Quantum States and Coherent Laser Radar

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Quantum States and Coherent Laser Radar

• Mark A. Rubin and Sumanth Kaushik
• MIT Lincoln Laboratory

This work was sponsored by the Air Force under
Air Force Contract FA8721-05-C-0002. Opinions,
interpretations, conclusions and recommendations
are those of the author and are not necessarily
endorsed by the U. S. Government.
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• I. Why Quantum Light?
• II. Squeezed Light
• III. Entangled Light
• IV. Summary

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I. Why Quantum Light?

• Isnt all light quantum?
• Limit of measurement precision in classical
  light
• Classical from familiar sources, incl.
  lasers
• is due to quantum fluctuations of
  measurement results
• Shot noise limit, photon statistics
• If all light is quantum, how can quantum limits
  be surpassed?
• But
• Limits on measurement depend on quantum nature of
  light and specific quantum state
• Familiar quantum limits like shot-noise limit
  arise in context of classical states of light
  from thermal and laser sources
• So, make enhanced measurements by using light in
  quantum states significantly different from the
  usual states
• There are lots of other states!
• Two types of nonclassical states have been widely
  studied
• Squeezed states
• Statistical fluctuations of in a single beam of
  light are altered
• Entangled states
• Statistical fluctuations in two (or more) beams
  are correlated

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II. Squeezed Light

• Theory
• Heisenberg uncertainty principle limits products
  of precisions of repeated measurements
• E.g. particle position x and momentum p
• ?x?p gt h
• Particular quantum state determines the actual
  precision of measurement of any quantity
• Classical states ?x ? ?p
• Squeezed states ?x lt ?p, ?x gt ?p
• Laser radar applications Want to minimize
  statistical fluctuations in detector measurement
  for given target properties
• Direct detection Number of photoelectrons per
  pulse
• Heterodyne detection Fourier component of
  photoelectron rate
• Experimental status
• Squeezed light has been produced in laboratory
• To date, degree of squeezing and brightness are
  limited

x
p
p
x
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Squeezed Light and Laser Radar

• Known
• Target-return beam of any laser radar has large
  loss
• Squeezed states revert to classical statistics in
  presence of large loss. (Caves, Phys Rev D,
  81).
• Use squeezed light in local oscillator (LO) of
  heterodyne system, avoiding large loss in target
  return beam (Li et al., PRL 99 )
• Expectation
• Squeezed light can have smaller fluctuations in
  photoelectron rate
• sub-Poissonian statistics
• Noise in heterodyne system thought of as
  primarily LO shot noise
• So Squeezing LO should increase SNR
• Actuality---i.e., QFT calculation---is
  different

Squeezed LO
Detector
Target
Fabry-Perot etalon (Rubin Kaushik,07)
Coherent beam
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No-go for Squeezed LO

• Squeezing LO decreases SNR (Rubin Kaushik, Opt.
  Lett. 07)
• Why is expectation wrong?
• Squeezing reduces time-average LO noise, but it
  is quantum fluctuations of the signal Fourier
  component at the heterodyne frequency that are
  relevant for heterodyne laser radar SNR
• Yuen Chan, Opt. Lett. 78
• Not always good to picture light as stream of
  photons
• Lamb, Anti-photon, Appl. Phys. B,95
• For which applications does squeezed LO decrease
  SNR?
• Target detection
• Phase measurement
• Direction-determination with split detector
• Squeezed LO version (Rubin Kaushik,
  quant-ph/071245) of quantum laser pointer,
  Treps et al. PRL 02

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III. Entangled Light

• Theory
• Statistics in two beams are correlated because
  some quantity not property of beam or the other,
  but of both at once
• Example Photon , Mach-Zehnder interferometer
  with single-? source
• 1,00,1?2-1/2 ( 1 ?, lower? 0 ?,
  upper? 0 ?, lower? 1 ?, upper? )
• I.e., a type of Schrodinger cat
  state----photon both above and below
• Generalization NOON state
• N,00,N?2-1/2 ( N ?, lower? 0 ?,
  upper? 0 ?, lower? N ?, upper? )
• Experimental status N4 largest to date

mirror
upper path
5050 beam splitter
5050 beam splitter
lower path
Single- ? source
mirror
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Entangled Light and Laser Radar

• Known
• In absence of loss, NOON-state phase measurement
  precision using N photons improves as 1/N
  (Heisenberg limit)
• Vs 1/?N for classical light (standard quantum
  limit)
• Transmitter, detector easy to describe
  mathematically, hard to construct experimentally
• Mitchell et al., Nature 04 (N3) Walther et
  al., Nature 04 (N4)
• N gt4???
• Target-return beam is part of entangled state
• Unavoidable large loss
• Expectation Loss will degrade NOON precision
  advantage
• Entangled state ? classical statistical mixture
• How severely will loss impact NOON-state
  precision boost?

NOON transmitter
lower path
NOON detector
upper path
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Critical Value for NOON-State Boost

• For loss above critical value L ? .586,
  NOON-state phase-measurement precision inferior
  to use of classical light
• Rules out radar application
• For small loss, L ? 0, NOON states superior by
  factor ?L
• Relevant for laboratory and technological
  applications
• (Rubin Kaushik, Phys Rev A 07)
• Ratio of NOON/classical minimum phase
  measurement as a function of number N of
  entangled photons in NOON state, equal total
  photons

L10-6
L.99
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IV. Summary

• Examined specific laser-radar applications of
  quantum states
• Squeezed light
• Target detection
• Phase measurement
• Direction-determination
• NOON-state entangled light
• Phase measurement
• Found no benefit
• Loss-sensitivity of squeezed and NOON states
  makes application to laser radar difficult
• Loss limits on NOON states must be taken into
  account in non-radar applications
• Quantitative expressions for NOON performance
  impact
• Only these specific applications/techniques have
  been shown not to be useful
• There are lots of states, and lots of
  possibilities remain to be explored