Exploiting the Entanglement in Classical Optics Systems

Transcription

1 February 23 th, 2015 Dep. of Physics - University of Virginia Exploiting the Entanglement in Classical Optics Systems Carlos Eduardo R. de Souza carloseduardosouza@id.uff.br $$$ Financial Support $$$

2 Universidade Federal Fluminense UFF: Niterói

3 Niterói Rio de Janeiro - Brazil Contemporary's Art Museum (MAC) Oscar Niemeyer Itacoatiara Beach

4 Quantum Optics and Information group at UFF Experimental Physics Antonio Z. Khoury Carlos E. R. Souza (Cadu) Teoretical Physics José A. O. Huguenin UFF - Volta Redonda Ernesto Galvão Kaled Dechoum Daniel Jonathan Marcelo Sarandy Thiago Oliveira

5 Summary Optical Vortices Spin-Orbit Entanglement Optical devices for Quatum Information Topological Phase in Spin-Orbit transformations Conclusions

6 Optical Vortices Light with Orbital Angular Momentum (OAM) From the Classical Electromagnetism where is the angular momentum density. L o = 0 L o 0 L s Spin component polarization L o Orbital component - wavefront Poynting vector parallel to optical axis A. E. Siegman - Lasers Poynting vector rotates around optical axis.

7 Optical Vortices Light with Orbital Angular Momentum (OAM) Paraxial optics lasers (Wave Equation) considering with, (Helmholtz Equation) Considering too (Paraxial Equation) A. E. Siegman - Lasers

8 Optical Vortices Light with Orbital Angular Momentum (OAM) (Paraxial Equation) Retangular Cylindrical 1 th 1order th A. E. Siegman - Lasers

9 Optical Vortices Light with Orbital Angular Momentum (OAM) Paraxial optics lasers Solutions of the paraxial equation in retangular coordenates: HG modes (Paraxial Equation) GOUY phase N=m+n Solutions of the paraxial equation in cylindrical coordenates: LG modes N=m+n Topological charge A. E. Siegman - Lasers N=2p+ l - l=n-m - p=min(m,n)

10 Optical Vortices Analogy on the decompositions: Degrees of Freedom Polarization 1 th order modes

11 Optical Vortices Analogy on the decompositions: Degrees of Freedom Poincaré Sphere for polarization modes S 3 Poincaré Sphere for first order modes P 3 S 2 P 2 S 1 P 1 S i, P i ; i=1,2,3 are Stokes Parameters. Padgett e Courtial, Opt. Lett (1999)

12 Optical Vortices Photonic Qubits: Bloch Sphere analogy S 3 P 3 S 2 Encoding qubits into the electromagnetic field P 2 S 1 Polarization qubit P 1 Transverse Spatial degree qubit Padgett e Courtial, Opt. Lett (1999)

13 Optical Vortices Light with Orbital Angular Momentum (OAM) Experimental optical vortices: LG and HG modes Phase Masks

14 Optical Vortices Light with Orbital Angular Momentum (OAM) Experimental optical vortices: LG, HG modes and radial polarization S-WAVEPLATE (Radial Polarization Converter) Sold by Nanostrutured silica glass device Martynas Beresna et al, APPLIED PHYSICS LETTERS 98, (2011)

15 Optical Vortices Light with Orbital Angular Momentum (OAM) Experimental optical vortices: LG and HG modes SLM (Spatial Light Modulators) HG HAMAMATSU LG

16 Optical Vortices Mode Transformation: Astigmatic Mode Converters (AMC) Cylindrical lens Cylindrical lens Poincaré Sphere for first order modes P 3 AMC-π/2 Astigmatic Mode converter - π/2 Astigmatic Mode converter - π P 2 P 1 L. Allen et al, Phys. Rev. A (1992) e M. W. Beijersbergen et al, Opt Commun (1993).

17 Spin-Orbit Entanglement

18 Optical Setups for Quantum Information C-NOT universal gate Spin-Orbit mode This gate applies the inversion operation on one qubit (target) depending on the state of a second qubit (control). P M O A L O Truth table C. E. R. Souza e A. Z. Khoury, Opt. Express (2010).

19 Optical Setups for Quantum Information C-NOT universal gate Spin-Orbit mode Experimental results: classical beams * nonseparable mode Bell's State when the mode is ocupped by one photon C. E. R. Souza e A. Z. Khoury, Opt. Express (2010). * *

20 Optical Setups for Quantum Information Transverse Mode Selector: Splits 1 st order transverse modes in HG components Output modes Output modes Input mode Input mode C. E. R. Souza e A. Z. Khoury, Opt. Express (2010).

