Imaging with spatial correlation

Transcription

1 Società Italiana di Fisica XCVI Congresso Nazionale, Bologna, 0-4 Settembre, 010 Imaging with spatial correlation Alessandra Gatti Lucia Caspani Enrico Brambilla Luigi Lugiato The Theoretical Quantum Optics Group in Como CNR and Dept. of Physics and Mathematics, Insubria University, Como, Italy Experimental Collaborations: Ultrafast nonlinear optics lab (Como): Paolo Di Trapani, Ottavia Jedrkiewicz Light Scattering lab (Como) : Fabio Ferri, Davide Magatti Quantum Optics group (INRIM, Torino): Marco Genovese, Giorgio Brida, Ivano Ruo Berchera

2 SPATIAL ASPECTS of QUANTUM OPTICAL FLUCTUATIONS in the transverse distribution of light, tipically in wave-mixing phenomena involving a large number of spatial modes Reasons for interest: spatial properties of quantum states of light can be used to overcome the classical limits of imaging and to devise unconventional imaging schemes QUANTUM IMAGING. Quantum limits in the detection of small beam displacements (microscopy), Noiseless amplification of images, Quantum teleportation of optical images, Quantum superresolution and much more Quantum spatial correlations in light beams (the fundamental resource) High sensitivity imaging Ghost-imaging: imaging without interaction

3 Quantum spatial correlation of twin beams and high-sensitivity imaging

4 Classical spatial correlation Speckle pattern generated by impinging a laser beam on a ground glass. Splitting by a beam splitter: two classical copies of the pattern N 1 LASER TO CCD Brother patterns ROTATING GROUND GLASS BS N Splitting of light by the beam splitter: macroscopic process Partition of photons in the two arms is a random process partition noise N_=N 1 -N difference of photon numbers collected from two corresponding portions N = N1 + Imperfect (classical) spatial correlation δ N SHOT - NOISE LEVEL

5 Quantum Spatial correlation: the process of Parametric Down-Conversion Brambilla, Gatti, Bache, Lugiato, Phys Rev A 69, 0380 (004) signal - idler emission cones nm χ () TWIN PATTERNS z 0 l c pairs of twin photons q p =0, ω p pump 1 signal idler Microscopic process: momentum conservation creates correlation in the directions of propagation of twin photons δn = 0 Perfect quantum correlation between any two symmetric portions

6 Position-momentum entanglement of twin photons 1 k k χ () -k -k Momentum correlation : Direction of propagation of photon 1 determined from a measurement of the direction of propagation of photon 1 Position correlation: Position x of photon 1 determined from a measurement of the position of the photon Simultaneous presence of correlation in both position and momentum of the two photons Entangled (nonseparable) state, similar to the original EPR (Einstein-Podolsky Rosen, 1935) state Exp. test: Howell, Bennink, Bentley and Boyd, PRL , 004; Bennink, Bentley, Boyd, Howell, PRL (004) ; D Angelo Kim Kulik Shih PRL 9, (004)

7 First Experimental Demonstration of Quantum Spatial Correlation in high-gain PDC at Ultrafast Nonlinear Optics Lab in Como Pump pulses ( nm, mj, 1 mm waist) Spatial filtering 4 mm type II BBO η tot ~ 75% Jedrkiewicz, Jiang, Brambilla, Gatti, Bache, Lugiato, Di Trapani, PRL 93, (004) Far-field images signal aperture Portion of PDC fluorescence around collinear direction M Polarizing Beam-splitter M 1 f=10cm f=10cm CCD η ~ idler evident spatial correlation

8 Degree of correlation: noise in the difference N - of photocounts from symmetric signal-idler pixels σ = N δn 1 + N σ σ = N δn 1 + N Shot-noise N 1 + N Correlation are Sub-shot-noise up to gains characterized by N 1 + N In this region: beams are spatially correlated better than two classical copies. Twin beam effect over several (~4000) signal/idler spatial modes.

