1. Ghost Imaging Sean Crosby Supervisor: Associate Professor Ann Roberts Optics Annual Talks 8 March 2005

2. Outline  Why do I want to do this?  How do I do this?  Induction into the Optics group  How to improve it?  (Helpful) hints for grasshoppers….

3. What brought on the madness?  Einstein and his Posse of Rogues (EPR) thought of entanglement  Entanglement has become experimentally feasible -> no longer just a thought  Entanglement presents us with novel relations between individual photons  Lets use them!

4. 50c explanation of entangled sources  Two photons are created at the same time by destroying one incoming photon  All the photons have some relationship between them  Normally this relationship is conservation of momentum and/or energy Magic Media

5. Properties of entangled sources  The two photons are created at the same time  So we can be assured that if a photon is in one beam, there is another in the other beam -> temporal coherence between the beams  Because of momentum conservation, prediction of position of other photon is possible -> spatial coherence between the beams

6. Hang on Giles…….  This sounds expensive, and you need a lot of equipment to get this working  Magic Media…. Preposterous!  Can’t you do it using stuff the Egyptians could’ve conceived using?

7. In a word, Yes!  Need spatial and temporal coherence between two beams  First things first -> lets create two beams from one  Well, how do we create two beams from one?

8. Splitting the beam….. Beam 1 Beam 2 Thermal Light Source So simply by splitting the beam into two, we have a spatially “entangled” source

9. Surprise!  Even though not concurrently, every photon in one beam “exists” in the other beam  Spatial correlations become greater as intensity increases, because photons in time become “squished together” and “overlap”

10. Where to?  Lets get imaging……..  Source creates them at the same time -> at least we could do is measure them at the same time  Is this coincidental?

11. I sense something spooky….  Imaging in coincidence lets us “multiply” the information in the two beams to obtain an image -> object doesn’t have to be in both beams! Signal Beam Detector Idler Beam Object Detector

12. That’s a little simplistic….  We need to “image” the beam onto the detector Signal Beam Detector Idler Beam Object Detector F 2F

13. A World Exclusive…. Coincidence

14. So what’s happening physically?  Signal beam -> each pixel of the detector will have a single spatial frequency  Idler beam -> near field image of the beam at the conjugate object position  How do we know the multitude of photons hitting the detector are correlated with each other?

15. Coincidink… Image = -

16. I feel a little underwhelmed….  So, how do we make the image clearer, or my favourite, completely wreck it?  Coherence of source!  Increasing the coherence “smears” out the object image

17. Delocating…..  Given the position of one photon, Spatial coherence increases the “uncertainty” in the position of the other photon  Non-zero quantum probability of the photon being anywhere within predicted position +/- coherence length of source  Lose the ability to absolutely predict where the photons are -> decreased correlations

18. On the road to home…  Must quantify this coherence relationship -> My First Paper  I am still not using my $8000 presents….  Image something else  Extend to entanglement?  Quantify how the phase of the object affects the intensity measurement

19. Things I Have Learnt…  Make a regular time with your supervisor  Do write up as you go These talks are much easier to prepare These talks are much easier to prepare Answers to questions you ask yourself naturally flow when writing Answers to questions you ask yourself naturally flow when writing It makes everything link together in your mind -> so much more fun! It makes everything link together in your mind -> so much more fun!

21. What is entanglement?  A non-separability of the multi-particle wavefunction for 1 or more observables In the two entangled object case, if we measure one property (energy, momentum, polarisation) of one of the entangled objects, we can predict the SAME property of the other entangled object with absolute certainty In the two entangled object case, if we measure one property (energy, momentum, polarisation) of one of the entangled objects, we can predict the SAME property of the other entangled object with absolute certainty

22. How is it experimentally prepared?  Entanglement is analogous to conservation of an observable  If 1 photon “decays” into 2 photons, energy & momentum of the system must be conserved  If we know the energy of the initial photon, and one of the others, we know the energy of the final photon with absolute certainty  Entangled!

