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Shashi Shashi

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Prabhakar S Gangi Reddy A Aadhi Ashok Kumar Chithrabhanu P G K Samanta and R P Singh Physical Research Laboratory Ahmedabad 380 009 Feb 27 2014 IPQI 2014 ID: 439741

oam singh beam angular singh oam angular beam momentum spdc light pump polarization orbital entanglement vortex optical violation inequality

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Slide1

Shashi Prabhakar, S. Gangi Reddy, A. Aadhi, Ashok Kumar, Chithrabhanu P., G. K. Samanta and R. P. SinghPhysical Research Laboratory,Ahmedabad. 380 009.Feb 27, 2014IPQI 2014

Orbital angular momentum of light: Applications in quantum information

1

R. P. SinghSlide2

WhirlpoolsTornadoesSlide3

Outline of the talkHow light acquires orbital angular momentum (OAM)Experimental techniques to produce light with OAMSpontaneous Parametric Down-Conversion (SPDC)WhyWhatHowExperiments and resultsHyper and hybrid entanglementApplications – recent experimentsFuture planConclusion

3

R. P. SinghSlide4

Poynting showed classically for a beam of circularly polarized lightSpin Angular Momentum4 R. P. SinghAngular momentum

Polarized: per photon

Beth

Phys. Rev. 50, 115, 1936Slide5

Can a light beam possess orbital angular momentum?What would it mean?L = r x pDoes each photon in the beam have the same orbital angular momentum?Is the orbital angular momentum an integral number of ?5 R. P. SinghOrbital Angular MomentumSlide6

For a field amplitude distribution whereL. Allen, M. W. Beijersbergen, R. J. C. Spreeuw and J. P. WoerdmanPhys. Rev. 45, 8185, 19926 R. P. Singh

Orbital Angular Momentum contd…Slide7

7 R. P. SinghDifference in SAM and OAMSlide8

Intensity and phase plot of a beam carrying OAMHelical WavefrontEach photon carries anOrbital Angular Momentumof lħ, l order of vortex, can be any integer2π4πTopological charge

8

R. P. Singh

Optical Vortex

6

πSlide9

Optical vortices are generated as natural structures when light passes through a rough surface or due to phase modification while propagating through a medium.Controlled generationComputer generated hologram (CGH)Spiral phase plateAstigmatic mode converterLiquid crystal (Spatial light modulator)9 R. P. SinghGeneration of Vortices in lightSlide10

He-Ne Laser10 R. P. Singh

Generation using CGHSlide11

He-Ne Laser

B1

M1

M2

B2

A

CGH

L

Screen

CCD

11

R. P. Singh

Finding vortex order with InterferometrySlide12

The number of rings present in the Fourier transform of intensity The number dark lobes present at the focus of a tilted lens Opt. Lett. 36, 4398-4400 (2011)  Phys. Lett. A 377, 1154-1156 (2013) m=1 m=2m=2 m=3Finding order, other than Interferometry

12

R. P. SinghSlide13

EntanglementWhile generation of entangled particlesTotal energy is conservedTotal (spin/orbital/linear) momentum is conservedAnnihilation happensGenerated simultaneously from the sourcePreserve non-classical correlation with propagation13 R. P. SinghSlide14

Entanglement contd…Variables that can be chosen for entanglement Polarization Spin Orbital angular momentum Position and momentumAmong these, polarization is the one which can be easily handled and manipulated in the lab using λ/2, λ/4 plates and polarizing beam-splitters.The most common method to generate entangled photons in lab is Spontaneous parametric down conversion (SPDC).14 R. P. SinghSlide15

Spontaneous parametric down conversionEnergy Conservationp: Pump beams: Signal beam (High ω)i: Idler beam (Low ω)Phase-matching condition

Phy. Rev. A

31

, 2409 (1985)

15

R. P. SinghSlide16

Phase matching (Birefringence)birefringence Δn = ne – no16 R. P. SinghIncident lighte-ray(polarized)o-ray(polarized)

Optics axisSlide17

Type-I SPDCλ2λBBO crystal2λ

|H>|V>

|H>

e  o + o type interaction

Produces single cone

The two output photons (signal and idler) generated will be non-collinear

Collimated pump Strongly focused pump

Phy. Rev. A

83

, 033837 (2011)

17

R. P. SinghSlide18

Type-II SPDCλ2λBBO crystal2λ

|V>|V>

|H>

e  o + e type interaction

Produces double cone

The two output photons (signal and idler) generated can be both non-collinear and collinear

Phy. Rev. A

68

, 013804 (2003)

18

R. P. Singh

e-ray

o-ray

pump

e-ray

o-raySlide19

Specification of components usedBBO CrystalSize: 8×4×5 mm3θ = 26˚ (cut for 532 nm)Cut for type-1 SPDCOptical transparency: ~190–3300 nmne = 1.5534, no = 1.6776Diode LaserWavelength: 405 nm

Output Power: 50 mWInterference filter

Wavelength range 810±5 nm

19

R. P. SinghSlide20

20 R. P. SinghFirst OAM entanglement experimentMair et al., Nature, 2001 Polarization entanglement :Slide21

Mair et al., Nature 200121 R. P. SinghFirst OAM entanglement experiment contd…Slide22

22 R. P. SinghQuantum Entanglement of High Angular MomentaRobert Fickler, Radek Lapkiewicz, William N. Plick, Mario Krenn, Christoph Schaeff, Sven Ramelow, Anton Zeilinger, Science 338, 640-643 (2012).Slide23

23 R. P. SinghQuantum Entanglement of High Angular Momenta contdMeasured coincidence counts as a function of the angle of one mask and different angles of the other mask. Slide24

