R. P. Singh
This presentation is the property of its rightful owner.
Sponsored Links
1 / 48

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


  • 112 Views
  • Uploaded on
  • Presentation posted in: General

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.

Download Presentation

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

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


Shashi prabhakar s gangi reddy a aadhi ashok kumar chithrabhanu p

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


Shashi prabhakar s gangi reddy a aadhi ashok kumar chithrabhanu p

Whirlpools

Tornadoes


Outline of the talk

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


Shashi prabhakar s gangi reddy a aadhi ashok kumar chithrabhanu p

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


Shashi prabhakar s gangi reddy a aadhi ashok kumar chithrabhanu p

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


Shashi prabhakar s gangi reddy a aadhi ashok kumar chithrabhanu p

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


Shashi prabhakar s gangi reddy a aadhi ashok kumar chithrabhanu p

Difference in SAM and OAM

R. P. Singh

7


Shashi prabhakar s gangi reddy a aadhi ashok kumar chithrabhanu p

Optical Vortex

Intensity and phase plot of a beam carrying OAM

Helical Wavefront

Each photon carries an

Orbital Angular Momentum

oflħ, l order of vortex, can

be any integer

Topological charge

R. P. Singh

8


Shashi prabhakar s gangi reddy a aadhi ashok kumar chithrabhanu p

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


Shashi prabhakar s gangi reddy a aadhi ashok kumar chithrabhanu p

Generation using CGH

He-Ne Laser

R. P. Singh

10


Shashi prabhakar s gangi reddy a aadhi ashok kumar chithrabhanu p

M1

M2

CCD

CGH

A

L

B1

B2

He-Ne Laser

Screen

Finding vortex order with Interferometry

R. P. Singh

11


Shashi prabhakar s gangi reddy a aadhi ashok kumar chithrabhanu p

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


Entanglement

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


Entanglement contd

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).


Spontaneous parametric down conversion

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)


Phase matching birefringence

R. P. Singh

Phase matching (Birefringence)

Optics axis

e-ray

(polarized)

Incident light

o-ray

(polarized)

birefringence Δn = ne – no


Type i spdc

R. P. Singh

|H>

λ

|V>

|H>

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)


Type ii spdc

R. P. Singh

|V>

λ

|V>

|H>

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)


Specification of components used

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


Shashi prabhakar s gangi reddy a aadhi ashok kumar chithrabhanu p

First OAM entanglement experiment

Mair et al., Nature, 2001

Polarization entanglement :

R. P. Singh

20


Shashi prabhakar s gangi reddy a aadhi ashok kumar chithrabhanu p

First OAM entanglement experiment contd…

Mair et al., Nature 2001

R. P. Singh

21


Shashi prabhakar s gangi reddy a aadhi ashok kumar chithrabhanu p

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


Shashi prabhakar s gangi reddy a aadhi ashok kumar chithrabhanu p

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


Related works at prl

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


Generating correlated photon pairs

R. P. Singh

Generating correlated photon pairs


Generating correlated photons

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


Observing spdc at varying pump intensity

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


Spdc with gaussian pump beam

R. P. Singh

SPDC with Gaussian pump beam

1.0 mm

1.0 mm


Spdc with gaussian pump beam theory

R. P. Singh

SPDC with Gaussian pump beam (theory)

1.0 mm

1.0 mm


Spdc with gaussian pump beam1

R. P. Singh

SPDC with gaussian pump beam


Spdc with optical vortex beam

R. P. Singh

SPDC with optical vortex beam

S. Prabhakar et al., Optics Communications


Spdc with optical vortex pump beam

R. P. Singh

SPDC with optical vortex pump beam

1.0 mm

1.0 mm

Order of vortexm=1 m=3 m=5


Spdc with optical vortex pump beam1

R. P. Singh

SPDC with optical vortex pump beam


Shashi prabhakar s gangi reddy a aadhi ashok kumar chithrabhanu p

Multi-photon, multi- dimensional entanglement can be achieved using OPO

Our approach:

Orbital angular momentum conservation: mp = ms + mi

R. P. Singh

34


Classical entanglement

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).


Classical bell s violation for optical vortex beams

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


Experimental setup for determining tpcf

R. P. Singh

Experimental setup for determining TPCF

Violation of Bell’s inequality Experiment


Variation of non locality with order of vortex n

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


Results

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


Shashi prabhakar s gangi reddy a aadhi ashok kumar chithrabhanu p

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.


Shashi prabhakar s gangi reddy a aadhi ashok kumar chithrabhanu p

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


Shashi prabhakar s gangi reddy a aadhi ashok kumar chithrabhanu p

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

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


Thank you

R. P. Singh

Thank you!


Oam entanglement

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


Generating correlated photon pairs1

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


Spdc with gaussian pump beam2

R. P. Singh

SPDC with gaussian pump beam


Generating optical vortices

R. P. Singh

Generating optical vortices

Computer generated holography technique for the generation of optical vortices.


  • Login