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Incontri del Giovedì 2006 IEN, Torino, 8 giugno
2006
QUANTUM IMAGING Luigi A. Lugiato Università
dellInsubria, Como
Collaboratori Alessandra Gatti, Enrico
Brambilla (Como) Morten Bache (Lyngby,
Denmark) Exp 1 Paolo Di Trapani, Ottavia
Jedrkiewicz (Como) Exp 2 Fabio Ferri, Davide
Magatti (Como)
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QUANTUM IMAGING

• This field exploits the quantum nature of light
  and the natural
• parallelism of optical signals to devise novel
  techniques for optical
• imaging and for parallel information processing
  at the quantum
• level.

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QUANTUM
IMAGING - Quantum aspects of a very classical
field (imaging) - Spatial quantum properties of
light - Detection of faint objects beyond the
standard quantum limit - Amplification of weak
optical images preserving the S/N ratio
(noiseless amplification) - Quantum limits in the
detection of small beam displacements - Ghost
Imaging - Improvement of data storage - Quantum
teleportation of optical images
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MENU

• I Spatial entanglement and its applications
• - Parametric down-conversion
• - Spatial entanglement
• - Experimental observation demonstration of the
  quantum nature of spatial fluctuations in
  parametric down-conversion
• - Application 1 detection of faint objects
  beyond the standard quantum limit
• - Application 2 detection of small displacements
  beyond the standard quantum limit
• II Ghost imaging
• - What is ghost imaging
• - Debate on whether quantum entanglement is
  necessary or not in ghost imaging
• Ghost imaging with thermal-like beams,
  experiment.
• Comparison of thermal ghost imaging with the
  classic Hanbury-Brown and Twiss technique.

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Twin photons generated by parametric
down-conversion
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FAR FIELD
NEAR FIELD
pump
lc5mm
SIGNAL
IDLER

• Finite size of the pump waist wP --gt uncertainty
  in the propagation directions of twin photons
• uncertainty in the
  transverse momentum of photon 1 from a
  measurement of the momentum of photon 2
• Perfect intensity correlation recovered for
  detection areas larger than

• Finite crystal length--gt uncertainty in the twin
  photon position due to diffraction spread
• 
  uncertainty in the position of photon 1 from a
  measurement of the position of photon 2
• Perfect spatial intensity correlation for
  detection areas larger than

Brambilla, Gatti, Bache and Lugiato, Phys. Rev.
A 69, 023802 (2004)
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Ordinary twin beams photon number correlated
in time, but uncorrelated in space
Spatially entangled beams photon numbers
correlated in time and in the beam cross sections
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Experiment





Pump pulses
_at_ 352nm, 1ps





Pixel by pixel correlation - single shot spatial
statistics Pump beam waist 1 mm - Varying
gain

Spatial filter 200 mm teflon pnh











Selection of a portion of PDC fluorescence
around collinear direction








type II BBO

rectangular aperture



(4mm)
M
M





3
M
5
2





Polarizing Beamsplitter
h 89 _at_704nm





M
htot 75
3
CCD









M
M
Low-band pass filter
1
4
No Interference filter during measurements


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No interference filter during measurements to
reduce the transmission losses Spatial area used
for statistics selected around degeneracy
Photocounts (signal-idler) difference statistics
of pixel pairs
Quantity evaluated over single shot
Averages are only SPATIAL performed
inside box (4000 pixels).
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Evidence of twin beams
Zoomed signal
Zoomed idler
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Intensity difference variance normalized to
shot-noise level
O.Jedrkiewicz, Y.-K Jiang, E. Brambilla, A.Gatti,
M. Bache, L.A. Lugiato and P. Di Trapani, Phys.
Rev. Lett. 93 243601 (2004)
3.0
Spatial ensemble statistics performed over 100 x
40 pixels
2.5
2.0
1.5
SNL
1.0
0.5
1-h
noise reduction limit
0.0
(pe per pixel pair)
10
100
In this region 100 pe per spatial mode
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MENU

• I Spatial entanglement and its applications
• - Parametric down-conversion
• - Spatial entanglement
• - Experimental observation demonstration of the
  quantum nature of spatial fluctuations in
  parametric down-conversion
• - Application 1 detection of faint objects
  beyond the standard quantum limit
• - Application 2 detection of small displacements
  beyond the standard quantum limit
• II Ghost imaging
• - What is ghost imaging
• - Debate on whether quantum entanglement is
  necessary or not in ghost imaging
• Ghost imaging with thermal-like beams,
  experiment.
• Comparison of thermal ghost imaging with the
  classic Hanbury-Brown and Twiss technique.

