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

Ghost ImagingGhost Imaging

Sean CrosbySean CrosbySupervisor: Associate Professor Ann RobertsSupervisor: Associate Professor Ann Roberts

Optics Annual TalksOptics Annual Talks8 March 20058 March 2005

OutlineOutline

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

What brought on the madness?What brought on the madness?

Einstein and his Posse of Rogues (EPR) Einstein and his Posse of Rogues (EPR) thought of entanglementthought of entanglement

Entanglement has become experimentally Entanglement has become experimentally feasible -> no longer just a thoughtfeasible -> no longer just a thought

Entanglement presents us with novel Entanglement presents us with novel relations between individual photonsrelations between individual photons

Lets use them!Lets use them!

50c explanation of entangled 50c explanation of entangled sourcessources

Two photons are created at the same time by Two photons are created at the same time by destroying one incoming photondestroying one incoming photon

All the photons have some relationship between All the photons have some relationship between themthem

Normally this relationship is conservation of Normally this relationship is conservation of momentum and/or energymomentum and/or energy

Magic Media

Properties of entangled sourcesProperties of entangled sources

The two photons are created at the same timeThe two photons are created at the same time So we can be assured that if a photon is in one So we can be assured that if a photon is in one

beam, there is another in the other beam -> beam, there is another in the other beam -> temporal coherence temporal coherence between between the beamsthe beams

Because of momentum conservation, prediction Because of momentum conservation, prediction of position of other photon is possible -> spatial of position of other photon is possible -> spatial coherence coherence betweenbetween the beams the beams

Hang on Giles…….Hang on Giles…….

This sounds expensive, and you need a lot This sounds expensive, and you need a lot of equipment to get this working of equipment to get this working

Magic Media…. Preposterous!Magic Media…. Preposterous! Can’t you do it using stuff the Egyptians Can’t you do it using stuff the Egyptians

could’ve conceived using?could’ve conceived using?

In a word, Yes!In a word, Yes!

Need spatial and temporal coherence between Need spatial and temporal coherence between two beamstwo beams

First things first -> lets create two beams from First things first -> lets create two beams from oneone

Well, how do we create two beams from one?Well, how do we create two beams from one?

Splitting the beam…..Splitting the beam…..

Beam 1

Beam 2

ThermalLight Source

So simply by splitting the beam into two, we have a spatially “entangled” source

Surprise!Surprise!

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

Where to?Where to?

Lets get imaging……..Lets get imaging…….. Source creates them at the same time -> Source creates them at the same time ->

at least we could do is measure them at at least we could do is measure them at the same timethe same time

Is this coincidental?Is this coincidental?

I sense something spooky….I sense something spooky…. Imaging in coincidence lets us “multiply” Imaging in coincidence lets us “multiply”

the information in the two beams to obtain the information in the two beams to obtain an image -> object doesn’t have to be in an image -> object doesn’t have to be in both beams!both beams!

Signal Beam

DetectorIdler Beam

Object

Detector

That’s a little simplistic….That’s a little simplistic….

We need to “image” the beam onto the We need to “image” the beam onto the detectordetector

Signal Beam

DetectorIdler Beam

Object

Detector

F

2F2F

A World Exclusive….A World Exclusive….

Coincidence

So what’s happening physically?So what’s happening physically?

Signal beam -> each pixel of the detector Signal beam -> each pixel of the detector will have a single spatial frequencywill have a single spatial frequency

Idler beam -> near field image of the beam Idler beam -> near field image of the beam at the conjugate object positionat the conjugate object position

How do we know the multitude of photons How do we know the multitude of photons hitting the detector are correlated with hitting the detector are correlated with each other?each other?

Coincidink…Coincidink…

Image = <I1I2>-<I1><I2>

I feel a little underwhelmed….I feel a little underwhelmed….

So, how do we make the image clearer, or So, how do we make the image clearer, or my favourite, completely wreck it?my favourite, completely wreck it?

Coherence of source!Coherence of source! Increasing the coherence “smears” out the Increasing the coherence “smears” out the

object imageobject image

Delocating…..Delocating…..

