Semiclassical versus Quantum Imaging in Standoff Sensing

1
Semiclassical versus Quantum Imaging in Standoff
Sensing

• Jeffrey H. Shapiro

2
Laser Radar for Standoff Sensing

• 1-100 km target range
• angle-angle, range, and Doppler imaging
• Dominant loss is quasi-Lambertian reflection

3
Semiclassical versus Quantum Imaging

• Semiclassical theory for imaging laser radars
• radar equation for angle-angle imaging
• direct detection versus coherent detection
• Quantum theory for imaging laser radars
• conditions for reduction to the semiclassical
  theory
• prospects for quantum-enhanced imaging
• Type-I versus type-II sensors
• type-I sensors non-classical transmitter states
• type-II sensors non-standard receiver
  configurations
• Imaging with phase-sensitive light
• phase-conjugate optical coherence tomography
• ghost imaging
• Another semiclassical versus quantum comparison
  (poster)
• Single-mode vs. multi-mode vs. continuous-time
  phase sensing

4
Radar Equation for Speckle Targets

• Shot-noise limited signal-to-noise ratio

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Shot-Noise Limited Direct Detection

• Photon-counting configuration
• Semiclassical statistics

6
Balanced Heterodyne Detection

• Receiver configuration
• Semiclassical statistics

7
Angle, Range, and Doppler Resolution

• Diffraction-limited angle resolution
• Bandwidth-limited range resolution
• Dwell-limited Doppler resolution

8
Classical versus Quantum Diffraction

• Huygens-Fresnel principle with extinction
• Quantum version

Yuen Shapiro IEEE Trans Inf Thy 1978
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Quantum Statistics of Direct Detection

• Semiclassical theory for a single mode
• Quantum theory for a single mode

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Quantum Statistics of Heterodyne Detection

• Semiclassical theory
• Quantum theory

Yuen Chan Opt Lett 1983
Yuen Shapiro IEEE Trans Inf Thy 1980
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Semiclassical versus Quantum Imaging

• Semiclassical laser radar theory suffices IF
• transmitter state is classical
• propagation to and from the target is linear
• target interaction is linear
• receiver uses conventional photodetection
  configuration
• Quantum laser radar theory required IF
• any of the preceding four conditions is violated
• Our research assumes
• linear propagation and target interaction
• Two sensor types
• type-I sensors use non-classical transmitter
  states
• type-II sensors use non-standard receiver
  configurations

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GLM Time-of-Flight Ranging A Type-I Sensor

• Use -photon state of distinct modes
• Unentangled-state achieves SQL performance
• Entangled state achieves Heisenberg- limited
  performance

Giovannetti, Lloyd Maccone Nature 2001
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Loss is the Bane of Type-I Sensors

• GLM ranging with photons detected

Shapiro Proc SPIE 2007
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Standoff Sensing in High Loss

• Diffraction-limited spot resolves targets
• free-space transmitter-to-target loss is
  negligible
• Clear weather extinction is not problematic
• 0.5-1.0 dB/km is typical
• Target reflectivity is reasonable
• 10 or more is typical
• Quasi-Lambertian reflection is disastrous
• 100 dB of loss with 10 cm diameter pupil at 10 km
  standoff range
• For GLM ranging example

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Send-One-Detect-All Protocol (SODAP)

• SODAP ranging
• Conventional reception
• SODAP reception
• Average number of detected target-return photons
  

Shapiro Proc SPIE 2007
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Cryptographic Nature of SODAP Ranging

• Eavesdropper knows the SODAP photon emission
  times
• Eavesdropper measures the SODAP photon arrival
  times
• Eavesdroppers range measurement accuracy
• Cryptographic behavior is due to quantum pulse
  compression
• SODAP photon is in a high time-bandwidth state
• SODAP photon is mixed state cannot do classical
  pulse compression
• SODAP photon is part of an -photon entangled
  state
• SODAP system performs quantum pulse compression

Shapiro Proc SPIE 2007
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Issues with SODAP Ranging

• SODAP ranging is a type-I/type-II sensor
• single-photon transmission is a non-classical
  state
• -photon entangled state timing measurement is
  non-standard
• Classical pulse compression is pre-detection
  process
• SODAP pulse compression is post-detection process
• All background-light modes contribute to output
• Background light can severely degrade range
  accuracy