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Perspectives (PRIN project 2005) IMAGING OF A
FAINT OBJECT (WEAK ABSORBTION) WITH A SENSITIVITY
BEYOND STANDARD QUANTUM LIMIT
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Detection of a weak absorption (e.g. a
spectroscopic signal) typically a differential
measurement is used
Weak absorbtion
BS
1
N2-N1?signal
2
This schemes suppresses the excess noise in the
incoming beam, but is affected by the shot noise
in N2-N1
By using single-mode twin beams produced by cw
optical parametric oscillators ? improvement in
the signal to noise-ratio Souto Ribeiro, Schwob,
Maitre, Fabre, Opt. Lett. 22, 1893 (1997)1.9 dB
Jiangrui Gao et al., Opt.Lett. 23, 870 (1998)7dB
In the far field of the PDC emission twin beam
effect over several phase conjugate signal and
idler modes ? Can be used to enhance the
sensitivity of detection of weak images useful
e.g. in biological imaging or whenever there is
the need of illuminating the object with
ultra-low light intensity.
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Numerical simulation of the detection of a weak
object with spatially correlated twin
beams Parameters 1 ns Gaussian pump pulse pump
waist 1500 µm ?1 (perfect detection) Photons
per mode per pixel (evaluated from beam 2) Noise
in the photon number difference, without object
V_/SN0.21 Object a simple rectangular mask in
beam 1 with absorption coefficient ?0.04

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SIGNAL-TO-NOISE RATI0
Analytical results in the single-mode case
STANDARD QUANTUM LIMIT (coherent beam divided on
a BS)
TWIN-BEAMS
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Measurement of small beam displacements in the
transverse plane
i1(t)

light beam
D
light beam
O
-
i1(t)- i2(t)
i2(t)
x
Rayleigh limit
Standard Quantum Limit
D
number of photons measured in total beam
THE REAL LIMITATION IS QUANTUM NOISE ! Fabre,
Fouet, Maitre, Opt. Lett. 25, 76 (2000)
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USE OF SPATIAL ENTANGLEMENT
Field generated by single pass parametric
down-conversion, or by optical parametric
oscillators with mode-degenerate cavities
i1(t)

O
-
i2(t)
Parametric medium
x

• In the crystal, each generated parametric photon
• has its twin produced in a symmetric direction
• noise reduced on the intensity difference

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2 D positioning "the quantum laser pointer"
y
x
Laser beam
squeezed vacuum
squeezed vacuum
coherent state
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How to mix the different modes ?
1 beamsplitter
N. Treps, U. Andersen, B. Buchler, P.K. Lam, A.
Maître, H. Bachor, C. Fabre Phys. Rev. Letters 88
203601 (2002)
2 optical cavity
N. Treps, N. Grosse, W. Bowen C. Fabre, H.
Bachor, P.K. Lam Science, 301, 940 (2003)
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very small oscillation at 5 MHz
Laser beam
1 A
1 A
improvement to beam positioning accuracy with
respect to Standard Quantum Limit 1.7
horizontal, 1.6 vertical
displacement (oscillation amplitude)
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MENU
I Spatial entanglement and its applications -
Parametric down-conversion - Spatial
entanglement - Experimental observation
demonstration of the quantum nature of spatial
fluctuations in parametric down-conversion -
Application 1 detection of faint objects beyond
the standard quantum limit - Application 2
detection of small displacements beyond the
standard quantum limit

• II Ghost imaging
• - What is ghost imaging
• - Debate on whether quantum entanglement is
  necessary or not in ghost imaging
• Ghost imaging with thermal-like beams,
  experiment.
• Comparison of thermal
• ghost imaging with the classic Hanbury-Brown and
  Twiss technique.

