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Daniel Felinto* dfelinto@df.ufpe.br

Quantum Networks with Atomic Ensembles. C.W. Chou, H. Deng, K.S. Choi, H. de Riedmatten, J. Laurat, S. van Enk, H.J. Kimble Caltech Quantum Optics *Presently at Departamento de Física, UFPE International Workshop on Quantum Information Paraty, August 14, 2007.

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Daniel Felinto* dfelinto@df.ufpe.br

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  1. Quantum Networks with Atomic Ensembles C.W. Chou, H. Deng, K.S. Choi, H. de Riedmatten, J. Laurat, S. van Enk, H.J. Kimble Caltech Quantum Optics *Presently at Departamento de Física, UFPE International Workshop on Quantum Information Paraty, August 14, 2007 Daniel Felinto* dfelinto@df.ufpe.br

  2. B A • Theoretical issues • Does it “work” – capabilities beyond any classical system • Quantum computation, communication, & metrology • Experimental implementation • Physical processes for reliable generation, processing, & transport • of quantum states • A quantum interface between matter and light « Quantum Networking » Fundamental scientific questions and Diverse experimental challenges Quantum channel– transport / distribute quantum entanglement Quantum node generate, process, store quantum information Goal :develop the ressources that enable quantum repeaters, thereby allowing entanglement-based communication tasks on distance scales larger than set by the attenuation length of fibers

  3. . . • Purify the entanglement . . . . F<1 . . . . . . . . . . . . . . F~1 . . . . . . . . . . . . . . . . . . Quantum Repeaters : Principles • Divide into segments and generate entanglement Fidelity close to 1, long distance… But time exponentially large with the distance . . L0 L0 L0 L Entanglement (often) and purification (always) are probabilistic : each step ends at different times. . . • Connect the pairs

  4. . . • Purify the entanglement . . . . F<1 . . . . . . . . . . . . . . F~1 . . . . . . . . . . . . . . . . . . Quantum Repeaters : Principles • Divide into segments and generate entanglement Fidelity close to 1, long distance… But time exponentially large with the distance . . L0 L0 L0 L Entanglement (often) and purification (always) are probabilistic : each step ends at different times. . . « Scalability » :requires the storage of heralded entanglement • Connect the pairs : Quantum Memories

  5. One Approach : « DLCZ » Atomic ensembles in the single excitation regime

  6. Entanglement-based cryptography Entanglement connection Quantum teleportation Entanglement of two ensembles Capabilities Enabled by DLCZ Roadmap • Beyond the original protocols of DLCZ • Implementation of quantum memory • Realization of fully controllable • source for single photons • A source for entangled photon pairs • … • Universal quantum computation via • the protocol of Knill, LaFlamme, Milburn • Scalable long-distance • quantum communication via • quantum repeater architecture • Distribution of entanglement • over quantum networks

  7. Outline • « DLCZ building block » : writing, reading, memory time • Number-state entanglement between two ensembles • Polarization entanglement between two nodes (4 ensembles) • Towards entanglement swapping

  8. Large ensemble of atoms • With a L-type level configuration « Building Block » (DLCZ) Duan, Lukin, Cirac and Zoller, “Long-distance quantum communication with atomic ensembles and linear optics”, Nature 414, 413 (2001)

  9. Nonclassical correlations between field 1 and the ensemble : the excitation probability Write Collective atomic state Write Field 1 Field 1 Creating a Single Atomic Excitation

  10. Nonclassical correlations between field 1 and the ensemble Field 2 Read read Read Field 2 Nonclassical correlations between fields 1 and 2 Retrieving the Single Excitation

  11. Si APD 30 ns, Very weak 200 µm Experimental Setup Counter-propagating and off-axis configuration H Field 2 Read V Write H Field 1 V

  12. Field 2 Read Suppression of the two-photon component Multi-excitations Coherent state limit Plateau : Single excitation Sub-Poissonian qc~ 50% ? a = 0.7 ± 0.3% Background noise Conditional Field-2 Retrieval efficiency of the stored excitation J. Laurat et al., “Efficient retrieval of a single excitation stored in an atomic ensemble”, Opt. Express 14, 6912 (2006)

  13. Programmable Delay 10 to 20 µs Write Field 1 Storage Time of the Single Excitation Reading Writing Field 2 Read H. De Riedmatten et al., “Direct measurement of decoherence for entanglement between a photon and a stored excitation”, PRL 97, 113603 (2006) D. Felinto et al., “Control of decoherence in the generation of photon pairs from atomic ensembles”, Phys. Rev. A 72, 053809 (2005)

  14. Outline • « DLCZ building block » : writing, reading, memory time • Number-state entanglement between two ensembles • Polarization entanglement between two nodes (4 ensembles) • Towards entaglement swapping C.W. Chou, H. de Riedmatten, D. Felinto, S.V. Polyakov, S. van Enk, H.J. Kimble, Measurement-induced entanglement for excitation stored in remote atomic ensembles, Nature 438, 828 (2005)

  15. Light Atoms entangled Entanglement between Two Ensembles entangled Atoms Light 50/50 Beam splitter

  16. Entanglement between Two Ensembles 1 photon detected  1 atom transferred 50/50 Beam splitter

  17. here here General (and ideal) case there there where there = Entanglement between Two Ensembles 1 photon detected  1 atom transferred L Entangled R +

  18. Map matter state to field state atoms L entangled? où • Coherence d • Individual statistics pij atoms R / Concurrence C > 0  Entanglement of formation E > 0 W. K. Wootters, Phys. Rev. Lett. 80, 2245(1998) How to Verify the Entanglement ? • Tomography

