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Shashi Prabhakar , S. Gangi Reddy, A. Aadhi , Ashok Kumar, Chithrabhanu P.,

Orbital angular momentum of light: Applications in quantum information. Shashi 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. Whirlpools. Tornadoes.

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Shashi Prabhakar , S. Gangi Reddy, A. Aadhi , Ashok Kumar, Chithrabhanu P.,

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  1. R. P. Singh Orbital angular momentum of light: Applications in quantum information • ShashiPrabhakar, 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

  2. Whirlpools Tornadoes

  3. Outline of the talk How light acquires orbital angular momentum (OAM) Experimental techniques to produce light with OAM Spontaneous Parametric Down-Conversion (SPDC) Why What How Experiments and results Hyper and hybrid entanglement Applications – recent experiments Future plan Conclusion R. P. Singh 3

  4. Spin Angular Momentum Poyntingshowed classically for a beam of circularly polarized light Angular momentum per photon Polarized: Beth Phys. Rev. 50, 115, 1936 R. P. Singh 4

  5. Orbital Angular Momentum Can a light beam possess orbital angular momentum? What would it mean? L = rxp Does each photon in the beam have the same orbital angular momentum? Is the orbital angular momentum an integral number of ? R. P. Singh 5

  6. Orbital Angular Momentum contd… For a field amplitude distribution where L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw and J. P. Woerdman Phys. Rev. 45, 8185, 1992 R. P. Singh 6

  7. Difference in SAM and OAM R. P. Singh 7

  8. Optical Vortex Intensity and phase plot of a beam carrying OAM Helical Wavefront 2π 4π 6π Each photon carries an Orbital Angular Momentum oflħ, l order of vortex, can be any integer Topological charge R. P. Singh 8

  9. Generation of Vortices in light 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 generation • Computer generated hologram (CGH) • Spiral phase plate • Astigmatic mode converter • Liquid crystal (Spatial light modulator) R. P. Singh 9

  10. Generation using CGH He-Ne Laser R. P. Singh 10

  11. M1 M2 CCD CGH A L B1 B2 He-Ne Laser Screen Finding vortex order with Interferometry R. P. Singh 11

  12. Finding order, other than Interferometry • The number of rings present in the Fourier transform of intensity m=1 m=2 • The number dark lobes present at the focus of a tilted lens m=2 m=3 Opt. Lett. 36, 4398-4400 (2011)  Phys. Lett. A 377, 1154-1156 (2013)  R. P. Singh 12

  13. R. P. Singh Entanglement While generation of entangled particles • Total energy is conserved • Total (spin/orbital/linear) momentum is conserved • Annihilation happens • Generated simultaneously from the source • Preserve non-classical correlation with propagation

  14. R. P. Singh Entanglement contd… Variables that can be chosen for entanglement • Polarization • Spin • Orbital angular momentum • Position and momentum • Among 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).

  15. R. P. Singh Spontaneous parametric down conversion p: Pump beam s: Signal beam (High ω) i: Idler beam (Low ω) Phase-matching condition Energy Conservation Phy. Rev. A 31, 2409 (1985)

  16. R. P. Singh Phase matching (Birefringence) Optics axis e-ray (polarized) Incident light o-ray (polarized) birefringence Δn = ne – no

  17. R. P. Singh |H> 2λ λ |V> |H> 2λ BBO crystal Collimated pump Strongly focused pump Type-I SPDC • e  o + o type interaction • Produces single cone • The two output photons (signal and idler) generated will be non-collinear Phy. Rev. A 83, 033837 (2011)

  18. R. P. Singh |V> 2λ λ |V> |H> 2λ BBO crystal Type-II SPDC • e  o + e type interaction • Produces double cone • The two output photons (signal and idler) generated can be both non-collinear and collinear e-ray e-ray pump o-ray o-ray Phy. Rev. A 68, 013804 (2003)

  19. R. P. Singh Specification of components used BBO Crystal • Size: 8×4×5 mm3 • θ = 26˚ (cut for 532 nm) • Cut for type-1 SPDC • Optical transparency: ~190–3300 nm • ne = 1.5534, no = 1.6776 Diode Laser • Wavelength: 405 nm • Output Power: 50 mW Interference filter • Wavelength range 810±5 nm

