Generation of pure state photons in SPDC
• Peter Mosley et al. Phys. Rev. Lett. 100, 133601
  (2008)
• Peter Mosley et al. New J. Phys. 10, 093011
  (2008).
• Peter Mosley et al. J. Mod. Opt.
• Engineering spectral correlations in SFWM in
  fibers
• K. Garay-Palmett et al. Opt. Express 15, 14870
  (2007)
• Previous demonstrations of pair generation in
  optical fibers
• 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)

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Filtering
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Quantum Entanglement

• Entanglement is a result of the superposition
  principle applied to multiple quantum systems.
• Simply put, a two-particle (A B) quantum system
  is in an entangled state if the state (in Hilbert
  space) cannot be expressed as a product of
  individual state vectors for each quantum system
• There exist several ways to quantify
  entanglement, yet there still no consensus as to
  what is the correct measure of entanglement.
  This is particularly true of many-particle
  quantum systems.