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) Incontri del Giovedì 2006 IEN, Torino, 8 giugno 2006 QUANTUM IMAGING Luigi A. Lugiato Università dell’Insubria, Como

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.

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 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

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. MENU

Twin photons generated by parametric down-conversion

Brambilla, Gatti, Bache and Lugiato, Phys. Rev. A 69, (2004) SIGNAL IDLER Finite size of the pump waist w P --> 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 l c =5mm SIGNAL IDLER  (2) NEAR FIELD FAR FIELD Finite crystal length--> 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 pump

Ordinary twin beams: but uncorrelated in space photon number correlated in time, but uncorrelated in space i 1 (t) i 2 (t) i 3 (t) i 3 ’ (t) i 2 ’ (t) i 1 ’ (t) i 1 (t) i 2 (t) i 3 (t) i 3 ’ (t) i 2 ’ (t) i 1 ’ (t) Spatially entangled beams: and in the beam cross sections photon numbers correlated in time and in the beam cross sections

Pixel by pixel correlation - single shot spatial statistics Pump beam waist 1 mm - Varying gain Spatial filter +200  m teflon pnh Pump 352nm, 1ps M 5 M 4 Low - band pass filter M 3 M 2 M 1 Polarizing Beamsplitter M 3 type II BBO rectangular aperture (4mm) CCD  ~ Selection of a portion of PDC fluorescence around collinear direction No Interference filter during measurements ~  tot ~ 75%

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).

Zoomed signal Evidence of twin beams Zoomed idler

Intensity difference variance normalized to shot-noise level SNL  2 s-i /<n s +n i > si <n+n> Spatial ensemble statistics performed over 100 x 40 pixels noise reduction limit ~ 1-  In this region ~100 pe per spatial mode (pe per pixel pair) O.Jedrkiewicz, Y.-K Jiang, E. Brambilla, A.Gatti, M. Bache, L.A. Lugiato and P. Di Trapani, Phys. Rev. Lett (2004)

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. MENU

PDC crystal N1N1 N2N2 RATIO LOW FOR N 1 RATIO HIGH FOR N 1 -N 2 Perspectives (PRIN project 2005): IMAGING OF A FAINT OBJECT (WEAK ABSORBTION) WITH A SENSITIVITY BEYOND STANDARD QUANTUM LIMIT

Detection of a weak absorption (e.g. a spectroscopic signal): typically a differential measurement is used Weak absorbtion 1 2 N 2 -N 1  signal BS This schemes suppresses the excess noise in the incoming beam, but is affected by the shot noise in N 2 -N 1 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.

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_/SN=0.21 Object: a simple rectangular mask in beam 1 with absorption coefficient  =0.04

SIGNAL-TO-NOISE RATI0 STANDARD QUANTUM LIMIT (coherent beam divided on a BS) TWIN-BEAMS Analytical results in the single-mode case: Numerical results for spatially correlated twin beams: SNR as a function of the photon number ∝ pulse duration

light beam i 1 (t) i 2 (t) light beam i 1 (t)- i 2 (t) + - x O D Rayleigh limit : Standard Quantum Limit : number of photons measured in total beam x D Measurement of small beam displacements in the transverse plane THE REAL LIMITATION IS QUANTUM NOISE ! Fabre, Fouet, Maitre, Opt. Lett. 25, 76 (2000)

Field generated by single pass parametric down-conversion, or by optical parametric oscillators with mode-degenerate cavities i 1 (t) i 2 (t) + - x O In the crystal, each generated parametric photon has its “twin” produced in a symmetric direction noise reduced on the intensity difference Parametric medium USE OF SPATIAL ENTANGLEMENT

x flipped modey flipped modeTEM 00 y x amplitude squeezed vacuum coherent state x y Laser beam 2 D positioning : "the quantum laser pointer"

2 : optical cavity Beam shape y flipped mode N. Treps, U. Andersen, B. Buchler, P.K. Lam, A. Ma î tre, H. Bachor, C. Fabre Phys. Rev. Letters (2002) N. Treps, N. Grosse, W. Bowen C. Fabre, H. Bachor, P.K. Lam Science, 301, 940 (2003) How to « mix » the different modes ? 1 : beamsplitter Beam shape y flipped mode

1 A improvement to beam positioning accuracy with respect to Standard Quantum Limit : 1.7 horizontal, 1.6 vertical Laser beam intensity difference (dB scale) Coherent beam Non classical beam displacement (oscillation amplitude) 1 A very small oscillation at 5 MHz

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 MENU 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.

