Is Entanglement Dispensable in Quantum Lithography?

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14th CEWQO - Palermo, 1-5 June 2007
Is Entanglement Dispensable in Quantum
Lithography? Milena DAngelo Dipartimento di
Fisica - Università degli Studi di Bari Y.H.
Shih UMBC Baltimore, MD G. Scarcelli
Harvard Medical School Boston, MA A. Garuccio
Dip. di Fisica - Università degli Studi di Bari
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Outline

• Classical Lithography Rayleigh limit

• Quantum Lithography beyond Rayleigh limit

• Working principle

• Experimental proof of principle two-photon
  diffraction

• Can classical light simulate the effect of
  quantum lithography?

• What is special about quantum entanglement?

• EPR correlations and EPR inequalities

• Conclusions

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Classical optical lithography

• Optical lithography is a printing method in which
  light is used to etch a substrate (a reduced-size
  image of complicated patterned is reproduced onto
  a microchip).

DIFFRACTION point-to-spot relationship between
the OBJECT and the IMAGE planes
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 !!
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Classical Rayleigh Limit
The resolution is constrained by the Rayleigh
diffraction limit l/2 !!!
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Quantum Lithography beyond Rayleigh limit
Entangled N-photon states may beat the Rayleigh
diffraction limit by a factor of N (Boto et al.,
PRL 85, 2733 (2000))
Twice narrower point-spread function somb(x) ?
somb(2x)
The resolution may be improved by a factor of 2
(as if one used a classical source with
wavelength ?/2) !!
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Two-photon diffraction proof of principle of
Quantum Lithography
Boto et al., PRL 85, 2733 (2000) ? M.
DAngelo, M.V. Checkova, and Y.H.
Shih, PRL, 87, 013602 (2001).
Entangled N-photon states may beat the Rayleigh
diffraction limit by a factor of N twice
narrower interference/diffraction pattern!!
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Two-photon diffraction and quantum lithography
M. DAngelo, M.V. Checkova, and Y.H. Shih, PRL,
87, 013602 (2001).

• Degenerate Collinear type-II SPDC
• Double-slit VERY close to the crystal
• Dfscattering angle inside the crystal
  bdistance between slits Ddistance between
  input face of crystal and double slit

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Experimental Data
Two-photon diffraction beats the classical limit
by a factor of 2!
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Double Spatial Resolution on the Image Plane
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Double Spatial Resolution on the Image Plane
Classical (first order) imaging I(?i)
?Aobj d?o t(?o) somb (R/so 2p/l ?o ?i/m) 2
Quantum (two-photon) imaging G2(?1 , ?1)
?Aobj d?o t(?o) somb (R/so 4p/l ?o ?i/m) 2
Is Entanglement Dispensable in Quantum
Lithography?
G. Scarcelli, M. DAngelo, and Y.H. Shih, to be
published (soon on the archive)
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Coincidence imaging with chaotic light
Sub-wavelength Interfetrence experiments S.J.
Bentley et al., Opt. Expr. 12, 5735 (2004) A.
Peeret al. Opt. Expr. 12, 6600 (2004) G.
Scarcelli et al., Europhys. Lett. 68, 618 (2004)
Does this mean that we can replace N-photon
entangled systems with chaotic light to simulate
the effect of quantum lithography in N-photon
joint detection?
(Ghost) Imaging experiments A.Valencia, et al.,
PRL 94, 063601 (2005) F. Ferri, et al. PRL 94,
183602 (2005) D. Zhang et al., Opt. Lett., 30,
2354 (2005) G. Scarcelli, et al., PRL 96, 063602
(2006)
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Can classical light simulate quantum lithography?
Even in joint detection!
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What is special about quantum entanglement?
Einstein, Poldosky, Rosen (1935) entanglement is
base-independent!
BUT
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For SPDC two-photon
EPR inequalities, M. DAngelo, et al., PRA 72,
013810 (2005)
?
Object (? diffraction pattern) ? image without
loosing spatial information ? super-resolution!
In well thought experimental setups, the
non-local correlation implicit in entangled
systems allows one to overcome the Rayleigh
diffraction limit and obtain super-resolved images
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What is special about quantum entanglement?
Signal and idler are diffracted togheter, as a
whole (two-photon diffraction)!
The entangled photon-pair comes out from the same
point of the object plane!
Twice narrower PSF on the image plane somb(l/2)
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Conclusions

• Quantum lithography requires quantum
  entanglement!
• Only the peculiar nature of entangled systems
  allows generating an image with double spatial
  resolution
• the entangled pair comes out from one point of
  the object plane, undergoes two-photon
  diffraction and thus stops in the image plane
  within a twice narrower spot than the one
  characterizing classical images.
• Although two-photon interference of chaotic light
  partially reproduces a similar result, its random
  nature seems to reduce the overall resolution to
  the classical one
• the two photons contributing to a two-photon
  transition do not necessarily come from the same
  object point
• photons coming from any point in a certain
  neighborhood of the object plane may be
  diffracted independently of each other and still
  arrive in the same point of the image plane, thus
  contributing to a two-photon transition.
• the PRODUCT OF INDEPENDT Rayleigh limited images
  strongly compromises the two-photon diffraction
  effect (i.e., double resolution) ? impracticality
  of chaotic sources for lithographic purposes!

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Thanks!
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What is special about quantum entanglement?
Singal-idler from SPDC
On the output plane of the source
Signal and idler may come out from any point of
the object plane, BUT if the signal (idler) is
found in a certain position, the idler (signal)
must be found in the same position, with 100
certainty
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What is special about quantum entanglement?
M. DAngelo, A. Valencia, M.H. Rubin, Y.H. Shih,
submitted to PRA
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Identifying entanglement through quantum
ghost imaging and interference
D1 and D2 Ghost interference measures D(kx1
kx2) D1 and D3 Ghost image measures D(x1- x2)
M. D'Angelo, Y.H. Kim, S.P. Kulik, and Y.H. Shih,
PRL 92, 233601 (2004)
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Experimental results
Ghost interference
Ghost image
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• Precise knowledge about both x2 and kx2 can be
  obtained from non-local joint measurements
• Practical viewpoint quantum ghost imaging
  achieves high resolution and high visibility
• ?
• Entangled photon pairs allow non-local high-
  precision measurements, beyond the classical limit

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Coincidence imaging with chaotic light
Two-photon ghost imaging with thermal light
M 2.15 (Mtheory 2.16) V 12
(Vtheory 16.5)
A. Valencia, G. Scarcelli, M. DAngelo, and Y.H.
Shih, PRL 94, 063601 (2005).
F. Ferri, et al., PRL 94, 183602 (2005).
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For chaotic thermal light
Generates both ghost image and ghost
interference!
M. DAngelo, A. Valencia, M.H. Rubin, and Y.
Shih, PRA 72, 013810 (2005).
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Physics!
M. DAngelo, A. Valencia, M.H. Rubin, and Y.
Shih, PRA 72, 013810 (2005).
Applications!
G. Scarcelli, V. Berardi, and Y.H. Shih, PRL 96,
063602 (2006).
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EPR Inequalities
may satisfy