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Ghost imaging by means of two-photon quantum
entanglement Belinsky and Klyshko, Sov. Phys JETP
78, 259 (1994)
TEST ARM
REFERENCE ARM
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Generalization to the regime of many photon
pairs signal-idler intensity correlation
function Gatti, Brambilla, Lugiato, PRL 90,
133603 (2003)
POINT-LIKE DETECTOR, FIXED POSITION
1
OBJECT
Correlation function of intensities
h1(x1 , x)
Pump
?(2)
h2(x2 , x)
2
ARRAY OF DETECTORS
THE IMAGING INFORMATION IS CONTAINED IN THE
CORRELATION FUNCTION OF INTENSITY FLUCTUATIONS
.
Imaging information
no information, background
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(No Transcript)
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2f-2f schemeghost image
f-f schemeghost diffraction
DOUBLE SLIT
DOUBLE SLIT
10000 SHOTS
10000 SHOTS
By only operating on the optical set-up in the
path of beam 2 (which never went through the
object), one is able to pass from the
interference pattern to the image of the
object. Key point simultaneous presence of
spatial correlation both in the near and in the
far-field of the PDC beams. Feature that
distinguishes the entangled from the classical
source ?
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• DEBATE is entanglement of the two beams
  necessary for ghost imaging
• or not ?
• An essential literature
• Abouraddy, Saleh, Sergienko, Teich, Phys. Rev.
  Lett. 87, 123602 (2001)
• Bennink, Bentley, Boyd, Phys. Rev. Lett. 89,
  113601 (2002)
• Gatti, Brambilla, Lugiato, Phys. Rev. Lett. 90,
  133603 (2003)
• Gatti, Brambilla, Lugiato, quant-ph/0307187
  (2003) ? Phys. Rev. Lett. 93,
• 093602 (2004) Phys. Rev. A 70, 013802 (2004)
• Bennink, Bentley, Boyd, Howell, Phys. Rev. Lett.
  92, 033601 (2004)
• Cheng, Han, Phys. Rev. Lett. 92, 093903 (2004)
• Valencia, Scarcelli, DAngelo, Shih, Phys. Rev.
  Lett. 94, 063601 (2005)
• Wang, Cao, Phys. Rev. A 70, 041801R (2004)
• Cai, Zhu, Opt. Lett. 29, 2716 (2004)
• Ferri, Magatti, Gatti, Bache, Brambilla,
  Lugiato, Phys. Rev. Lett. 94,
• 183602 (2005)

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First guess it is not possible to realize both
the ghost image and the ghost diffraction
experiment using the same classical source
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Gatti Brambilla Bache Lugiato, PRL 93, 093602
(2004), Phys. Rev. A 70, 013802 (2004),
quant-phys/0307187 (2003). A surprising answer
A spatially incoherent thermal-like beam divided
on a beam splitter generates two spatially
correlated beams that can be used for ghost
imaging exactly in the same way as the entangled
beams, with the only exception of the visibility.
Nothing prevents two classical beams from being
spatially correlated both in the near and in the
far field up to an imperfect degree (i.e.
classically, or at shot noise)
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An old favourite of the 70-ties the speckle
pattern generated by impinging a laser beam on a
ground glass
Splitting symmetrically twin speckle
patterns If the cross-section is much larger than
the speckle size, the spatial correlation is
preserved upon propagation (Van Cittert-Zernike)
high degree of (classical) spatial correlation
both in the near and far zones.
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Experimental evidence of high resolution ghost
image and ghost diffraction with classically
correlated beams from a pseudo thermal source
Ferri, Magatti,Gatti, Bache, Brambilla, Lugiato,
Phys. Rev. Lett. 94, 183602 (2005)
coherence time 0.1 s speckles 25 ?m
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IMAGES OF A DOUBLE SLIT (160 ?m needle inside a
690 ?m aperture) OBTAINED BY CROSS-CORRELATING
THE REFERENCE ARM INTENSITY DISTRIBUTION WITH
THE TOTAL LIGHT IN THE OBJECT ARM
5000 FRAMES
30000 FRAMES
SECTION
IMAGE OBTAINED BY SHINING LASER LIGHT
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BY SIMPLY REMOVING THE LENS F IN THE REFERENCE
ARM DIFFRACTION PATTERN OF THE DOUBLE SLIT
FRINGES OBTAINED BY CROSS CORRELATION (500
FRAMES)
SECTION
FRINGES OBTAINED BY SHINING LASER LIGHT
INTENSITY DISTRIBUTION IN THE OBJECT ARM
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Second guess it is not possible to achieve
high resolution simultaneously in ghost image and
ghost diffraction, and the bound
?xn ?q gt 1 cannot be violated
?xn resolution in the ghost image
experiment ?q (2?/?f)?xf , ?xf
resolution in the ghost diffraction experiment
In the experiment Ferri et al., PRL 94, 183602
(2005) one has
?xn ?q 0.066ltlt1, and this does not
correspond to the violation of any EPR inequality.
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The only difference from an entangled source is a
lower visibility of the information. This
feature, however, does not prevent from
retrieving the image (ore the diffraction
pattern), unless the object is too weak.
Entanglement can be advantageous in high
sensitivity measurements (e.g. imaging of a faint
object or in quantum information (e.g.
cryptographic) schemes, no evident practical
advantages in imaging macroscopic classical
objects.
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MENU