  19. Experimental Density Matrix Populations Coherence D1c D1b <1, suppression of 2-photon events relative to single-excitation events p=9.10-4 160 Hz preparation rate J. Laurat et al., “Heralded Entanglement between Atomic Ensembles: Preparation, Decoherence, and Scaling”, arXiv:0706.0528

  20. Asymptotic value (no two-photon component) given in the ideal case by the retrieval efficiency (13.5%) times the overlap of the detected photons (95%) Scaling with Excitation Probability Decreasing excitation probability J. Laurat et al., “Heralded Entanglement between Atomic Ensembles: Preparation, Decoherence, and Scaling”, arXiv:0706.0528

  21. Outline • « DLCZ building block » : writing, reading, memory time • Number-state entanglement between two ensembles • Polarization entanglement between two nodes (4 ensembles) • Towards entaglement swapping

  22. R L 2LU 2RU DLa DRa BS BS 2LD 2RD DLb DRb “Effective” state giving one click on each side How Having one Click on Each Side ? 3 m Entangled ! Node R Node L Entangled ! LU RU LD RD

  23. “Effective” state giving one click on each side Polarization Entanglement 3 m Node R Node L 2L 2LU 2RU 2R LU RU 2LD 2RD LD RD

  24. Preparation x 35 p11 : Probability of both pairs are prepared in an entangled state Duration that the first entanged pair is stored before retrieval Results : Preparation and Bell Violation Asynchronous Preparation C.W. Chou, J. Laurat, H. Deng, K.S. Choi, H. de Riematten, D. Felinto, H.J. Kimble, Functional Quantum Nodes for Entanglement Distribution over a Scalable Quantum Networks, Science 316, 1316 (2007)

  25. Results : Preparation and Bell Violation Asynchronous Preparation Preparation x 35 Final state x 20 Duration that the first entanged pair is stored before retrieval D. Felinto, C.W. Chou, J. Laurat, H. de Riedmatten, H. Kimble, “Conditional control of the quantum states of remote atomic memories for Q. networking”, Nature Physics 2, 844 (2006) C.W. Chou, J. Laurat, H. Deng, K.S. Choi, H. de Riematten, D. Felinto, H.J. Kimble, Functional Quantum Nodes for Entanglement Distribution over a Scalable Quantum Networks, Science 316, 1316 (2007)

  26. Results : Preparation and Bell Violation Asynchronous Preparation Preparation x 35 Final state x 20 Bell Violation (CHSH) Large violation : quantum key distribution with security at minimum against individual attacks Duration that the first entanged pair is stored before retrieval C.W. Chou, J. Laurat, H. Deng, K.S. Choi, H. de Riematten, D. Felinto, H.J. Kimble, Functional Quantum Nodes for Entanglement Distribution over a Scalable Quantum Networks, Science 316, 1316 (2007)

  27. 2 nodes separated by 3m • 2 ensembles per node • Asynchronous preparation (memory) of 2 parallel number-state entangled pairs • Polarization coding and passive phase stability •  Polarization entanglement distribution, violating Bell, in a scalable fashion C.W. Chou, J. Laurat, H. Deng, K.S. Choi, H. de Riematten, D. Felinto, H.J. Kimble, Functional Quantum Nodes for Entanglement Distribution over Scalable Quantum Networks, Science 316, 1316 (2007)

  28. Outline • « DLCZ building block » : writing, reading, memory time • Number-state entanglement between two ensembles • Polarization entanglement between two nodes (4 ensembles) • Towards entanglement swapping

  29. 2LU 2RU 2LD 2RD Entangled ! One click at Node L projects the Node R into: Towards Entanglement Swapping 3 m Entangled ! Node R Node L Entangled ! LU RU LD RD

  30. Towards Entanglement Swapping Populations Coherence • From two entangled pairs with h(2)~0.15 and 90% vacuum • The transfert succeeds only 50% of the time, while the weight of two-photon events stays the same. •  Overall, h(2) multiplied by 4 <1, suppression of 2-photon events relative to single-excitation events J. Laurat et al., Towards entanglement swapping with atomic ensembles in the single excitation regime, arXiv:0704.2246

  31. 3m Node L Node R 2R 2L Field 1 LU RU LD RD In a Nutshell… • Q. Repeaters, DLCZ • …and Building Block Writing Reading Field 2 Write • Photon pair : a<1% • Efficient retrieval : 50% • Memory time ~ 10 µs Read • Number-state entanglement • Heralded and stored • C=0.9±0.3 for the atoms • Polarization Entanglement • 2 nodes, 4 ensembles • Asynchronous preparation • Bell violation • Towards swapping • Coherence transfert

  32. Raman E  1/ t Decoherence 1) MOT magnetic field Each atom sees a different field  Inhomogeneous broadening of the ground states B z t ~ 100 ns Solution : Switching off the trapping field

  33. Typical storage time t ~ 10 µs ~ 100 m MOT temperature 500 K  t ~ 200 s Storage Time of the Excitation « Timing » and linewidth Perspectives ?? Better cancellation of residual fields @ 40 Hz MOT off 6 ms

  34. LU LD Experimental Setup Repumper Write PBS BSW Read LU BSR RU LD RD D2LV D2RV BS1 D2LH D2RH l/2 l/4 D1Va D1Vb Compensator Beam displacer D1Ha D1Hb

  35. Experimental Setup Interferometers Entangling the (U, D) Pairs Repumper Write PBS BSW Read LU BSR RU LD RD D2LV D2RV BS1 D2LH D2RH l/2 l/4 D1Va D1Vb Compensator Beam displacer D1Ha D1Hb

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