Ghost imaging by means of two-photon quantum entanglement Belinsky and Klyshko, Sov. Phys JETP 78, 259 (1994) 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 EXP Ribeiro, Padua, Machado da Silva, Barbosa, PRA. 49, 4176, (1994) Strekalov, Sergienko, Klyshko and Shih, PRL 74, 3600 (1995) Abouraddy, Saleh, Sergienko, Teich, Phys.Rev.Lett. 87, (2001) THEORY GHOST DIFFRACTION EXP TEST ARM REFERENCE ARM

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)]

Possibility of performing coherent imaging using incoherent light Two arm configuration: more flexibility in comparison with standard imaging illuminating the object with one frequency and detecting the light at an other frequency image processing by only operating on the optics in the reference arm 2

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

DEBATE : is entanglement of the two beams necessary for ghost imaging or not ? An essential literature: -Abouraddy, Saleh, Sergienko, Teich, Phys. Rev. Lett. 87, (2001) -Bennink, Bentley, Boyd, Phys. Rev. Lett. 89, (2002) -Gatti, Brambilla, Lugiato, Phys. Rev. Lett. 90, (2003) -Gatti, Brambilla, Lugiato, quant-ph/ (2003)  Phys. Rev. Lett. 93, (2004); Phys. Rev. A 70, (2004) -Bennink, Bentley, Boyd, Howell, Phys. Rev. Lett. 92, (2004) - Cheng, Han, Phys. Rev. Lett. 92, (2004) - Valencia, Scarcelli, D’Angelo, Shih, Phys. Rev. Lett. 94, (2005) - Wang, Cao, Phys. Rev. A 70, R (2004) - Cai, Zhu, Opt. Lett. 29, 2716 (2004) - Ferri, Magatti, Gatti, Bache, Brambilla, Lugiato, Phys. Rev. Lett. 94, (2005)

First guess: it is not possible to realize both the ghost image and the ghost diffraction experiment using the same classical source

Gatti Brambilla Bache Lugiato, PRL 93, (2004), Phys. Rev. A 70, (2004), quant-phys/ (2003). A surprising answer : b1b1 b2b2 vacuum 50:50 BS Beam in a thermal-like state N1N1 N2N2 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) 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.

An old favourite of the 70-ties: the speckle pattern generated by impinging a laser beam on a ground glass LASER BS ROTATING GROUND GLASS TO CCD 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.

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, (2005) CCD He-Ne LASER BS GROUND GLASS OBJECT D=3mm near-field plane TURBID MEDIUM coherence time ~ 0.1 s speckles ~25  m

IMAGE OBTAINED BY SHINING LASER LIGHT 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 FRAMES30000 FRAMES SECTION

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

Second guess: it is not possible to achieve high resolution simultaneously in ghost image and ghost diffraction, and the bound  x n  q > 1 cannot be violated  x n = resolution in the ghost image experiment  q = (2  / f)  x f,  x f = resolution in the ghost diffraction experiment In the experiment Ferri et al., PRL 94, (2005) one has  x n  q =0.066<<1, and this does not correspond to the violation of any EPR inequality.

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.

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. MENU

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. 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. This is equivalent to measuring the spatial autocorrelation of the field transmitted by the object BS OBJECT Thermal light Far field

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. Cross- correlation Auto-correlation BS OBJECT Thermal light BS OBJECT Thermal light Far field GHOST IMAGING TECHNIQUE HBT TECHNIQUE

80 grooves / mm, λ=532nm OBJECT: TRANSMISSION GRATING BEAM SPLITTER order -2 order -1 order 0 order 1 order 2

 x n = 2  m = speckle size in the near field using the near field scattering (Giglio et al., Phys. Rev. Lett. 85, 1416 (2000)): INCOHERENT LIGHT Experimental demonstration of ghost diffraction of a pure phase object by incoherent light Snapshot of the speckles recorded by the CCD camera in the far field plane Ghost diffraction pattern (average over snaphots) Reference Test P1P1

COMPARISON OF GHOST DIFFRACTION AND DIRECT LASER ILLUMINATION Bache, Brambilla, Gatti, Magatti, Ferri, Lugiato, Phys.Rev.A 73, (2006)

INCOHERENT ILLUMINATION: WITH THE HBT TECHNIQUE ONE DOES NOT OBTAIN THE DIFFRACTION PATTERN OF THE PHASE OBJECT

CONCLUSIONI

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.