Given the position of one photon, Spatial Given the position of one photon, Spatial coherence increases the “uncertainty” in coherence increases the “uncertainty” in the position of the other photonthe position of the other photon

Non-zero quantum probability of the Non-zero quantum probability of the photon being anywhere within predicted photon being anywhere within predicted position +/- coherence length of sourceposition +/- coherence length of source

Lose the ability to absolutely predict where Lose the ability to absolutely predict where the photons are -> decreased correlationsthe photons are -> decreased correlations

On the road to home…On the road to home…

Must quantify this coherence relationship Must quantify this coherence relationship -> My First Paper-> My First Paper

I am still not using my $8000 presents….I am still not using my $8000 presents…. Image something elseImage something else Extend to entanglement?Extend to entanglement? Quantify how the phase of the object Quantify how the phase of the object

affects the intensity measurementaffects the intensity measurement

Things I Have Learnt…Things I Have Learnt…

Make a regular time with your supervisorMake a regular time with your supervisor Do write up as you go Do write up as you go

These talks are much easier to prepareThese talks are much easier to prepare Answers to questions you ask yourself Answers to questions you ask yourself

naturally flow when writingnaturally flow when writing It makes everything link together in your mind It makes everything link together in your mind

-> so much more fun!-> so much more fun!

What is entanglement?What is entanglement?

A non-separability of the multi-particle wavefunction for A non-separability of the multi-particle wavefunction for 1 or more observables1 or more observables

In the two entangled object case, if we measure one In the two entangled object case, if we measure one property (energy, momentum, polarisation) of one of property (energy, momentum, polarisation) of one of the entangled objects, we can predict the SAME the entangled objects, we can predict the SAME property of the other entangled object with absolute property of the other entangled object with absolute certaintycertainty

)(),...,,( 21 nnn xxxx

How is it experimentally prepared?How is it experimentally prepared?

Entanglement is analogous to Entanglement is analogous to conservation of an observableconservation of an observable

If 1 photon “decays” into 2 photons, If 1 photon “decays” into 2 photons, energy & momentum of the system must energy & momentum of the system must be conservedbe conserved

If we know the energy of the initial photon, If we know the energy of the initial photon, and one of the others, we know the energy and one of the others, we know the energy of the final photon with absolute certaintyof the final photon with absolute certainty

Entangled!Entangled!

How is it experimentally prepared?How is it experimentally prepared?

Perturbation to the ground state Perturbation to the ground state Hamiltonian by the 3-photon non-linear Hamiltonian by the 3-photon non-linear term is proportional to term is proportional to ΧΧ(2)(2) and for the 4- and for the 4-photon term photon term ΧΧ(3)(3)

Media with high Media with high ΧΧ(2)(2) or or ΧΧ(3)(3) can produce can produce entangled photons entangled photons

How is it experimentally prepared?How is it experimentally prepared?

Laser Laser

Signal Idler

High ΧΧ(3)(3) media

Signal

Idler

Laser

High ΧΧ(2) media(2) media

Typical mediais Barium Borateor Lithium Niobate

Typical media is Lithium Niobate, doped fibres, and Rb vapour

Properties of entangled beamsProperties of entangled beams

Every pair of entangled photons are created at Every pair of entangled photons are created at different times & positions in the media, different times & positions in the media, therefore each individual beam is non-coherenttherefore each individual beam is non-coherent

Because both photons in a pair are created at Because both photons in a pair are created at the same time and transverse momentum the same time and transverse momentum entanglement/conservation - exhibits high inter-entanglement/conservation - exhibits high inter-beam coherencebeam coherence

Signal

Idler

Properties of entangled beamsProperties of entangled beams

As incoming laser becomes spatially As incoming laser becomes spatially smaller, spatial entanglement is lostsmaller, spatial entanglement is lost The two photons are entangled with the The two photons are entangled with the

incoming photonincoming photon Small laser size – infinite spatial frequency Small laser size – infinite spatial frequency

spectrumspectrum Can’t predict third photon’s spatial frequencyCan’t predict third photon’s spatial frequency Unentangled!Unentangled!

u=ui

u=u1

u=-(u1+ui)

How can it be used for imaging?How can it be used for imaging?

