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Correlated imaging, quantum and classical aspects INFM, Università dell’Insubria, Como, Italy Quantum Optics II Cozumel, Mexico, December 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

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INTRODUCTION Large emission bandwidth in the spatial frequency domain Parametric down-conversion process (PDC) in a (2) nonlinear crystal PUMP 2 (2) SIGNAL IDLER PUMP 2 Spatial aspects of quantum optical fluctuations New potential applications exploiting the quantum properties of the light for image processing or multi-channel operation quantum imaging The quantum laser pointer Entangled two-photon imaging (ghost imaging) Noiseless image amplification Quantum lithography Quantum superresolution Quantum teleportation of images

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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. OUTLINE OF THE TALK I -First experimental observation of spatial correlation at the quantum level in the macroscopic regime of parametric down- conversion

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Twin-photons generated by parametric down-conversion

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Microscopic generation of twin photons: at the origin of spatial correlation of signal and idler beams at the crystal output (near field) Finite crystal length--> uncertainty in the relative position of the twin photons 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 broader than l c =5mm SIGNAL IDLER (2) NEAR FIELD pump Signal/ idler twin photons are are always created at the same position the intensity distributions of signal and idler beams are spatially correlated

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SIGNAL IDLER (2) FAR FIELD pump Finite size of the pump waist w P --> 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, (2004); quant-ph/ (2003) Perfect intensity correlation in symmetric far field positions of the two beams q=0, -q q signal idler - Phase matching: at the origin of far-field spatial correlation of PDC photons Plane-wave pump

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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 Detection of sub-shot-noise Spatial Correlation in the high-gain regime of PDC Experiment 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

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Spatial filter +200 m teflon pnh M 3,M,M 4,M,M 5 M 5 M 4 Low - band pass filter M 3 M 2 M 1 Polarizing Beamsplitter M 3 type II BBO rectangular aperture CCD ~ Selection of a portion of PDC fluorescence around collinear direction No Interference filter during measurements tot ~ 75% Experimental set-up The nonlinear crystal: BBO (L=4mm) =49.05°, =0° type II; degenerate 704 nm Pump nm, 3rd harmonic of Nd:Glass laser, 1.5ps, Rep. rate 2 Hz, Ep ~ 0.1mJ – 0.5 mJ, 1 mm waist Gain varying between 10 and 10 3 Pump nm

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Zoomed signalZoomed idler evident spatial correlation between the two images Far field image of the selected portion of PDC fluorescence SPATIAL statistics performed inside boxes (4000 pix) for each single laser pulse Boxes correspond to a 20x8 mrad angular bandwidth around collinear direction and <10 nm bandwidth around degeneracy

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Sub-shot-noise correlation up to gains characterized by corresponding to 100 pe per mode (transverse size of the coherence areas in that regime about 2-4 pixels) Photocounts (signal-idler) difference noise statistics

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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 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/cm 2 Pump intensity I~ 50 GW/cm 2

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In summary: twin beam effect over several phase conjugate signal and idler modes PDC crystal I1I1 I2I2 RATIO LOW FOR I 1 RATIO HIGH FOR I 1 -I 2 Perspectives: IMAGING OF A FAINT OBJECT (WEAK ABSORBTION) WITH A SENSITIVITY BEYOND STANDARD QUANTUM LIMIT

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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.

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Ghost imaging by means of two-photon quantum entanglement Photon-pair created by PDC in the ultra- low gain regime POINT-LIKE DETECTOR, FIXED POSITION OR BUCKET DETECTOR 2 1 (2) Pump ARRAY OF DETECTORS h 2 (x 2,x 2 ’) h 1 (x 1,x 1 ’) Coincidence counts as a function of x 2 OBJECT x2x2 x1x1 The imaging information is extracted from the coincidence counts as a function of the position of the reference photon 2 Pittman, Shih, Strekalov and Sergienko, PRA 52, R3429 (1995) GHOST IMAGE Ribeiro, Padua, Machado da Silva, Barbosa, PRA. 49, 4176, (1994) Strekalov, Sergienko, Klyshko and Shih, PRL 74, 3600 (1995) GHOST DIFFRACTION

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Imaging information no information, background THE IMAGING INFORMATION IS CONTAINED IN THE CORRELATION FUNCTION OF INTENSITY FLUCTUATIONS. Correlation function of intensities POINT-LIKE DETECTOR, FIXED POSITION 2 1 (2) Pump ARRAY OF DETECTORS h 1 (x 1, x) h 2 (x 2, x) OBJECT Generalization to the regime of many photon pairs: signal-idler intensity correlation function [Gatti, Brambilla, Lugiato, PRL 90, (2003)]

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Is entanglement really necessary to perform ghost imaging? Yes: Abouraddy, Saleh, Sergienko, Teich, Phys. Rev. Lett. 87, (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” Theory in arbitrary gain regime Gatti, Brambilla and Lugiato, PRL 90, (2003) The results of each single experiment can be reproduced by a classical source. But... Ghost image experiment by using laser pulses with classical angular correlation. Bennink, Bentley and Boyd, PRL 89, (2002) Although the result of any single ghost imaging experiment can be reproduced by classical sources, “a classical source cannot mimic a quantum source in a pure state for all test and reference systems unless that state is nonentangled.” No,but..

