Correlated imaging, quantum and classical aspects

1
Correlated imaging, quantum and classical aspects
Quantum Optics II
Cozumel, Mexico, December 6-9 2004
INFM, Università dellInsubria, Como, Italy
Theory Alessandra Gatti, Enrico Brambilla,
Morten Bache and Luigi Lugiato
Lab. I Ottavia Jederkievicz, Yunkun Jiang
Paolo Di Trapani
Lab. II Fabio Ferri, Davide Magatti
2
INTRODUCTION
3
OUTLINE OF THE TALK
I -First experimental observation of spatial
correlation at the quantum level in the
macroscopic regime of parametric down-conversion

• II-Ghost imaging tecnique optical imaging by
  means of the spatial correlation (spatial
  entanglement) of two beams
• Comparison between ghost imaging with entangled
  beams and classically correlated beam from a
  thermal source
• ? Results which combine in a surprising way
  quantum and classical optics bringing together
  the two communities to a common discussion.

4
Twin-photons generated by parametric
down-conversion
5
Microscopic generation of twin photons at the
origin of spatial correlation of signal and idler
beams at the crystal output (near field)
Signal/ idler twin photons are are always
created at the same position ? the intensity
distributions of signal and idler beams are
spatially correlated
NEAR FIELD
pump
lc5mm
SIGNAL
IDLER
6

Phase matching at the origin of far-field
spatial correlation of PDC photons
Plane-wave pump
?Perfect intensity correlation in symmetric far
field positions of the two beams
FAR FIELD
pump
Finite size of the pump waist wP --gt uncertainty
in the propagation directions of twin photons ?
Perfect intensity correlation only for detection
areas broader than a coherence area
Brambilla, Gatti, Bache, Lugiato, Phys Rev A 69,
023802 (2004) quant-ph/0306116 (2003)
7
Detection of sub-shot-noise Spatial Correlation
in the high-gain regime of PDCExperiment
performed at Como Lab. (Ottavia Jedrkiewicz,
Yunkun Jiang, Paolo Di Trapani)

• Literature in the low gain regime single photon
  pairs resolved in time by photodetectors ?
  coincidence measurements
• In the high-gain regime large number of photons
  emitted into each mode ?detection in single shot
  by means of a high Q.E. CCD

• GOALS of THE EXPERIMENT
• Investigate the single-shot spatial intensity
  correlation in the far field, between the signal
  and idler beams.
• Check if the far-field signal and idler intensity
  distributions coincide within the shot noise

8
Experimental set-up
Pump pulses _at_352 nm





The nonlinear crystal BBO (L4mm) ?49.05,
?0 type II degenerate ls,i _at_ 704 nm Pump
pulses _at_352 nm, 3rd harmonic of NdGlass laser,
1.5ps, Rep. rate 2 Hz, Ep 0.1mJ 0.5 mJ, 1 mm
waist Gain varying between ?10 and 103






Spatial filter 200 mm teflon pnh










Selection of a portion of PDC fluorescence
around collinear direction








type II BBO

rectangular aperture



M
M





3
M
5
2





Polarizing Beamsplitter
h 89 _at_704nm





M
htot 75
3
CCD









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


9
Far field image of the selected portion of PDC
fluorescence
Boxes correspond to a 20x8 mrad angular bandwidth
around collinear direction and lt10 nm bandwidth
around degeneracy
SPATIAL statistics performed inside
boxes (4000 pix) for each single laser pulse

Zoomed signal
Zoomed idler
evident spatial correlation
between the two images
10
Photocounts (signal-idler) difference noise
statistics
11
Transition from the quantum to classical regime
attributed to a broadening of the far field
coherence area with increasing gain

Pump intensity I 5 GW/cm2
Pump intensity I 50 GW/cm2
The down-converted fields map the gain profile On
increasing the pump intensity, the gain profile
gets narrow despite of the fixed pump waist ? the
far-field coherence area broadens ? Detection
areas (single pixels) become smaller than the
coherence area
12
In summary twin beam effect over several phase
conjugate signal and idler modes
13
GHOST IMAGING TECHNIQUE Optical imaging by means
of the spatial correlation (spatial entanglement)
of two beams Flexible way of performing coherent
imaging with incoherent light
IN THIS TALK Comparison between ghost imaging
with entangled beams and classically correlated
beam from a thermal source Results which combine
in a surprising way quantum and classical optics
bringing together the two communities to a
common discussion.
14
Ghost imaging by means of two-photon quantum
entanglement
15
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
16
Is entanglement really necessary to perform ghost
imaging?

