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Orbital Angular Momentum: Interference, Entangelement…home.iitk.ac.in/~akjha/Talks and...

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Orbital Angular Momentum: Interference, Entangelement, and Precision Measurement Anand Kumar Jha* and Robert W. Boyd The Institute of Optics, University of Rochester, Rochester, NY Physics of Quantum Electronics (PQE) Snowbird, Utah, January 2-6, 2011 Girish S. Agarwal Department of Physics, Oklahoma State University, Stillwater, Oklahoma *now at Intel Corporation, Hillsboro, OR
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Page 1: Orbital Angular Momentum: Interference, Entangelement…home.iitk.ac.in/~akjha/Talks and Presentations/Angular-Sensitivity... · Orbital Angular Momentum: Interference, Entangelement,

Orbital Angular Momentum: Interference, Entangelement, and Precision Measurement

Anand Kumar Jha* and Robert W. BoydThe Institute of Optics, University of Rochester, Rochester, NY

Physics of Quantum Electronics (PQE)Snowbird, Utah, January 2-6, 2011

Girish S. AgarwalDepartment of Physics, Oklahoma State University, Stillwater, Oklahoma

*now at Intel Corporation, Hillsboro, OR

Page 2: Orbital Angular Momentum: Interference, Entangelement…home.iitk.ac.in/~akjha/Talks and Presentations/Angular-Sensitivity... · Orbital Angular Momentum: Interference, Entangelement,

Orbital Angular Momentum: Basics

Barnett and Pegg, PRA 41, 3427 (1990)Franke-Arnold et al., New J. Phys. 6, 103 (2004)Forbes, Alonso, and Siegman J. Phys. A 36, 707 (2003)

Allen et al., PRA 45, 8185 (1992)

Angular position

l=0 l=2l=1

with p=0Laguerre-Gauss basis

Page 3: Orbital Angular Momentum: Interference, Entangelement…home.iitk.ac.in/~akjha/Talks and Presentations/Angular-Sensitivity... · Orbital Angular Momentum: Interference, Entangelement,

OAM-mode distribution:

E. Yao et al., Opt. Express 14, 13089 (2006)Jha, Jack, Yao, Leach, Boyd, Buller, Barnett, Franke-Arnold, Padgett, PRA 78, 043810 (2008)

Orbital Angular Momentum: Interference

Page 4: Orbital Angular Momentum: Interference, Entangelement…home.iitk.ac.in/~akjha/Talks and Presentations/Angular-Sensitivity... · Orbital Angular Momentum: Interference, Entangelement,

Jha, Leach, Jack, Franke-Arnold, Barnett, Boyd, and Padgett, PRL 104, 010501 (2010)

Orbital Angular Momentum Entanglement1. Angular two-photon interference

2. EPR Correlations

Leach, Jack, Romero, Jha, Yao, Franke-Arnold, Ireland, Barnett, Boyd, and Padgett, Science 329, 662 (2010)

Page 5: Orbital Angular Momentum: Interference, Entangelement…home.iitk.ac.in/~akjha/Talks and Presentations/Angular-Sensitivity... · Orbital Angular Momentum: Interference, Entangelement,

NOON State & Precision phase measurement (overview)

(ii) 2-photon N00N state

(iii) 4-photon N00N state

(i) N-single photons

Intensity ~

Sensitivity ~

Intensity ~

Sensitivity ~

Given N photons, how precisely can the optical phase be measured?

Page 6: Orbital Angular Momentum: Interference, Entangelement…home.iitk.ac.in/~akjha/Talks and Presentations/Angular-Sensitivity... · Orbital Angular Momentum: Interference, Entangelement,

NOON State & Precision angle measurement (overview)(i) N-single photons Given N photons with OAM l per

photon, how precisely can angular displacements be measured?

Intensity ~

Sensitivity ~(ii) 2-photon N00N state

(iii) 4-photon N00N state

Intensity ~

Sensitivity ~

Page 7: Orbital Angular Momentum: Interference, Entangelement…home.iitk.ac.in/~akjha/Talks and Presentations/Angular-Sensitivity... · Orbital Angular Momentum: Interference, Entangelement,

Transformation properties of OAM modesBeam Splitter

Mirror

Dove Prism

Page 8: Orbital Angular Momentum: Interference, Entangelement…home.iitk.ac.in/~akjha/Talks and Presentations/Angular-Sensitivity... · Orbital Angular Momentum: Interference, Entangelement,

Transformation properties of OAM modes

Page 9: Orbital Angular Momentum: Interference, Entangelement…home.iitk.ac.in/~akjha/Talks and Presentations/Angular-Sensitivity... · Orbital Angular Momentum: Interference, Entangelement,

Super-sensitive measurement with two-photon entangled state

Two-photon state:

Measurement Operator:

Page 10: Orbital Angular Momentum: Interference, Entangelement…home.iitk.ac.in/~akjha/Talks and Presentations/Angular-Sensitivity... · Orbital Angular Momentum: Interference, Entangelement,

Super-sensitive measurement with four-photon entangled state

Two-photon state:

Measurement Operator:

Page 11: Orbital Angular Momentum: Interference, Entangelement…home.iitk.ac.in/~akjha/Talks and Presentations/Angular-Sensitivity... · Orbital Angular Momentum: Interference, Entangelement,

(i) N-single photons Given N photons with OAM l per photon, how precisely can angular displacements be measured?

Intensity ~

Sensitivity ~(ii) 2-photon N00N state

(iii) 4-photon N00N state

Intensity ~

Sensitivity ~

Super-sensitive measurement with four-photon entangled state

Page 12: Orbital Angular Momentum: Interference, Entangelement…home.iitk.ac.in/~akjha/Talks and Presentations/Angular-Sensitivity... · Orbital Angular Momentum: Interference, Entangelement,

Conclusions

1. use of entangled photons having non-zero orbital angular momentum increases the resolution and sensitivity of angular displacement measurements

2. the resolution of improves as Nl while the sensitivity increases as 1/2Nl.

Acknowledgement

1. MURI grant from the U.S. Army Research Office

2. DARPA InPho program

Page 13: Orbital Angular Momentum: Interference, Entangelement…home.iitk.ac.in/~akjha/Talks and Presentations/Angular-Sensitivity... · Orbital Angular Momentum: Interference, Entangelement,

Angular One-Photon Interference

Page 14: Orbital Angular Momentum: Interference, Entangelement…home.iitk.ac.in/~akjha/Talks and Presentations/Angular-Sensitivity... · Orbital Angular Momentum: Interference, Entangelement,

Angular One-Photon Interference


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