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2f-2f scheme:ghost image SHOTS f-f scheme:ghost diffraction 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 ? reference beam 2 test beam 1 (2) ff ff x reference beam 2 test beam 1 (2) ff 2f x DOUBLE SLIT

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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 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 2f-2f scheme: image of the object BUT no information about the diffraction pattern in the f-f scheme Gatti, Brambilla, Lugiato, Phys. Rev. Lett. 90, (2003)

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Simultaneous presence of “perfect” Simultaneous presence of “perfect” spatial correlation in the near and in the far-field of the PDC beams. [ Brambilla, Gatti, Bache, Lugiato, PRA 69, (2004)} w P =160 m 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 (2) 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 q’ IDLER SIGNAL IDLER SIGNAL -q’ -q q

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EPR-like inequality for the conditional variancies of position and momentum of two photons satisfied only by entangled (nonseparable) states Bennink, Bentley, Boyd, PRL (2004) ; see also D’Angelo Kim Kulik Shih PRL 92, (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?

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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) coherent state (no correlation) Cauchy-Schwartz (perfect correlation) b1b1 b2b2 vacuum 50:50 BS Beam in a thermal-like state N1N1 N2N2 HIGH LEVEL OF CORRELATION BUT STILL CLASSICAL!

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LASER BS ROTATING GROUND GLASS TO CCD “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

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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 h 1 (x 1, x) b1b1 x1x1 point-like detector h 2 (x 2, x) b2b2 x2x2 array of pixel detectors x vacuum 50:50 BS beam in a thermal (or pseudo-thermal) state OBJECT

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Correlated imaging : parallel between the use of (a) ENTANGLED PDC BEAMS and (b) CLASSICALLY CORRELATED BEAMS BY SPLITTING THERMAL RADIATION Correlation function of intensity fluctuations at the detection planes Signal-idler field cross-correlation (two-photon propagator) Second order correlation of the thermal radiation correlation length = coherence length of PDC beams 1/ q correlation length = coherence length of thermal radiation 1/ q Correlation length in the far field: inversely proportional to the pump beam-waist Correlation length in the far field: inversely proportional to the cross- section of the thermal source Gatti et al. quant-phys/ (2003), PRL 93, (2004), Phys. Rev. A 70, (2004)

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(b) CORRELATEDTHERMAL BEAMS a) ENTANGLED PDC BEAMS RELEVANT DIFFERENCE: VISIBILITY OF THE INFORMATION RETRIEVED VIA CORRELATION MEASUREMENTS Background term is negligible in the coincidence count regime Background term is never negligible The entangled configuration, in the regime of coincidence counts, offers a better visibility of the information Imaging information no information, background

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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, quant-ph/ (2004), submitted to PRL CCD He-Ne LASER BS GROUND GLASS OBJECT D=3mm near-field plane TURBID MEDIUM

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IMAGE OBTAINED BY SHINING LASER LIGHT 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 FRAMES30000 FRAMES SECTION

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FRINGES OBTAINED BY SHINING LASER LIGHT BY SIMPLY REMOVING THE LENS F’ IN THE REFERENCE ARM: DIFFRACTION PATTERN OF THE DOUBLE SLIT SECTION FRINGES OBTAINED BY CROSS CORRELATION (500 FRAMES) INTENSITY DISTRIBUTION IN THE OBJECT ARM

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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 x n and x f. The product of x n q we obtain is much smaller than the value 1, which was suggested as a lower bound for the resolution of classically correlated beams. x n q = < 1 We find x n = 34.3 m x f =15.6 m

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SUMMARY AND CONCLUSIONS 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 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

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(b) CORRELATED THERMAL BEAMS a) ENTANGLED PDC BEAMS 2f-2f scheme: image spatial resolution determined by the near-field PDC coherence length spatial resolution determined by the near-field thermal coherence length f-f scheme: diffraction pattern mean photon number per mode spatial resolution determined by the far- field coherence length, inverse of the pump waist spatial resolution determined by the far field coherence length, inverse of the source cross-section Gatti et al. quant-phys/ (2003), PRL 93, (2004), Phys. Rev. A 70, (2004)

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1D NUMERICAL SIMULATION FOR THE RECOSTRUCTION OF THE INTERFERENCE FRINGES VIA IN THE f-f SCHEME shots 1000 shots FRINGE VISIBILITY 5 IN BOTH CASES HOWEVER, EFFICIENT RECONSTRUCTION AFTER A REASONABLE NUMBER OF PUMP SHOTS

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ONLY RELEVANT DIFFERENCE: VISIBILITY OF THE INFORMATION (b) CORRELATED THERMAL BEAMS a) ENTANGLED PDC BEAMS Background term is negligible in the coincidence count regime Background term is never negligible The entangled configuration, in the regime of coincidence counts, offers a better visibility of the information Imaging information no information, background Precise formal analogy between the use of classically correlated beams from a thermal source and entangled beams from PDC all the features of ghost imaging can be reproduced without entanglement ! Gatti et al. quant-phys/ (2003), PRL 93, (2004), Phys. Rev. A 70, (2004)

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