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Transcript

Quantum Imaging Yanhua Shih, Morton H. Rubin, and Fow-Sen Choa University of Maryland Baltimore County Baltimore, MD 21250 Quantum Imaging - UMBC Objective • Study the physics of multi-photon imaging for entangled state, coherent state and chaotic thermal state: distinguish their quantum and classical nature, in particular, the necessary and/or unnecessary role of quantum entanglement in quantum imaging and lithography. • “Magic” mirror for “ghost” imaging. • Muti-photon sources and measurement devices. Approach • Using entangled two-photon and three-photon states created via optical nonlinear interaction in spontaneous and stimulated modes for multiphoton spatial correlation study and imaging; • Using chaotic pseudothermal source, coherent source for two-photon spatial correlation study and ghost imaging; • Using photon counting and classical currentcurrent correlation circuit to explore the nature of two-photon correlation. Experimentally observed triphoton wavepacket. Accomplishments * The physics of quantum lithography: “Is entanglement dispensable in quantum lithography?” (submitted for publication). * The physics of two-photon imaging of chaotic thermal light: PRL, 96, 063602 (2006). * The source: Generation of true triphoton state: immediately applicable for three-photon imaging and lithography (submitted for publication). * The detector: Fabrication of 2-D APD arrays with improved photon counting characteristics. Quantum Imaging - UMBC Part I The physics of quantum imaging and lithography - Is entanglement dispensable in quantum lithography? Classical Lithography Optical lithography is a printing method in which light is used to etch a substrate (a reduced-size image of complicated patterns is reproduced onto a microchip). Geometric Optics: POINT-to-POINT relationship between the OBJECT and the IMAGE planes. t( E(i,zi ,ti ) d d g(,; ,z z ) e i (t i to ) i o i o I( i ) E o (,) d t( ) ( /m) o o o 2 i If light always follows the law of geometrical optics, the image plane and the object plane would have a “point-to-point” relationship which means an unlimited ability of making demagnified image. Classical Lithography Optical lithography is a printing method in which light is used to etch a substrate (a reduced-size image of complicated patterns is reproduced onto a microchip). DIFFRACTION: POINT-to-SPOT relationship between the OBJECT and the IMAGE planes t( E(i,zi ,ti ) i (t i to ) d d g( , ; ,z z ) e E o (,) i o i o I( i ) do t(o ) 2J1 (R /so 2 / o i /m ) R /so 2 / o i /m 2 Unfortunately, light is wave. The finite size of the spot, defined by the “point-spread function”, determines the spatial resolution of the imaging setup and limits the ability to produce demagnified images !! Classical Rayleigh Limit t 1/so+1/si = 1/f m =si / so R: lens radius | ∫obj dρo t(ρo) somb (R/so 2/ |ρo + ρi/m|) |2 Coherent I(ρi) = ∫obj dρo |t(ρo)|2 |somb (R/so 2/ |ρo + ρi/m|)|2 Incoherent somb(x) = 2J1(x) / x “point-spread function” (resolution) The resolution is constrained by the Rayleigh diffraction limit: /2 !!! Quantum Lithography: beyond classical limit 1/so+1/si = 1/f m =si / so R: lens radius () () () () 2 ˆ ˆ ˆ ˆ G ( 1,t1; 2 ,t 2 ) E1 E 2 E 2 E1 (1,t1; 2,t 2 ) (2) somb( /2) R 2 G ( 1,2 ) do t (o ) somb( o i /m ) so /2 (2) 2 2 The resolution is improved by a factor of 2 (as if one used a classical