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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R. P. Singh
Orbital angular momentum of light:
Applications in quantum information
Physical Research Laboratory,
Ahmedabad. 380 009.
Feb 27, 2014
IPQI 2014
Whirlpools
Tornadoes
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
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Spin Angular Momentum
Poyntingshowed classically for a beam of
circularly polarized light
Angular momentum
per photon
Polarized:
Beth
Phys. Rev. 50, 115, 1936
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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
?
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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
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Difference in SAM and OAM
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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
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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
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Generation using CGH
He-Ne Laser
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M1
M2
CCD
CGH
A
L
B1
B2
He-Ne Laser
Screen
Finding vortex order with Interferometry
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Finding order, other than Interferometry
m=1 m=2
m=2 m=3
Opt. Lett. 36, 4398-4400 (2011)
Phys. Lett. A 377, 1154-1156 (2013)
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While generation of entangled particles
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Variables that can be chosen for entanglement
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p:Pump beam
s:Signal beam (High ω)
i:Idler beam (Low ω)
Phase-matching condition
Energy Conservation
Phy. Rev. A 31, 2409 (1985)
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Optics axis
e-ray
(polarized)
Incident light
o-ray
(polarized)
birefringence Δn = ne – no
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|H>
2λ
λ
|V>
|H>
2λ
BBO crystal
Collimated pump Strongly focused pump
Phy. Rev. A 83, 033837 (2011)
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|V>
2λ
λ
|V>
|H>
2λ
BBO crystal
e-ray
e-ray
pump
o-ray
o-ray
Phy. Rev. A 68, 013804 (2003)
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BBO Crystal
Diode Laser
Interference filter
First OAM entanglement experiment
Mair et al., Nature, 2001
Polarization entanglement :
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First OAM entanglement experiment contd…
Mair et al., Nature 2001
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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).
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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.
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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
IF: Interference filter 810±5 nm
EMCCD: Electron Multiplying CCD
Generating correlated photons
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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
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1.0 mm
1.0 mm
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1.0 mm
1.0 mm
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S. Prabhakar et al., Optics Communications
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1.0 mm
1.0 mm
Order of vortexm=1 m=3 m=5
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Multi-photon, multi- dimensional entanglement can be achieved using OPO
Our approach:
Orbital angular momentum conservation: mp = ms + mi
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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).
Violation of Bell’s inequality contd…
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.
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Violation of Bell’s inequality Experiment
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Violation of Bell inequality contd…
Magnitude of violation of Bell inequality increases with the increase in the order of vortex
Violation of Bell’s inequality contd…
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m=0, n=1, X1 = 0; PX1 = 0; X2 = X; PX2 = 0;
Y1 =0; PY1 = 0; Y2 = 0; PY2 = PY ,
PY
x
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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.
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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
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
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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
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Lens
f = 5 cm
λ/2
plate
Blue Laser
EMCCD
405 nm & 50 mW
BBO
crystal
IF
IF: Interference filter 810±5 nm
EMCCD: Electron Multiplying CCD
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Computer generated holography technique for the generation of optical vortices.