9 High-Sensitivity Imaging A classical differential scheme suppresses the excess noise, but it is limited by the partition noise (=shot-noise in N -N 1 ) : a weak absorbtion can be hidden by noise χ () N 1 α(x) N 1 N ' = N1' N SOURCE Twin beams 50/50 BS N reference The classical limit can be beaten by replacing the two classical copies with two quantum copies : twin beams with sub-shot noise spatial correlation Signal-to-noise ratio improved with respect to the classical limit Original Image Classical copies Twin beams Theoretical proposal: Brambilla, Caspani, Jedrkiewicz, Lugiato, Gatti, PRA (008) SNR=1. SNR=3.3

10 The regime of Como experiment is not suitable for imaging, because correlation remain subshot noise only for a very low photon number ( background noise detrimental) IDEA: WORKING at LOWER-GAIN, WITH A LONGER PUMP PULSE SHOULD MAKE CORRELATION MORE ROBUST Numerics: degree of correlation σ as a function of the detected photon number, in the presence of un unbalance X shift fixed = 4 μm 1, τ pump =15ps τ pump =50ps τ pump =150 ps σ = N δn 1 + N 1,0 0,8 0,6 shot-noise τ pump =1000ps 0,4 0, 0, <N 1 + N > Correlation is more robust for long pump pulses, low excess noise sub-shot noise correlation at higher photon number

11 Second experimental demonstration of sub-shot noise spatial correlation at INRIM (Torino) Nanosecond pump pulses Sub-shot noise spatial correlation for higher intensities photons per pixel, NO background noise correction Suitable for imaging! σ = δn N s + N i Shot-noise Brida, Caspani, Gatti, Genovese, Meda, Berchera,, Phys. Rev. Lett. 10, 1360 (009)

12 010: Experimental realization of sub-shot noise imaging [Brida, Genovese, Berchera, Nature Photonics 4 7, 010] SNR SNR Quantum Classical σ Quantum correlations of light can be used to obtain higher signal-to-noise ratios than those possible through classical imaging methods.

13 II-Ghost imaging Imaging without interaction Debate about the role of the entanglement/quantum nonlocality vs classical correlation

14 Ghost imaging (imaging through light correlation) = unconventional way of imaging Light source Light source Correlation with the test pattern object spatial information REFERENCE ARM Classical or quantum copy of the test pattern Form the correlation as a function of position in the reference arm object transmission function

15 Quantum illumination: Imaging with spatially entangled photons Entangled photon pairs from PDC Single detector (bucket detector) pump χ () object Coincidence counts as a function of x correlation function (a.u.) Array of detectors: records the arrival position of photon x /l coh The image emerges from the coincidence counts, as a function of the arrival position of photon, that never sees the object Ghost Image [Pittman, Shih, Strekalov and Sergienko, PRA 5, R349 (1995) ] By simply changing the optical set-up in the path of photon Ghost Diffraction [Ribeiro, Padua, Machado da Silva, Barbosa, PRA. 49, 4176, (1994); Strekalov, Sergienko, Klyshko and Shih, PRL 74, 3600 (1995)]

16 Classical illumination: Evidence of high resolution ghost image and ghost diffraction with classically correlated beams from a pseudo-thermal source Gatti Brambilla Bache Lugiato, PRL 93, (004); Ferri, Magatti,Gatti, Bache, Brambilla, Lugiato, PRL 94, (005) He-Ne LASER OBJECT ARM OBJECT ARM GROUND GLASS 400 mm TURBID MEDIUM Classically correlated speckle patterns BS DOUBLE SLIT q F F eff q 1 = F focal of eff F' F F F CCD the two lens system CROSS CORRELATION between the total light in the object arm and the intensity distribution in the reference arm CROSS CROSS CORRELATION CORRELATION between between a single single pixel pixel in in the the object object arm arm and and the the intensity frame in distribution the reference in arm the reference arm