• I Spatial entanglement and its applications
• - Parametric down-conversion
• - Spatial entanglement
• - Experimental observation demonstration of the
  quantum nature of spatial fluctuations in
  parametric down-conversion
• - Application 1 detection of faint objects
  beyond the standard quantum limit
• - Application 2 detection of small displacements
  beyond the standard quantum limit
• II Ghost imaging
• - What is ghost imaging
• - Debate on whether quantum entanglement is
  necessary or not in ghost imaging
• Ghost imaging with thermal-like beams,
  experiment.
• Comparison of thermal ghost imaging with the
  classic Hanbury-Brown and Twiss technique.

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In the case of a pure amplitude object, such as a
double slit, the diffraction pattern can be
observed using the well known Hanbury - Brown and
Twiss technique.
This is equivalent to measuring the spatial
autocorrelation of the field transmitted by the
object
Far field
OBJECT
Thermal light
BS
In this way one obtains the Fourier transform of
the modulus square of the object. In the case of
a double slit, this coincides with the Fourier
transform of the object. But in presence of
phase modulation in the object, this is lost in
the measurement.
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HBT TECHNIQUE
Far field
OBJECT
Auto-correlation
Thermal light
BS
GHOST IMAGING TECHNIQUE
OBJECT
Far field
Thermal light
Cross- correlation
BS
In this case, one obtains the Fourier transform
of the object even in the presence of phase
modulation. Hence this is truly coherent imaging
with incoherent light.
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OBJECT TRANSMISSION GRATING BEAM SPLITTER
order -2
order -1
order 0
order 1
order 2
80 grooves / mm, ?532nm
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Experimental demonstration of ghost diffraction
of a pure phase object by incoherent light
Reference
Snapshot of the speckles recorded by the CCD
camera in the far field plane
Test
P1
Ghost diffraction pattern (average over 18000
snaphots)
?xn 2?m speckle size in the near field using
the near field scattering (Giglio et al., Phys.
Rev. Lett. 85, 1416 (2000)) INCOHERENT LIGHT
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COMPARISON OF GHOST DIFFRACTION AND DIRECT LASER
ILLUMINATION
Bache, Brambilla, Gatti, Magatti, Ferri, Lugiato,
Phys.Rev.A 73, 053802 (2006)
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INCOHERENT ILLUMINATION WITH THE HBT TECHNIQUE
ONE DOES NOT OBTAIN THE DIFFRACTION PATTERN OF
THE PHASE OBJECT
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CONCLUSIONI
Il Quantum Imaging e' interessante !
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USEFULNESS FOR QUANTUM INFORMATION AND
COMMUNICATION
VERY LARGE NUMBER OF ENTANGLED SPATIAL MODES
(CONTINUOUS VARIABLES ENTANGLEMENT)
ONE HAS A VERY LARGE NUMBER OF REPLICAS OF THE
SAME SYSTEM (PAIR OF ENTANGLED SPATIAL MODES) IN
A SINGLE PUMP PULSE. THIS PROVIDES A PARALLEL
(FAX) CONFIGURATION FOR QUANTUM INFORMATION
PROCESSING, ALTERNATIVE TO THE SEQUENTIAL
(TELEPHONE) CONFIGURATION OF THE REGIME IN
WHICH ONE DETECTS SINGLE ENTANGLED PHOTON PAIRS.