Related works at PRLSpatial distribution of down-converted photons byGaussian pump beamOptical vortex pump beamBell inequality violation for light with OAMOAM qubit generation 24 R. P. SinghSlide25

Generating correlated photon pairs25 R. P. SinghSlide26

Generating correlated photonsGenerating correlated photonsBlue Laser405 nm & 50 mW

Lensf = 5 cm

BBOcrystal

IF

EMCCD

λ

/2

plate

Angle(

λ

/2

) = 45

˚

and 0

˚ Background subtracted

IF: Interference filter 81

0

±5

n

m

EMCCD: Electron Multiplying CCD

26

R. P. SinghSlide27

Observing SPDC at varying pump intensity 3mW 5mW 8mWWidth of the SPDC ring is independent of the intensity of the light beam. 50 100 150Width of the SPDC ring is independent of number of accumulations taken by EMCCD camera.

27 R. P. SinghSlide28

SPDC with Gaussian pump beam1.0 mm1.0 mm28 R. P. SinghSlide29

SPDC with Gaussian pump beam (theory)1.0 mm1.0 mm29 R. P. SinghSlide30

SPDC with gaussian pump beam30 R. P. SinghSlide31

SPDC with optical vortex beam31 R. P. SinghS. Prabhakar et al., Optics CommunicationsSlide32

SPDC with optical vortex pump beam1.0 mm1.0 mmOrder of vortex m=1 m=3 m=532 R. P. SinghSlide33

SPDC with optical vortex pump beam33 R. P. SinghSlide34

Orbital angular momentum conservation: mp = ms + miOur approach: 34 R. P. SinghMulti-photon, multi- dimensional

entanglement can be achieved using OPOSlide35

R. P. Singh35Classical EntanglementThe Bell-CHSH inequalityFor continuous variables, Wigner Distribution Function can be used instead of E(a, b)Here, (X, PX) and (Y, PY) are conjugate pairs of dimensionless quadraturesP. Chowdhury et al. Phys. Rev. A 88, 013803 (2013).Violation

of Bell’s inequality for light beams with OAMSlide36

36Classical Bell’s Violation for Optical Vortex beamsWigner Distribution Function (WDF) can be defined asIn other words, WDF is the Fourier Transform of TPCF. Experimentally, TPCF can be determined by using Shearing-Sagnac Interferometry.n (azimuthal) and m (radial) are the two indices in the electric field for LG beams with OAM.

R. P. SinghViolation of Bell’s inequality contd…Slide37

R. P. Singh37Experimental setup for determining TPCFViolation of Bell’s inequality ExperimentSlide38

R. P. Singh38Variation of non-locality with order of vortex (n)Magnitude of violation of Bell inequality increases with the increase in the order of vortexViolation of Bell inequality contd…Slide39

39ResultsOrder (n)Theoretical (|Bmax|)Experimental (|Bmax|)022.01350 ± 0.0126912.172.18460 ± 0.0593322.242.26326 ± 0.08063Violation of Bell’s inequality contd…R. P. Singhm=0, n=1, X1 = 0; PX1 = 0; X2 = X; PX2 = 0; Y1 =0; PY1 = 0; Y2 = 0; PY2 = PY ,xPYSlide40

All the OAM Qubits on the Poincare sphere can be realized by projecting the non separable state of polarization and OAM into different polarization basis.Non separable polarization – OAM state This state can be generated from Q-plate or modified Sagnac interferometer with vortex lens. Polarization Poincare sphere OAM Poincare sphereR. P. Singh

Generation of OAM

qubits

40Slide41

OAM qubitOV lens

λ

/2

PBS

State Preparation

λ

/2 (

α

)

λ

/4 (

β

)

PBS

Projective measurements in polarization basis

Horizontal

polarization will acquire OAM of +2 Vertical polarization will get OAM of -2.

HWP (

λ

/2(

α

)) and QWP (

λ

/2(

β

)) with PBS will project the state in to different polarization basis.

Each combination of HWP and QWP will generate corresponding points on

the

P

oincare sphere of OAM.

Generation of non separable state

H

V

R. P. Singh

41Slide42

α=0 ̊ α= 22.5 ̊ α=45 ̊ α=67.5 ̊ α=90 ̊ α=112.5 ̊ α=135 ̊ α=157.5 ̊ α=45 ̊ β=0 ̊ β = 0 ̊ β =0 ̊ β =0 ̊ β =0 ̊ β =0 ̊ β =0 ̊ β=0 ̊ β =90 ̊

Experimental resultsSlide43

Conclusion and future outlookOptical Vortices and orbital angular momentum of lightSpontaneous Parametric Down-conversion can be used to generate entangled photons in different degrees of freedomSpatial distribution of SPDC ring with higher order optical vorticesProposal to generate multi-photon, multi- dimensional entanglementBell inequality violation for light beams with OAMOAM qubit generation with non separable OAM-polarization state Using hybrid entanglement for quantum teleportation and quantum key distribution43 R. P. SinghSlide44

Thank you!44 R. P. SinghSlide45

OAM entanglementFuture planl = -2 -1 +1 +2The rotation in phase provides orbital angular momentum of lћ to the photons.Rotation of phase front as the beam propagates45 R. P. SinghSlide46

Generating correlated photon pairsBlue Laser405 nm & 50 mW

Lensf = 5 cmBBOcrystalIF

EMCCD

λ

/2

plate

IF: Interference filter 810

±5

nm

EMCCD: Electron Multiplying CCD

46

R. P. SinghSlide47

SPDC with gaussian pump beam47 R. P. SinghSlide48

Generating optical vorticesComputer generated holography technique for the generation of optical vortices.48 R. P. Singh

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