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Imaging with Phase-Sensitive Light

• Phase-Sensitive Light
• Single-mode and two-mode examples
• Quantum Huygens-Fresnel principle coherence
  propagation
• Optical Coherence Tomography
• Conventional versus quantum versus
  phase-conjugate operation
• Is quantum light needed for resolution gain and
  dispersion immunity?
• Ghost Imaging
• Quantum versus thermal versus phase-sensitive
  operation
• What aspects of ghost imaging are truly quantum?
• Concluding Remarks
• Phase-sensitive versus quantum imaging

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Light with Phase-Sensitive Coherence

• Example squeezed states of light

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Zero-Mean Gaussian-State Quantum Fields

• Positive-frequency, photon-units field operator
• Paraxial, -propagating
• Zero-mean Gaussian state completely characterized
  by
• Phase-insensitive correlation function
• Phase-sensitive correlation function
• If
• State is always classical (has proper
  P-representation)
• Laser light, LED light, thermal light
• If
• State may be classical or non-classical
• Squeezed light, classical phase-sensitive light

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Zero-Mean Gaussian-State Quantum Fields

• Spontaneous parametric downconversion with vacuum
  inputs
• Coupled-mode solutions for frequency-domain
  envelopes
• Outputs are in zero-mean jointly Gaussian state
• phase-insensitive auto-correlation,
  phase-sensitive cross-correlation
• low-flux approximation is vacuum plus biphoton
  state

Bogoliubov transformation
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Classical versus Quantum Temporal Coherence

• Single spatial mode, photon-units field
  operators,
• SPDC generates in stationary,
  zero-mean jointly Gaussian state, with non-zero
  correlations
• When ,

Maximum phase-sensitive correlation in quantum
physics
Maximum phase-sensitive correlation in classical
physics
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Quantum Huygens-Fresnel Principle Propagation

• Correlation propagation from to

Huygens-Fresnel principle
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Conventional Optical Coherence Tomography
C-OCT

• Thermal-state light source bandwidth
• Field correlation measured with Michelson
  interferometer (Second-order interference)
• Axial resolution
• Axial resolution degraded by group-velocity
  dispersion

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Quantum Optical Coherence Tomography
Abouraddy et al. PRA (2002)
Q-OCT

• Spontaneous parametric downconverter source
  output in biphoton limit bandwidth
• Intensity correlation measured with
  Hong-Ou-Mandel interferometer (fourth-order
  interference)
• Axial resolution
• Axial resolution immune to even-order dispersion
  terms

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Phase-Conjugate Optical Coherence Tomography
PC-OCT

• Classical light with maximum phase-sensitive
  correlation

Erkmen Shapiro Proc SPIE (2006), PRA (2006)

• Conjugation

, impulse response
quantum noise,
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Comparing C-OCT, Q-OCT and PC-OCT

• Mean signatures of the three imagers

C-OCT
Q-OCT
PC-OCT
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Mean Signatures from a Single Mirror

• Gaussian source power spectrum,
• Broadband conjugator,
• Weakly reflecting mirror,
  with

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Physical Significance of PC-OCT

• Resolution improvement and dispersion immunity in
  Q-OCT and PC-OCT are due to phase-sensitive
  coherence between signal and reference beams
• Entanglement is not the key property yielding the
  benefits
• Q-OCT obtained from an
  actual sample illumination and a virtual sample
  illumination
• PC-OCT obtained via two
  sample illuminations
• PC-OCT combines advantages of C-OCT and Q-OCT
  using classical phase-sensitive light

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Ghost Imaging Setup

• Output contains image of the object
  intensity
• Its a ghost image because
• the bucket detector has no spatial resolution and
• the object is not in the path to the pinhole
  detector

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Quantum versus Classical Ghost Imaging