Want to use the higher order coherence Want to use the higher order coherence properties of sourceproperties of source

We want to use both beams for the We want to use both beams for the measurementmeasurement

We want to measure amplitude & phase of We want to measure amplitude & phase of objectobject

Detector

Detector

Object

How can it be used for imaging?How can it be used for imaging? Ghost-imagingGhost-imaging

Signal Beam

Detector

Non-linear Media

Idler Beam

Laser

Object

Detector

Intensity = Coincidence counts between detectors = Transmission function of object

Spengler

Surprise!Surprise! We are only using spatial “entanglement” We are only using spatial “entanglement”

Signal

Idler

We can create a classical, spatially “entangled” source

Differences between the twoDifferences between the two

Quantum entanglement exists in both Quantum entanglement exists in both momentum and position – near field and momentum and position – near field and far field. Correlations exist only in near far field. Correlations exist only in near field or far field.field or far field.

Visibility of object information is increased Visibility of object information is increased in Quantum schemein Quantum scheme

New directions?New directions?

Phase imagingPhase imaging Hanbury-Brown/Twiss Hanbury-Brown/Twiss

scheme cannot scheme cannot measure phase of measure phase of objectobject

Can we reconstruct Can we reconstruct phase using ghost phase using ghost imaging?imaging?

Detector

Detector

New directions?New directions?

Degree of spatial entanglementDegree of spatial entanglement Can we use the higher order coherence Can we use the higher order coherence

for funky things?for funky things?

ConclusionConclusion

Ghost imaging is a system that uses Ghost imaging is a system that uses higher order coherence to image objectshigher order coherence to image objects

It is not restricted exclusively to entangled It is not restricted exclusively to entangled light sources, but entanglement increases light sources, but entanglement increases quality of imagequality of image

Sources of entanglementSources of entanglement

Four wave mixingFour wave mixing 2 beams into media with high 32 beams into media with high 3rdrd order non linearity order non linearity

ΧΧ(3)(3) produces 2 entangled beams out produces 2 entangled beams out Performed in a Rb vapour cellPerformed in a Rb vapour cell

Spontaneous parametric down conversionSpontaneous parametric down conversion 1 beam into media with high 21 beam into media with high 2ndnd order non linearity order non linearity

ΧΧ(2)(2) produces 2 entangled beams out 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 101 in 1066 photons undergo this process photons undergo this process• Conservation of energy and momentumConservation of energy and momentum

Spontaneous Parametric Down Spontaneous Parametric Down ConversionConversion

Generates photons that have no spatial or Generates photons that have no spatial or temporal coherence in each individual temporal coherence in each individual beambeam We can’t use an individual beam to obtain We can’t use an individual beam to obtain

object information – non coherentobject information – non coherent But it does have high 4But it does have high 4thth order coherence order coherence Intensity CORRELATIONS!Intensity CORRELATIONS!

Imaging objects with detectors that Imaging objects with detectors that have “no” spatial resolutionhave “no” spatial resolution

“Bucket” detector – no spatial resolution

Light

Outputs photon number, but not position

We can image this object using ghost-imagingMarginal Intensity:

Object

121)2(

2 ),()( dxxxGxI

SimulationsSimulations0.1 mm Pump size

Co

inci

den

ce C

ou

nt

Rat

e

Idler Detector Position

EntanglementEntanglement

So as entanglement increases (because So as entanglement increases (because pump size is increasing), fringe visibility in pump size is increasing), fringe visibility in interference experiments also increasesinterference experiments also increases

This is one way in the literature that they This is one way in the literature that they define “Degree of entanglement”define “Degree of entanglement”

Phase ImagingPhase Imaging

Imaging of phase objects has been attempted – no Imaging of phase objects has been attempted – no retrieval attemptedretrieval attempted

Can we retrieve the phase?Can we retrieve the phase? Classical optics IntensityClassical optics Intensity

Ghost-imaging IntensityGhost-imaging Intensity

If we assume that , then the two equations If we assume that , then the two equations become “equal”.become “equal”.

dxesiu

xtsiu

xtuIxsi

s

ui

sisi

sis

)(2

1111*

~ 112))(

2())(

2()(

211 )( ssi ssi T.I.E

ResultsResults

Ret

riev

ed

Ph

ase