source with wavelength λ/2) !! What is so special about entangled two-photon state? Can quantum mechanical physical reality be considered complete? Einstein, Poldosky, Rosen, Phys. Rev. 47, 777 (1935). (1) Proposed the entangled two-particle state according to the principle of quantum superposition: x1, x 2 p1, p2 dp p x 2 u p x1 (x1 x 2 x 0 ) dx x x 2 v x x1 ( p1 p2 ) (2) Pointed out a surprising phenomenon: the momentum (position) for neither subsystem is known; however, if one particle is measured to have a certain momentum (position), the momentum (position) of its “twin” is known with certainty, despite the distance between them! What is so special about entangled two-photon states? ( s i p ) (k s k i k p ) aˆ s aˆ i 0 s,i EPR correlation: (s i ) (s i ) () () () () 2 ˆ ˆ ˆ ˆ G ( 1,t1; 2 ,t 2 ) E1 E 2 E 2 E1 (1,t1; 2 ,t 2 ) (2) (s, i ) (s i ) On the output plane of the source In EPR’s language, the signal and the idler may come out from any point of the object plane; however, if the signal (idler) is found in a certain position, the idler (signal) must be found in the same position, with 100% certainty. What is so special about entangled two-photon states? (s i ) ks ki (s i ) somb( /2) The entangled photon pair comes out from a point of the object plane, undergoes thus, results in twice two-photon diffraction, narrower point spread function on the image plane. E(, z,t) it ˜ d d g( , ; , z) e E (,) g(,; o,z zo ) Green’s function, or optical transfer function (Fourier optics) ( ) ( ) ( ) ( ) ( ) ( ) ˆ ˆ ˆ ˆ ˆ ˆ G (1, 2 ) E1 E 2 E 2 E1 0 E 2 E1 (2) (1, 2 ) 0 Eˆ 2 Eˆ 1 () () 2 2 Biphoton Coherent G(2) ( ) R 2 o /m ) so /2 R 2 G ( 1,2 ) do t( o ) somb( o 1 /m ) so 2 R 2 o 2 /m ) so 2 (2) Chaotic do t 2 (o ) somb( 2 do t(o ) somb( 2 2 R 2 G(2) ( ) do t( o ) 2 somb( o /m ) s o Two-photon diffraction: proof of principle of Quantum Lithography Boto et al., PRL 85, 2733 (2000) M. D’Angelo, M.V. Checkova, and Y.H. Shih, PRL, 87, 013602 (2001). The measurement was on the Fourier transform plane instead of the image plane: twice narrower interference/diffraction pattern!! Unfolded version Two-photon diffraction and quantum lithography M2 PBS P s and i (916 nm) D1 F D2 M1 BBO Pump (458 nm) Slit M F Coincidence Circuit M. D’Angelo, M.V. Checkova, and Y.H. Shih, PRL, 87, 013602 (2001). Rc Degenerate Collinear type-II SPDC Double-slit VERY close to the crystal b D (asai bsbi ) 0 The measurement is on the Fourier transform plane. Experimental Data SPDC: 916nm R c ( ) sinc 2[(2a/) ] cos 2[(2b/) ] Classical Laser light: 916nm I() sinc 2[(a/) ] cos2[(b/) ] After 2nd Fourier transform, on the image plane, the spatial resolution gains a factor of 2, beyond the classical limit! Classical Diffraction Diffraction of an entangled pair Double Spatial Resolution on the Image Plane Is Entanglement Dispensable in Quantum Lithography? The unique EPR correlation of (x1 - x2) & (p1 + p2) made entangled state very special: the pair comes out from a point on the object plane, under goes two-photon diffraction, and stops at a point on the image plane. The twophoton diffraction provide us sub-wavelength spatial resolution (/). “Is Entanglement Dispensable in Quantum Lithography?” to be published, 2006, G. Scarcelli, M. D’Angelo and Y.H. Shih. Quantum Imaging - UMBC Part II The physics of second-order correlation of chaotic light - “ghost” imaging of thermal light Hanbury Brown and Twiss 1956 