23. How is it experimentally prepared?  Perturbation to the ground state Hamiltonian by the 3-photon non-linear term is proportional to Χ (2) and for the 4- photon term Χ (3)  Media with high Χ (2) or Χ (3) can produce entangled photons

24. How is it experimentally prepared? Laser SignalIdler Χ(3) High Χ(3) media Signal Idler Laser Χ(2) media High Χ(2) media Typical media is Barium Borate or Lithium Niobate Typical media is Lithium Niobate, doped fibres, and Rb vapour

25. Properties of entangled beams  Every pair of entangled photons are created at different times & positions in the media, therefore each individual beam is non-coherent  Because both photons in a pair are created at the same time and transverse momentum entanglement/conservation - exhibits high inter- beam coherence Signal Idler

26. Properties of entangled beams  As incoming laser becomes spatially smaller, spatial entanglement is lost The two photons are entangled with the incoming photon The two photons are entangled with the incoming photon Small laser size – infinite spatial frequency spectrum Small laser size – infinite spatial frequency spectrum Can’t predict third photon’s spatial frequency Can’t predict third photon’s spatial frequency Unentangled! Unentangled! u=u i u=u 1 u=-(u1+ui)

27. How can it be used for imaging?  Want to use the higher order coherence properties of source  We want to use both beams for the measurement  We want to measure amplitude & phase of object Detector Object

28. How can it be used for imaging?  Ghost-imaging Signal Beam Detector Non-linear Media Idler Beam Laser Object Detector Intensity = Coincidence counts between detectors = Transmission function of object Spengler

29. Surprise!  We are only using spatial “entanglement” Signal Idler We can create a classical, spatially “entangled” source

30. Differences between the two  Quantum entanglement exists in both momentum and position – near field and far field. Correlations exist only in near field or far field.  Visibility of object information is increased in Quantum scheme

31. New directions?  Phase imaging Hanbury-Brown/Twiss scheme cannot measure phase of object Hanbury-Brown/Twiss scheme cannot measure phase of object Can we reconstruct phase using ghost imaging? Can we reconstruct phase using ghost imaging? Detector

32. New directions?  Degree of spatial entanglement  Can we use the higher order coherence for funky things?

33. Conclusion  Ghost imaging is a system that uses higher order coherence to image objects  It is not restricted exclusively to entangled light sources, but entanglement increases quality of image

34. Sources of entanglement  Four wave mixing 2 beams into media with high 3 rd order non linearity Χ (3) produces 2 entangled beams out 2 beams into media with high 3 rd order non linearity Χ (3) produces 2 entangled beams out Performed in a Rb vapour cell Performed in a Rb vapour cell  Spontaneous parametric down conversion 1 beam into media with high 2 nd order non linearity Χ (2) produces 2 entangled beams out 1 beam into media with high 2 nd order non linearity Χ (2) produces 2 entangled beams out Performed in a birefringent crystalPerformed in a birefringent crystal Two beams commonly called SIGNAL and IDLERTwo beams commonly called SIGNAL and IDLER 1 in 10 6 photons undergo this process1 in 10 6 photons undergo this process Conservation of energy and momentumConservation of energy and momentum

35. Spontaneous Parametric Down Conversion  Generates photons that have no spatial or temporal coherence in each individual beam We can’t use an individual beam to obtain object information – non coherent We can’t use an individual beam to obtain object information – non coherent  But it does have high 4 th order coherence  Intensity CORRELATIONS!

36. Imaging objects with detectors that have “no” spatial resolution “Bucket” detector – no spatial resolution Light Outputs photon number, but not position We can image this object using ghost-imaging Marginal Intensity: Object

37. Simulations 0.1 mm Pump size Coincidence Count Rate Idler Detector Position

38. Entanglement  So as entanglement increases (because pump size is increasing), fringe visibility in interference experiments also increases This is one way in the literature that they define “Degree of entanglement”

39. Phase Imaging  Imaging of phase objects has been attempted – no retrieval attempted  Can we retrieve the phase? Classical optics Intensity Classical optics Intensity Ghost-imaging Intensity Ghost-imaging Intensity If we assume that, then the two equations become “equal”. T.I.E

40. Results Retrieved Phase