Quantum Imaging

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MURI Kick-Off Meeting Rochester, June 9-10, 2005
Quantum Imaging
- Entangled state and thermal light -
Foundamental and applications
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Optical Projection (Chinese shadow, x-ray, )
Momentum (p1) Momentum (p2)
No image plane is defined.
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Optical Imaging
Point (object Plane) Point (image
plane)
Position (x1)
Position (x2)
Geometric optics
and
Image lens
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Spatial Resolution
Imaging lens finite size
Image Plane
Point (object plane)
Spot (image plane)
??function
somb-function
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Ghost Imaging with entangled photon pairs
Point x1 (object plane)
Point x2 (image plane)
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So
Si
Ghost Image and Ghost Interference EPR
Experiment in momentum-position PRL, 74, 3600
(1995) PRA, 52, R3429 (1995).
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Classical never! - classical statistical
measurements
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Space-like separated measurement events.

• No interaction between two distant quanta
• (2) No action-at-a-distance between individual
• measurements.
• To EPR the two quanta are independent as well as
  
• the measurements, so that

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Classically correlated systems one may consider
building an ensemble of particle-pairs to force
each pair with and
, so that
. In this case, however,

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Quantum yes! - EPR if the two quanta are
entangled
Although
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Can quantum mechanical physical reality
beconsidered complete?
Einstein, Poldosky, Rosen, Phys. Rev. 47, 777
(1935).

• Proposed the entangled two-particle state
  according to the principle of quantum
  superposition

(2) Pointed out an surprising phenomenon the
momentum (position) for neither subsystem is
determinate however, if one particle is measured
to have a certain momentum (posit-ion), the
momentum (position) of its twin is determined
with certainty, despite the distance between them!
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The apparent contradiction deeply troubled
Einstein. While one sees the measurement on
(p1p2) and (x1-x2) of two individual particles
satisfy the EPR ?-function and believes the
classical inequality, one might easily be trapped
into considering either there is a violation of
the uncertainty principle or there exists
action-at-a-distance.
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Violation of the uncertainty principle ?
Simultaneously !
(p1p2) and (x1-x2) are not conjugate variables
!!!!
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Conjugate Variables
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EPR ?-function -- perfect entangled system
Although
EPR Inequality -- non-perfect entangled system
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Then, why Einstein ?
Observation
Believing
Conclusion
(Violation of the )
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The interpretation ?
Quantum entanglement
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Two-photon is not two photons !
Classical Two Wavepackets
Entanglement A non-factorable 2-D Wavepacket
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Biphoton State Spontaneous Parametric Down
Conversion
Two-photon Pure State The signal (idler)
photon can have any energy (momentum), however,
if one of the photons is measured at certain
energy (momentum) its twin must be at a certain
energy (momentum).
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Operational approach
Pure state
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SPDC A biphoton
Effective Two-photon wavefunction
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Two-photon imaging
Field Operators
Greens function (optical transfer function).
determined by the experimental setup.
The calculation of G(2) is lengthy but
straightforward
It is the two-photon coherent superposition made
it possible!
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Although questions regarding fundamental
issues of quantum theory still exist, quantum
entanglement has indeed brought up a novel
concept or technology in nonlocal position-ing
and timing measurements with high accuracy, even
beyond the classical limit.
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Question
Can ghost image be simulated classically ?
Image but not projection!!!
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Yes Experimentally
Thermal Light Imaging
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Magic Mirror and Ghost Imaging
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M 2.15 (Mtheory 2.16) V 12 (Vtheory
16.5)
Experimental Result Ghost image of a
double-slit. A. Valencia, G. Scarcelli, M.
D'Angelo, and Y.H. Shih, Phys. Rev. Lett. 94,
063601 (2005).
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Measurement on the image plan.
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Two-photon thermal light Imaging


Incoherent imaging
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Magic Mirror ?
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Measurement on the mirror plan.
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It is useful !
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A Ghost Camera in Space (Nonlocal)
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A Magic Mirror for X-ray 3-D Imaging
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It is fundamentally interesting !!
50 momentum-momentum, position-position EPR
correlation
Where it comes from ?
Remember thermal light is chaotic !
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It comes from Hanbeury Brown - Twiss ??? It
comes from photon bunching ??? We are not
satisfied !
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The physics behind ???
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Two-photon film
Slit A
Fourier transform function (??or ???) ?
Slit B
f
Different Input State
Fourier Transform Plane
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Correlated Lasers
f
A product of two independent first-order-pattern.
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SPDC
2
0


0
f
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Thermal
2
2
2
0




0
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Quantum lithography (ultra-resolution beyond
classical limit)
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Optical Lithography
Fourier Transform One
Fourier Transform Two
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Optical Lithography
Laser
Fourier Transform One
Fourier Transform Two
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Optical Lithography
SPDC
Fourier Transform One
Fourier Transform Two
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Optical Lithography
Thermal
Fourier Transform One
Fourier Transform Two
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Two-photon diffraction and quantum lithography
Experiment M. DAngelo, et al, PRL, 87, 013602
(2001). Theory A.N. Boto, et al. PRL 85, 2733
(2000).
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Experimental Data
SPDC two-photon at
Classical laser light at
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It is the result of two-photon coherent
superposition. It measures the second-order
correlation between the object plane and the
image plane, defined by the Gaussian thin lens
equation.
The published measurement was on the Fourier
transform plane (far-field). PRL, 87,
013602 (2001).
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Super-resolution
Classical diffraction
Diffraction of a pair
Double (super) Spatial Resolution on the Image
Plane
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Ghost Shadow (Projection)
Bennink et al. PRL 89, 113601 (2002)