Counts D1 a b Position of Detector Counts D2 Position of Detector Coincidences Joint Detection Position of Detector (2) I1 I2 ~ I02{1 sinc 2[(x1 x2 )/ ]} It isinterpretation: a trivial wrong idea: An G(2) = constant for laser light. Laser Beam Copies of “Speckles” More Problems Coincidences Entangled Photon Source Joint Detection I1I2 I11I2 I2 I1 II12I2 I1I2 1 0 Position of Detector I1 0 I 0 sinc [ (x x ) / ] ~ sinc [~1 (x x ) / ] 2 1 2 1 2 2 2 ??? Classical Statistical Correlation of Intensity Fluctuations does not work for Entangled States The physics ? “Can Two-photon Correlation of Chaotic Light Be Considered as Correlation of Intensity Fluctuations?” PRL, 96, 063602 (2006) (G. Scarcelli,V. Berardi, and Y.H. Shih). Two-Photon Imaging S.C D2 X2 X2 C.C D1 S.C X2 X2 Ghost Image with chaotic light Pseudothermal source Martienssen-Spiller (1964) Correlator Photon Counting Correlation Measurement Near-field 10 / d Correlation Results True Image ? 1 1 1 S0 Si f Correlation Measurement so db d a si d ' b Results Question 1 What is the similarity and difference between this experiment and HBT? Ghost Imaging and HBT k-k Momentum-Momentum Correlation IMAGE x-x Position-Position Correlation 10 / d Question 2 Why the statistical correlation between intensity fluctuations is not valid for this experiment ? (1)Statistical Correlation of Intensity Fluctuations? No ! Unlike HBT, it is not in “far-field”…every point of the image plane is “hit” by many k’s of the radiation. For chaotic light, all modes are chaotically independent! Source BS Image Plane Object Plane (2) Statistical Correlation of Intensity Fluctuations? No ! The correlations are washed out by the “bucket detection” Source BS Image Plane Object Plane Bucket Detector Question 3 Alternative Interpretation ? Two-photon interference Glauber theory G(2) (x1, x2 ) E () (x1)E () (x2 )E () (x2 )E () (x1) Source BS Image Plane x1 E1( ) ( x1 ) g1 ( x1 ; q )aˆ q q E Object Plane x2 1q ,1q ' 1q ,1q ' q ,q ' () 2 ( x2 ) g 2 ( x2 ; q )aˆ q q Two-photon Chaotic light Two-photon interference () () G ( x2 ; x1 ) 0 E ( x2 ) E ( x1 ) 1q ,1q ' ( 2) 2 q ,q ' 2 g 2 ( x2 , q ) g1 ( x1 , q ' ) g 2 ( x2 , q ' ) g1 ( x1 , q ) q ,q ' Indistinguishable two-photon probability amplitudes result in a “click-click” joint detection event. Source q' D1 q' q q D2 Two-photon interference G ( x1 , x2 ) ( 2) 2 2 g1 ( x1 , q ) g 2 ( x2 , q ) q q g ( x2 , q ) g1 ( x1 , q ) q * 2 IMAGE G (x1, x1 )G (x 2 , x 2 ) G (x1, x 2 )G (x 2, x1 ) (1) 11 (1) 22 (1) 12 (1) 21 Back to the “standard result” in terms of first-order correlation functions 2 A possible application: “ghost” camera. The ground camera is pointed to a “magic mirror” in space. A point like photo-detector D1 collects all photons coming from the object and records the photon registration time. By studying the time correlation between the photon registration times of D1 and each of the CCD element, a “ghost” image is obtained in “coincidences”. Quantum Imaging - UMBC Part III Multi-photon sources - A true entangled three-photon state 1 p 1’ 3 p 2’ Feynman diagram: three-photon generation. Keller, Rubin, Shih, Wu, PRA 57, 2076 (1998). 2 (2 ˆ ˆ ˆ ) (2k G k k k ) a a a p 1 2 3 p 1 2 3 k1 k 2 k 3 0 k 1 ,k 2 ,k 3 The triphoton state 2D photonic crystal: hexagonally poled LiTaO3 Schematic setup of the three-photon correlation measurement G(3) measurement Experimental data & Numerical simulation