  20. First OAM entanglement experiment Mair et al., Nature, 2001 Polarization entanglement : R. P. Singh 20

  21. First OAM entanglement experiment contd… Mair et al., Nature 2001 R. P. Singh 21

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

  23. Quantum Entanglement of High Angular Momenta contd Measured coincidence counts as a function of the angle of one mask and different angles of the other mask. R. P. Singh 23

  24. R. P. Singh Related works at PRL • Spatial distribution of down-converted photons by • Gaussian pump beam • Optical vortex pump beam • Bell inequality violation for light with OAM • OAM qubit generation

  25. R. P. Singh Generating correlated photon pairs

  26. R. P. Singh Lens f = 5 cm λ/2 plate Blue Laser EMCCD 405 nm & 50 mW BBO crystal IF Angle(λ/2) = 45˚ and 0˚ Background subtracted Generating correlated photons IF: Interference filter 810±5 nm EMCCD: Electron Multiplying CCD Generating correlated photons

  27. R. P. Singh Observing SPDC at varying pump intensity Width of the SPDC ring is independent of the intensity of the light beam. 3mW 5mW8mW Width of the SPDC ring is independent of number of accumulations taken by EMCCD camera. 50 100 150

  28. R. P. Singh SPDC with Gaussian pump beam 1.0 mm 1.0 mm

  29. R. P. Singh SPDC with Gaussian pump beam (theory) 1.0 mm 1.0 mm

  30. R. P. Singh SPDC with gaussian pump beam

  31. R. P. Singh SPDC with optical vortex beam S. Prabhakar et al., Optics Communications

  32. R. P. Singh SPDC with optical vortex pump beam 1.0 mm 1.0 mm Order of vortex m=1 m=3 m=5

  33. R. P. Singh SPDC with optical vortex pump beam

  34. Multi-photon, multi- dimensional entanglement can be achieved using OPO Our approach: Orbital angular momentum conservation: mp = ms + mi R. P. Singh 34

  35. R. P. Singh Classical Entanglement Violation of Bell’s inequality for light beams with OAM The Bell-CHSH inequality For continuous variables, Wigner Distribution Function can be used instead of E(a, b) Here, (X, PX) and (Y, PY) are conjugate pairs of dimensionless quadratures P. Chowdhury et al. Phys. Rev. A 88, 013803 (2013).

  36. Violation of Bell’s inequality contd… Classical Bell’s Violation for Optical Vortex beams Wigner Distribution Function (WDF) can be defined as In 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. Singh

  37. R. P. Singh Experimental setup for determining TPCF Violation of Bell’s inequality Experiment

  38. R. P. Singh Variation of non-locality with order of vortex (n) Violation of Bell inequality contd… Magnitude of violation of Bell inequality increases with the increase in the order of vortex

  39. Violation of Bell’s inequality contd… R. P. Singh Results m=0, n=1, X1 = 0; PX1 = 0; X2 = X; PX2 = 0; Y1 =0; PY1 = 0; Y2 = 0; PY2 = PY , PY x

  40. R. P. Singh Generation of OAM qubits Polarization Poincare sphere OAM Poincare sphere All the OAM Qubitson 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 Sagnacinterferometer with vortex lens.

  41. R. P. Singh Projective measurements in polarization basis PBS λ/2 (α) λ/4 (β) PBS State Preparation λ/2 OV lens Generation of non separable state OAM qubit 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 Poincare sphere of OAM. H V

  42. 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 results

  43. R. P. Singh Conclusion and future outlook • Optical Vortices and orbital angular momentum of light • Spontaneous Parametric Down-conversion can be used to generate entangled photons in different degrees of freedom • Spatial distribution of SPDC ring with higher order optical vortices • Proposal to generate multi-photon, multi- dimensional entanglement • Bell inequality violation for light beams with OAM • OAM qubit generation with non separable OAM-polarization state • Using hybrid entanglement for quantum teleportation and quantum key distribution

  44. R. P. Singh Thank you!

  45. R. P. Singh OAM entanglement The rotation in phase provides orbital angular momentum of lћto the photons. l = -2 -1 +1 +2 Rotation of phase front as the beam propagates Future plan

  46. R. P. Singh Lens f = 5 cm λ/2 plate Blue Laser EMCCD 405 nm & 50 mW BBO crystal IF Generating correlated photon pairs IF: Interference filter 810±5 nm EMCCD: Electron Multiplying CCD

  47. R. P. Singh SPDC with gaussian pump beam

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

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