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 entangle- ment in quantum imaging and lithography. “Magic” mirror for “ghost” imaging. Muti-photon sources and measurement devices. ApproachAccomplishments Using entangled two-photon and three-photon states created via optical nonlinear interaction in spontaneous and stimulated modes for multi- photon 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 current- current correlation circuit to explore the nature of two-photon correlation. * The physics of two-photon imaging of chaotic thermal light: PRL, 96, (2006). * The physics of quantum lithography: “ Is entangle- ment dispensable in quantum lithography? ” (submitted for publication). * The source: Generation of true triphoton state: immediately applicable for three-photon imaging and lithography (submitted for publication). Experimentally observed triphoton wavepacket. * 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. 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. t(   

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 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 !! t(   

Classical Rayleigh Limit somb(x) = 2J 1 (x) / x  “point-spread function” (resolution) | ∫ obj dρ o t(ρ o ) somb (R/s o 2  |ρ o + ρ i /m|) | 2 Coherent I(ρ i ) = ∫ obj dρ o |t(ρ o )| 2 |somb (R/s o 2  |ρ o + ρ i /m|)| 2 Incoherent The resolution is constrained by the Rayleigh diffraction limit: /2 !!! 1/s o +1/s i = 1/f m =s i / s o R: lens radius t

Quantum Lithography: beyond classical limit The resolution is improved by a factor of 2 (as if one used a classical source with wavelength λ/2) !! 1/s o +1/s i = 1/f m =s i / s o R: lens radius

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). (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! (1)Proposed the entangled two-particle state according to the principle of quantum superposition:

What is so special about entangled two-photon states? EPR correlation: 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. On the output plane of the source

The entangled photon pair comes out from a point of the object plane, undergoes two-photon diffraction, thus, results in twice narrower point spread function on the image plane. What is so special about entangled two-photon states? ksks kiki

Green’s function, or optical transfer function (Fourier optics)

Biphoton Coherent Chaotic

Two-photon diffraction: proof of principle of Quantum Lithography The measurement was on the Fourier transform plane instead of the image plane: twice narrower interference/diffraction pattern!! Boto et al., PRL 85, 2733 (2000)  M. D’Angelo, M.V. Checkova, and Y.H. Shih, PRL, 87, (2001). Unfolded version

Two-photon diffraction and quantum lithography Degenerate Collinear type-II SPDC Double-slit VERY close to the crystal The measurement is on the Fourier transform plane. M. D’Angelo, M.V. Checkova, and Y.H. Shih, PRL, 87, (2001).

Experimental Data After 2 nd Fourier transform, on the image plane, the spatial resolution gains a factor of 2, beyond the classical limit! SPDC:  916nm Classical Laser light:  916nm

Double Spatial Resolution on the Image Plane Classical Diffraction Diffraction of an entangled pair 

Is Entanglement Dispensable in Quantum Lithography? The unique EPR correlation of  (x 1 - x 2 ) &  (p 1 + p 2 ) 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 two- photon diffraction provide us sub-wavelength spatial resolution (  ). G. Scarcelli, M. D’Angelo and Y.H. Shih. “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 Position of Detector Counts Position of Detector Counts Joint Detection Position of Detector Coincidences D1D1 D2D2 aa bb

An interpretation: Copies of “Speckles” Laser Beam It is a trivial wrong idea: G (2) = constant for laser light.

More Problems Joint Detection Entangled Photon Source Classical Statistical Correlation of Intensity Fluctuations does not work for Entangled States ??? Position of Detector Coincidences 0 1

The physics ? “Can Two-photon Correlation of Chaotic Light Be Considered as Correlation of Intensity Fluctuations?” PRL, 96, (2006) (G. Scarcelli,V. Berardi, and Y.H. Shih).

S.C X2X2 X2X2 D2D2 D1D1 Two-Photon Imaging X2X2 C.C X2X2

Pseudothermal source Ghost Image with chaotic light Correlator Photon Counting Correlation Measurement Near-field Martienssen-Spiller (1964)

Results

True Image ? Correlation Measurement

Results

What is the similarity and difference between this experiment and HBT? Question 1

Ghost Imaging and HBT k-k Momentum-Momentum Correlation x-x Position-Position Correlation IMAGE

Why the statistical correlation between intensity fluctuations is not valid for this experiment ? Question 2

Source Image Plane Object Plane BS 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! (1)Statistical Correlation of Intensity Fluctuations? No !

(2) Statistical Correlation of Intensity Fluctuations? No ! The correlations are washed out by the “bucket detection” SourceImage Plane Object Plane BS Bucket Detector

Question 3 Alternative Interpretation ?

Two-photon interference Two-photon Chaotic light Source Image Plane Object Plane BS Glauber theory

Two-photon interference Indistinguishable two-photon probability amplitudes result in a “click-click” joint detection event. D1D1 D2D2 Source

Two-photon interference Back to the “standard result” in terms of first-order correlation functions IMAGE

The ground camera is pointed to a “magic mirror” in space. A point like photo-detector D 1 collects all photons coming from the object and records the photon registration time. By studying the time correlation between the photon registration times of D 1 and each of the CCD element, a “ghost” image is obtained in “coincidences”. A possible application: “ghost” camera.

Quantum Imaging - UMBC Part III Multi-photon sources - A true entangled three-photon state

1 1’ 2 2’ 3 pp pp    Feynman diagram: three-photon generation. The triphoton state Keller, Rubin, Shih, Wu, PRA 57, 2076 (1998).

2D photonic crystal: hexagonally poled LiTaO 3

Schematic setup of the three-photon correlation measurement

G (3) measurement Experimental data & Numerical simulation