1. October 1, 2007 Semiclassical versus Quantum Imaging in Standoff Sensing Jeffrey H. Shapiro

2. 2 Laser Radar for Standoff Sensing  1-100 km target range  angle-angle, range, and Doppler imaging  Dominant loss is quasi-Lambertian reflection

3. 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. 4 Radar Equation for Speckle Targets  Shot-noise limited signal-to-noise ratio

5. 5 Shot-Noise Limited Direct Detection  Photon-counting configuration  Semiclassical statistics

6. 6 Balanced Heterodyne Detection  Receiver configuration  Semiclassical statistics

7. 7 Angle, Range, and Doppler Resolution  Diffraction-limited angle resolution  Bandwidth-limited range resolution  Dwell-limited Doppler resolution

8. 8 Classical versus Quantum Diffraction  Huygens-Fresnel principle with extinction  Quantum version Yuen & Shapiro IEEE Trans Inf Thy 1978

9. 9 Quantum Statistics of Direct Detection  Semiclassical theory for a single mode  Quantum theory for a single mode

10. 10 Quantum Statistics of Heterodyne Detection  Semiclassical theory:  Quantum theory: Yuen & Shapiro IEEE Trans Inf Thy 1980 Yuen & Chan Opt Lett 1983

11. 11 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

12. 12 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  GLM xmtr target  GLM rcvr target Giovannetti, Lloyd & Maccone Nature 2001

13. 13 Loss is the Bane of Type-I Sensors  GLM ranging with photons detected Shapiro Proc SPIE 2007

14. 14 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 

15. 15 Send-One-Detect-All Protocol (SODAP)  SODAP ranging:  Conventional reception:  SODAP reception:  Average number of detected target-return photons: SODAP rcvr target SODAP xmtr  target Shapiro Proc SPIE 2007

16. 16 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

17. 17  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 Issues with SODAP Ranging matched filter envelope detector chirped pulse compressed output uncompressed output

18. 18 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

19. 19 Light with Phase-Sensitive Coherence  Example: squeezed states of light Amplitude-squeezedNo squeezingPhase-squeezed

20. 20  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 Zero-Mean Gaussian-State Quantum Fields

21. 21 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 pump signal idler Bogoliubov transformation

22. 22 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

23. 23 Quantum Huygens-Fresnel Principle Propagation  Correlation propagation from to Huygens-Fresnel principle

24. 24  Thermal-state light source: bandwidth  Field correlation measured with Michelson interferometer (Second-order interference)  Axial resolution  Axial resolution degraded by group-velocity dispersion Conventional Optical Coherence Tomography C-OCT

25. 25 Quantum Optical Coherence Tomography  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 Q-OCT Abouraddy et al. PRA (2002)

26. 26  Conjugation: Phase-Conjugate Optical Coherence Tomography PC-OCT  Classical light with maximum phase-sensitive correlation Erkmen & Shapiro Proc SPIE (2006), PRA (2006) quantum noise,, impulse response

27. 27 Comparing C-OCT, Q-OCT and PC-OCT  Mean signatures of the three imagers: C-OCT: Q-OCT: PC-OCT:

28. 28  Gaussian source power spectrum,  Broadband conjugator,  Weakly reflecting mirror, with Mean Signatures from a Single Mirror

29. 29 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

30. 30 Ghost Imaging Setup  Output contains image of the object intensity  It’s a ghost image because…  the bucket detector has no spatial resolution and  the object is not in the path to the pinhole detector

31. 31 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

32. 32 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

33. 33 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 >>

34. 34 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. 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

36. 36 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

37. 37 Future Research  Gaussian-state theory of two-photon imaging  System theory for quantum laser radar Laboratory experiments by P. Kumar, Northwestern Type-II SPDC correlator object PBS image

38. 38 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

39. 39 Semiclassical versus Quantum Imaging in Standoff Sensing Jeffrey H. Shapiro, MIT,e-mail: jhs@mit.edu MURI, year started 2005 Program Manager: Peter Reynolds 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 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 GAUSSIAN-STATE GHOST IMAGING