orbital angular momentum: interference, entangelement…home.iitk.ac.in/~akjha/talks and...
TRANSCRIPT
![Page 1: Orbital Angular Momentum: Interference, Entangelement…home.iitk.ac.in/~akjha/Talks and Presentations/Angular-Sensitivity... · Orbital Angular Momentum: Interference, Entangelement,](https://reader031.vdocuments.site/reader031/viewer/2022021505/5af119c17f8b9aa17b8fd5bd/html5/thumbnails/1.jpg)
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,](https://reader031.vdocuments.site/reader031/viewer/2022021505/5af119c17f8b9aa17b8fd5bd/html5/thumbnails/2.jpg)
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,](https://reader031.vdocuments.site/reader031/viewer/2022021505/5af119c17f8b9aa17b8fd5bd/html5/thumbnails/3.jpg)
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,](https://reader031.vdocuments.site/reader031/viewer/2022021505/5af119c17f8b9aa17b8fd5bd/html5/thumbnails/4.jpg)
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,](https://reader031.vdocuments.site/reader031/viewer/2022021505/5af119c17f8b9aa17b8fd5bd/html5/thumbnails/5.jpg)
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,](https://reader031.vdocuments.site/reader031/viewer/2022021505/5af119c17f8b9aa17b8fd5bd/html5/thumbnails/6.jpg)
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,](https://reader031.vdocuments.site/reader031/viewer/2022021505/5af119c17f8b9aa17b8fd5bd/html5/thumbnails/7.jpg)
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,](https://reader031.vdocuments.site/reader031/viewer/2022021505/5af119c17f8b9aa17b8fd5bd/html5/thumbnails/8.jpg)
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,](https://reader031.vdocuments.site/reader031/viewer/2022021505/5af119c17f8b9aa17b8fd5bd/html5/thumbnails/9.jpg)
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,](https://reader031.vdocuments.site/reader031/viewer/2022021505/5af119c17f8b9aa17b8fd5bd/html5/thumbnails/10.jpg)
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,](https://reader031.vdocuments.site/reader031/viewer/2022021505/5af119c17f8b9aa17b8fd5bd/html5/thumbnails/11.jpg)
(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,](https://reader031.vdocuments.site/reader031/viewer/2022021505/5af119c17f8b9aa17b8fd5bd/html5/thumbnails/12.jpg)
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,](https://reader031.vdocuments.site/reader031/viewer/2022021505/5af119c17f8b9aa17b8fd5bd/html5/thumbnails/13.jpg)
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,](https://reader031.vdocuments.site/reader031/viewer/2022021505/5af119c17f8b9aa17b8fd5bd/html5/thumbnails/14.jpg)
Angular One-Photon Interference