Shashi Prabhakar, S. Gangi Reddy, A. Aadhi, Ashok Kumar, Chithrabhanu P., G. K. Samanta and R. P. Singh Physical Research Laboratory, Ahmedabad Feb 27, 2014 IPQI 2014 Orbital angular momentum of light: Applications in quantum information Orbital angular momentum of light: Applications in quantum information 1R. P. Singh

Whirlpools Tornadoes

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 3R. P. Singh

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

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

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

7R. P. Singh Difference in SAM and OAM

Intensity and phase plot of a beam carrying OAM Helical Wavefront Each photon carries an Orbital Angular Momentum of lħ, l order of vortex, can be any integer 2π2π4π4π Topological charge 8R. P. Singh Optical Vortex 6π6π

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 1.Computer generated hologram (CGH) 2.Spiral phase plate 3.Astigmatic mode converter 4.Liquid crystal (Spatial light modulator) 9R. P. Singh Generation of Vortices in light

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

He-Ne Laser B1 M1M2 B2 A CGH L Screen CCD 11R. P. Singh Finding vortex order with Interferometry

 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, (2011) Phys. Lett. A 377, (2013) m=1 m=2 m=2 m=3 Finding order, other than Interferometry 12R. 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 13R. P. Singh

Entanglement contd… Variables that can be chosen for entanglement Polarization Spin Orbital angular momentum Position and momentum 1.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. 2.The most common method to generate entangled photons in lab is Spontaneous parametric down conversion (SPDC). 14R. P. Singh

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

Phase matching (Birefringence) birefringence Δn = n e – n o 16R. P. Singh Incident light e-ray (polarized) o-ray (polarized) Optics axis

Type-I SPDC λ 2λ2λ BBO crystal 2λ2λ |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, (2011) 17R. P. Singh

Type-II SPDC λ 2λ2λ BBO crystal 2λ2λ |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, (2003) 18R. P. Singh e-ray o-ray pump e-ray o-ray

Specification of components used BBO Crystal Size: 8×4×5 mm 3 θ = 26˚ (cut for 532 nm) Cut for type-1 SPDC Optical transparency: ~190– 3300 nm n e = , n o = Diode Laser Wavelength: 405 nm Output Power: 50 mW Interference filter Wavelength range 810±5 nm 19R. P. Singh

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

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

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

23R. P. Singh 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.

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 24R. P. Singh

Generating correlated photon pairs 25R. P. Singh

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

Observing SPDC at varying pump intensity 3mW 5mW 8mW Width of the SPDC ring is independent of the intensity of the light beam Width of the SPDC ring is independent of number of accumulations taken by EMCCD camera. 27R. P. Singh

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

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

SPDC with gaussian pump beam 30R. P. Singh

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

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

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

Orbital angular momentum conservation: m p = m s + m i Our approach: 34R. P. Singh Multi-photon, multi- dimensional entanglement can be achieved using OPO

R. P. Singh35 Classical Entanglement The Bell-CHSH inequality For continuous variables, Wigner Distribution Function can be used instead of E(a, b) Here, (X, P X ) and (Y, P Y ) are conjugate pairs of dimensionless quadratures P. Chowdhury et al. Phys. Rev. A 88, (2013). Violation of Bell’s inequality for light beams with OAM

36 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 Violation of Bell’s inequality contd…

R. P. Singh37 Experimental setup for determining TPCF Violation of Bell’s inequality Experiment

R. P. Singh38 Variation of non-locality with order of vortex (n) Magnitude of violation of Bell inequality increases with the increase in the order of vortex Violation of Bell inequality contd…

39 Results Order (n)Theoretical (|B max |)Experimental (|B max |) ± ± ± Violation of Bell’s inequality contd… R. P. Singh m=0, n=1, X1 = 0; PX1 = 0; X2 = X; PX2 = 0; Y1 =0; PY1 = 0; Y2 = 0; PY2 = PY, x PY

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 sphere R. P. Singh Generation of OAM qubits 40

OAM qubit OV l ens 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 Poincare sphere of OAM. Generation of non separable state H V R. P. Singh41

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

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 43R. P. Singh

Thank you! 44R. P. Singh

OAM entanglement Future plan l = The rotation in phase provides orbital angular momentum of lћ to the photons. Rotation of phase front as the beam propagates 45R. P. Singh

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

SPDC with gaussian pump beam 47R. P. Singh

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