Quantum Interferometric Lithography:

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Quantum Interferometric Lithography

• Beating the Diffraction Limit with Three-Photon
  NOON States

Sabrina Liao Supervisor Professor
Steinberg Summer 2006
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Outline

• Background Information and Motivation
• Lithography, NOON States Entangled Photons
• Underlying Mathematics
• The Experiment
• Set-up, Results, Future Work
• Conclusion

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Quantum Optics Lab

• Principle Investigator
• Professor Aephraim Steinberg
• Post-Doc
• An-Ning Zhang
• Ph.D.
• Rob Admason
• Krister Shalm

• Collaborators (University of Rochester)
• Professor Robert Boyd
• Collin OSullivan-Hale

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Background Information
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Lithography

• Problem Rayleigh Criterion (L)

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Rayleigh Criterion (L)
?
A amplitude, k optical wave number
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Entangled Photons

• NOON State
• N0gtHV N, 0gtHV 0, NgtHV
• 3-Photon Noon State
• 30gtHV 3, 0gtHV 3, NgtHV Hgt1Hgt2Hgt3
  Vgt1Vgt2Vgt3
• Schrodingers Cat State

?catgt decaygtcat deadgt no decaygtcat alivegt
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Underlying Mathematics
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Math, Math More Math
Total output operator, e c d Intensity lt?
d ?gt, d (e)N(e)N / N!
B Beamsplitter M Mirror P Phase Shifter

• Model of the System

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Math, Math More Math

• Key step in achieving super-resolution
• ?gt 1gta 1gtb ? (0gta 2gtb 2gta
  0gtb ) /
• For an N-entangled number state, the intensity is
  proportional to 1 cos( 2Nf )
• Rayleigh Limit ? / 2 ? ? / 2N

f oscillation
Nf oscillation
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The Experiment
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Experimental Set-up

• Design Considerations
• Micron scale imaging
• Design wavelength 810nm
• Physical Constraints
• Angle of beam intersection 4.62
• Total length lt 1m

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Schematic Diagram
collimation lens
1-micron aperture
h
telescope system
photodiode
(HWP)
W0
BS (PBS)

• Angle of Intersection
• T h / f
• Number of Observed Fringes (in 1 standard
  deviation)
• Geometrically N a h / W0
• Gaussian Beam Optics N h / W0

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Classical Results
Beam A Profile
Interference Pattern
Beam B Profile
Visibility 99
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Future Work

• Ronchi Ruling
• 3-Photon Coincidence Detection

40/60 BS
50/50 BS
Single-photon detectors
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Conclusion

• Optical lithography with classical light is
  diffraction limited.
• N entangled photons can potentially be used in
  lithography to decrease the size of microchips
  and semiconductors by a factor of N2.