17 The ability to produce both the ghost image and the ghost diffraction pattern was initially attributed to the entanglement of the quantum state (simultaneous presence of position and momentum correlation) Long debate about the need of entanglement for Ghost Imaging An essential literature: - Abouraddy, Saleh, Sergienko, Teich, Phys. Rev. Lett. 87, 1360 (001) - Bennink, Bentley, Boyd, Phys. Rev. Lett. 89, (00) - Gatti, Brambilla, Lugiato, Phys. Rev. Lett. 90, (003) - Gatti, Brambilla, Lugiato, Phys. Rev. Lett. 93, Phys. Rev. A 70, (004) - Bennink, Bentley, Boyd, Howell, Phys. Rev. Lett. 9, (004) - Cheng, Han, Phys. Rev. Lett. 9, (004) - Valencia, Scarcelli, D Angelo, Shih, Phys. Rev. Lett. 94, (005) - Wang, Cao, Phys. Rev. A 70, R (004) - Cai, Zhu, Opt. Lett. 9, 716 (004) - Ferri, Magatti, Gatti, Bache, Brambilla, Lugiato, Phys. Rev. Lett. 94, (005) - Abouraddy, Stone, Sergienko, Saleh,Teich, Phys. Rev. Lett. 93, (004) - Bache, Magatti, Ferri, Gatti, Brambilla Lugiato Phys. Rev. A 73, 5380, (006). - A. Gatti et al., J. Mod Opt. 53, 739 (006). - Scarcelli, Berardi, and Shih, Phys. Rev. Lett. 96, (006) - Gatti, Bondani, Lugiato, Paris, Fabre, Phys. Rev. Lett. 98, (007) - J.H. Shapiro, Phys. Rev. A 78, (008). - Scarcelli, Berardi, Shih, Appl. Phys. Lett. 88, , (006) - Basano and Ottonello, Appl. Phys. Lett. 89, , (006). - Ferri, Magatti, Sala, Gatti, Appl. Phys. Lett. 9, (008) Etc. etc. etc

18 The main message that emerged: Caution should be taken when dealing with concepts such as quantum nonlocality or entanglement Classical correlations are also powerful tools

19 Imaging in a noisy environment Light source reference pattern X Correlation object transmission function Imaging throught scattering media (biological tissues, fog, clouds ) Bio-medical imaging Remote sensing

20 Possibility of compressive sensing In conventional imaging N pixels of the image are detected, being the minimum number of N determined by Nyquist sampling principle In ghost imaging the object is sampled by a single detector, and the image is retrieved from a statistical evaluation of the correlation with the test patterns, performed over M independent patterns Can M be significantly smaller than N? Guess (inspired by researches at the The Weizmann Institute of Science on compressive imaging): Maybe yes if the image is compressible Katz, Bromberg, and Silberberg, Appl. Phys. Lett. 95, (009)

21 Fundamental issue: the signal-to-noise ratio of ghost imaging schemes The signal-to-noise ratio of conventional ghost imaging is low So far, imaging of simple binary objects Recent progress: Ferri, Magatti, Lugiato, Gatti, PRL 104, (010) Differential ghost imaging (DGI), a novel scheme that overcomes the SNR limitation (enhancement of SNR of ghost imaging by orders of magnitudes) Bringing ghost imaging from an academic subject to real world applications Original Conventional GI (m=10 5 ) Differential GI (m=10 5 ) Measured (SNR) DGI / (SNR) GI ~ 6.4

22 Two small particles (d 1 = 400 µm, d = 80 µm) in a large beam (L=5.7 mm) Experiment # Conventional GI Differential GI m = mm 5.7 mm (SNR) DGI (SNR) = Measured DGI 66 (SNR) (SNR) Expected 5 GI GI The new protocol DGI allows the location and sizing of small particles (not feasible with conventional GI)

23 CONCLUSIONS Example I: High sensitivity imaging with spatially correlated twin beams Sub-shot-noise correlations are the fundamental resource that permits to surpass the classical limit in sensitivity useful for weakly absorbing object, whenever a low disturbance is needed Example II: Ghost Imaging Classical sources can completely mimic the behaviour of quantum sources Poor signal-to-noise ratio, overcome by a novel scheme (DGI) DGI enhables experiments not feasible with conventional GI, opens the access to the potentialities of GI Work in progress Imaging in scattering media, compressive sensing