• Pittman et al. PRA (1995) used SPDC in biphoton
  limit
• with photon-counting bucket and pinhole detectors
• plus coincidence counting electronics
• and obtained an image without background
• interpreted as a quantum phenomenon owing to
  entanglement
• Valencia et al. PRL (2005) and Ferri et al. PRL
  (2005) used pseudothermal light
• with photon counting (Valencia) or a CCD camera
  (Ferri)
• plus coincidence counting (Valencia) or
  correlation (Ferri)
• and obtained an image with background
• showing that entanglement is not necessary for
  ghost imaging

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Ghost Imaging with Gaussian-State Light

• SPDC outputs are in joint Gaussian state
• vacuum plus biphoton is low-flux approximation
• Pseudothermal light is in Gaussian state
• Gaussian mixture of coherent states

• Gaussian-state result for the ghost-image
  correlation

image-bearing terms
background
Erkmen Shapiro quant-ph/0612070 Shapiro
Erkmen ICQI 2007
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Gaussian-State Correlation Functions

• Gaussian Schell-Model Phase-Insensitive
  Auto-Correlation
• Thermal Light
• Phase-insensitive cross-correlation
  phase-insensitive auto-correlation
• No phase-sensitive auto-correlation or
  cross-correlation
• Phase-Sensitive Light
• No phase-insensitive cross-correlation
• No phase-sensitive auto-correlation
• Maximum classical or quantum phase-sensitive
  cross-correlation

photon flux
beam radius
coherence length
coherence time
gtgt
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Gaussian-State Ghost Imaging Comparison

• Near-field operation
• Thermal light
• resolution field-of-view
• Classical, phase-sensitive light
• resolution field-of-view
• Quantum, phase-sensitive light
• resolution field-of-view
• Background term negligible for quantum light
• All images are erect

Erkmen Shapiro quant-ph/0612070 Shapiro
Erkmen ICQI 2007
35
Gaussian-State Ghost Imaging Comparison

• Far-field operation
• Thermal light
• resolution field-of-view
• Classical, phase-sensitive light
• resolution field-of-view
• Quantum, phase-sensitive light
• resolution field-of-view
• Background term negligible for quantum light
• Phase-sensitive images are inverted

Erkmen Shapiro quant-ph/0612070 Shapiro
Erkmen ICQI 2007
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Ghost Imaging Discussion

• Gaussian-state analysis provides uniform
  framework for analyzing many ghost imaging
  configurations
• Ghost image formation is a classical phenomenon
  governed by Huygens-Fresnel principle coherence
  propagation
• When constrained to have same auto-correlation
  functions, the use of biphoton-limit
  non-classical light offers resolution improvement
  in the near field and field-of-view improvement
  in the far field
• Biphoton-limit non-classical light provides a
  contrast advantage over classical light

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Future Research

• Gaussian-state theory of two-photon imaging
• System theory for quantum laser radar

Laboratory experiments by P. Kumar, Northwestern
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Synergy with DARPA Quantum Sensors Program

• Phase-conjugate ranging proof-of-principle
  experiment
• System theory for quantum image enhancement

Laboratory experiments by F.N.C. Wong, MIT
Laboratory experiments by P. Kumar, Northwestern
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Semiclassical versus Quantum Imaging in Standoff
Sensing
Jeffrey H. Shapiro, MIT,e-mail jhs_at_mit.edu
MURI, year started 2005 Program Manager
Peter Reynolds
GAUSSIAN-STATE GHOST IMAGING

• OBJECTIVES
• Gaussian-state theory for quantum imaging
• Distinguish classical from quantum regimes
• New paradigms for improved imaging
• Laser radar system theory
• Use of non-classical light at the transmitter
• Use of non-classical effects at the receiver

• APPROACH
• Establish unified coherence theory for classical
  and non-classical light
• Establish unified imaging theory for classical
  and non-classical Gaussian-state light
• Apply to optical coherence tomography (OCT)
• Apply to ghost imaging
• Seek new imaging configurations
• Propose proof-of-principle experiments

• ACCOMPLISHMENTS
• Derived coherence propagation behavior of
  Gaussian-Schell model phase-sensitive light
• Showed that phase-conjugate OCT may fuse best
  features of C-OCT and Q-OCT
• Unified Gaussian-state analysis of ghost imaging
• Introduced send-one-detect-all protocol for
  cryptographic ranging at the SQL
• Advantages of continuous-time phase sensing