• Yes
• Abouraddy, Saleh, Sergienko, Teich, Phys. Rev.
  Lett. 87, 123602 (2002) Josa B 19,1174 (2002)
• the distributed quantum-imaging scheme truly
  requires entanglement in the source and cannot be
  achieved by using a classical source with
  correlations but without entanglement

17
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 ?
18
Intensity operators in the far field and in the
near field of each beam ARE NON COMMUTING
OBSERVABLES
Replace the pure EPR state with a statistical
mixture that exactly preserves the far-field
spatial correlation ? the near field spatial
correlation is completely lost
f-f scheme diffraction pattern of the
object BUT no information about the image in the
2f-2f scheme
2f-2f scheme image of the object BUT no
information about the diffraction pattern in the
f-f scheme
Replace the pure EPR state with a statistical
mixture that exactly preserves the near-field
spatial correlation ? the far-field spatial
correlation is completely lost
Gatti, Brambilla, Lugiato, Phys. Rev. Lett . 90,
133603 (2003)
19
Simultaneous presence of perfect spatial
correlation in the near and in the far-field of
the PDC beams. Brambilla, Gatti, Bache, Lugiato,
PRA 69, 023802 (2004)
q
SIGNAL
q
?(2)
-q
IDLER
-q
SIGNAL
wP160?m
IDLER
FAR FIELD INTENSITY CORRELATION Directions of
propagation of twin photons are correlated
because of phase matching Momentum q of signal
photon determined from a measurement of the
momentum -q of the idler photon
NEAR-FIELD INTENSITY CORRELATION Twin photons are
generated at the same position inside the
cristal Position x of signal photon determined
from a measurement of the position of the idler
photon
20
EPR-like inequality for the conditional
variancies of position and momentum of two
photons satisfied only by entangled
(nonseparable) states Bennink, Bentley, Boyd, PRL
92 033601 (2004) see also DAngelo Kim Kulik
Shih PRL 92, 233601 (2004)
Claim this inequality limits the resolution
capabilities of ghost imaging with classically
correlated beams. High-resolution ghost image and
ghost diffraction are possible only with an
entangled source of photons Is that true?
21
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)
Beam in a thermal-like state
N1
b1
5050 BS
b2
N2
vacuum
22
Twin speckle pattern generated by impinging a
laser beam on a ground glass and then splitting
simmetrically.
Fabio Ferri and Davide Magatti lab in Como
TO CCD
LASER
BS
ROTATING GROUND GLASS
23
Moreover, the correlation is preserved from the
near-field to the far-field, provided the source
cross-section is much larger than the coherence
length ? the classically correlated thermal
beams can be used for ghost imaging exactly in
the same way as the entagled beams from PDC
24
Correlated imaging parallel between the use of
(a) ENTANGLED PDC BEAMS and (b)
CLASSICALLY CORRELATED BEAMS
BY SPLITTING THERMAL RADIATION
Gatti et al. quant-phys/0307187 (2003), PRL 93,
093602 (2004), Phys. Rev. A 70, 013802 (2004)
25
RELEVANT DIFFERENCE VISIBILITY OF THE
INFORMATION RETRIEVED VIA CORRELATION
MEASUREMENTS
Imaging information
no information, background
(b) CORRELATEDTHERMAL BEAMS
The entangled configuration, in the regime of
coincidence counts, offers a better visibility of
the information
26
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,
quant-ph/0408021 (2004), submitted to PRL
27
IMAGES OF A DOUBLE SLIT (190 ?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
28
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
29
RESOLUTION OF GHOST IMAGING WITH CORRELATED
THERMAL BEAMS
The resolution of the ghost imaging and ghost
diffraction schemes are determined by the widths
of the near- field and far-field
auto-correlation functions ?xn and ?xf.
?xn ?q 0.066 lt 1
The product of ?xn ?q we obtain is much smaller
than the value 1, which was suggested as a lower
bound for the resolution of classically
correlated beams.
30
SUMMARY AND CONCLUSIONS
First experimental investigation of quantum
spatial correlation in the high-gain regime of
PDC sub-shot noise intensity correlations of
signal and idler far fields

• Ghost Imaging results that question the role of
  entanglement
• Experimental evidence of high resolution ghost
  imaging and ghost diffraction with a pseudo
  thermal source .
• Information processed by only operating on the
  reference beam.
• The suggested lower bound for the product in the
  resolutions (near and far field) does not exist.
• The only difference from an entangled source is
  a lower visibility of the information.

?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
advantage in imaging macroscopic classical object
31
(b) CORRELATED THERMAL BEAMS
a) ENTANGLED PDC BEAMS
Gatti et al. quant-phys/0307187 (2003), PRL 93,
093602 (2004), Phys. Rev. A 70, 013802 (2004)
32
1D NUMERICAL SIMULATION FOR THE RECOSTRUCTION OF
THE INTERFERENCE FRINGES VIA
IN THE f-f SCHEME
1000 shots
10000 shots
33
(No Transcript)