21 Topological Phase in Spin-Orbit modes Classical Entanglement: Topological Phase in Spin-Orbit modes

22 Topological Phase in Spin-Orbit modes Geometrical Phase in Spin-Orbit modes: one qubit In a cyclical evolution where, the total phase is given by: 1- M. Berry, Proc. R. Soc. Lond. A Sci. 392, 45 (1984)

23 1- S. Pancharatnam, Proc. Indian Acad. Sci. A 44, 247 (1956). 2- Galvez et al, Phys. Rev. Lett (2003). Topological Phase in Spin-Orbit modes The geometrical phase is observed in classical systems too. Pancharatnam Phase in polarization modes¹ Geometrical phase in first order modes 2

24 1- P. Milman, Phys. Rev A (2006). Topological Phase in Spin-Orbit modes Photonic Qubits: Geometrical phase in Spin-Orbit modes: two qubit pure state Bloch Ball Concurrence

25 1- P. Milman, Phys. Rev A (2006). Topological Phase in Spin-Orbit modes Photonic Qubits: Geometrical phase in Spin-Orbit modes: two qubit pure maximally entangled state C=0 separable state / C=1 Maximally Entangled state

26 1- P. Milman, Phys. Rev A (2006). Topological Phase in Spin-Orbit modes Photonic Qubits: Geometrical phase in Spin-Orbit modes: two qubit pure maximally entangled state Two Homotopy class 0-type π-type C=1 Maximally Entangled state

27 Topological Phase in Spin-Orbit modes Geometrical phase in Spin-Orbit modes: two qubit pure state maximally entangled

28 Topological Phase in Spin-Orbit modes Combining the spin and orbital degree of freedom in the framework of the classical theory

29 Topological Phase in Spin-Orbit modes Combining the spin and orbital degree of freedom in the framework of the classical theory Maximally Entangled State Separable State

30 W. LiMing - Phys.Rev.A (2004) Topological Phase in Spin-Orbit modes Geometrical phase in Spin-Orbit modes: two qubit pure state maximally entangled Parametrization with and

31 W. LiMing - Phys.Rev.A (2004) Topological Phase in Spin-Orbit modes Geometrical phase in Spin-Orbit modes: two qubit pure state maximally entangled Parametrization with and Waveplates Astigmatic Mode Converters

32 C. E. R. Souza, J. A. O. Huguenin and A. Z. Khoury - JOSA-A 31 No (2014) Topological Phase in Spin-Orbit modes Geometrical phase in Spin-Orbit modes: two qubit pure state maximally entangled

33 C. E. R. Souza, J. A. O. Huguenin and A. Z. Khoury - JOSA-A 31 No (2014) Topological Phase in Spin-Orbit modes Geometrical phase in Spin-Orbit modes: two qubit pure state maximally entangled

34 C. E. R. Souza, J. A. O. Huguenin and A. Z. Khoury - JOSA-A 31 No (2014) Topological Phase in Spin-Orbit modes Geometrical phase in Spin-Orbit modes: two qubit pure state maximally entangled

35 C. E. R. Souza, J. A. O. Huguenin and A. Z. Khoury - JOSA-A 31 No (2014) Topological Phase in Spin-Orbit modes Results and Analysis Teoretical Results Experimental Results

36 C. E. R. Souza et al - Phys.Rev.Lett (2007). Topological Phase in Spin-Orbit modes Results and Analysis: Visibility vs Separability Interferency patern on CCD camera Visibility

37 Classical Entanglement Some works in classical entanglement at UFF... BB84 quantum cryptografy

38 Classical Entanglement Some works in classical entanglement at UFF... Quantum Game

39 Classical Entanglement Some works in classical entanglement at UFF... Optical devices to Quantum Information

40 Classical Entanglement Some works in classical entanglement at UFF... Phase-gate

41 Violating the Bell's inequality using classical spin-orbit modes

42 Optical Vortices in non-linear process

43 Conclusions The use of transverse modes increases the computacional power of the light. We can use classical Spin-Orbit modes to study some particularities of the quantum systems. It constitutes an important tool for the Quantum Computing and the Quantum Information. Applied devices for Quantum Computation with Spin-Orbit modes - CNOT gates, Q-Phase gates and the BB84 setup - can be built and tested.

44 Conclusions Thank you!! (Obrigado)