Quantum Networks with Atomic Ensembles

Transcription

1 Quantum Networks with Atomic Ensembles Daniel Felinto* 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 XI Escola de Verão Jorge André Swieca São Paulo, Fevereiro 21, 2008

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

3 Quantum Repeaters : Principles 1) Divide into segments and. generate.. entanglement... L 0 L 0 L 0 L Fidelity close to 1, long distance But time exponentially large with the distance F< F~1 2) Purify the entanglement Entanglement (often) and purification (always) are probabilistic : each step ends at different times ) Connect the pairs

4 Quantum Repeaters : Principles 1) Divide into segments and. generate.. entanglement... L 0 L 0 L 0 L Fidelity close to 1, long distance But time exponentially large with the distance F< F~1 2) Purify the entanglement ) Connect the pairs Entanglement (often) and purification (always) are probabilistic : each step ends at different times. «Scalability» : requires the storage of heralded entanglement : Quantum Memories

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

6 Capabilities Enabled by DLCZ Roadmap Entanglement-based cryptography Quantum teleportation 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 Entanglement of two ensembles Entanglement connection

7 Outline «DLCZ building block» : writing, reading, memory time Synchronization of two single photon source Number-state entanglement between two ensembles Polarization entanglement between two nodes (4 ensembles)

8 «Building Block» (DLCZ) Large ensemble of atoms Witha Λ-type level configuration Duan, Lukin, Cirac and Zoller, Long-distance quantum communication with atomic ensembles and linear optics, Nature 414, 413 (2001)

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

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

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

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

13 Memory Source of Decoherence Quadrupole Magnetic Field σ I σ I σ + σ σ + : Magnetic field σ + : Laser beams ( M, N) Each atom sees a different field : Inhomogeneous broadening of the ground states

14 Source of Decoherence Quadrupole Magnetic Field t at large t

15 Decoherence control: turning off the magnetic field Cancelation of the magnetic field: Raman Spectroscopy + Measurements of optical depth g times increase of coherence time g 1,2 = 2 classical limit storage time [μs] Felinto et.al., PRA 72, (2005)

16 Generation of polarization entangled photons F =4 (unpolarized atoms) F=4 F=3 m F Writing Ideal state for Field 1 and 2 π + π + ψ12 = vac + p cos( η ) σ 1, σ 2 + sin( η ) σ 1, σ 4 4 Experimental setup F =4 F=4 F=3 m F Fiber T 2 Reading η is given by Clebsch-Gordan coefficients. For Cs : η =0.86 Write σ + λ/2 λ/4 PBS 4 2 Field 2 R 2 Atoms Field 1 filter Level Scheme λ/2 λ/4 R 1 PBS Read σ - Fiber T 1 Matsukevich et al., PRL 95, (2005)

17 Violation of CHSH inequality vs g12 S = E(θ 1,θ 2 ) + E(θ 1,θ 2 ) + E(θ 1,θ 2 ) + E(θ 1,θ 2 ) de Riedmatten et.al., PRL 97, (2006)

18 Outline «DLCZ building block» : writing, reading, memory time Syncronization of two single photon sources Polarization entanglement between two nodes (4 ensembles) Towards entaglement swapping D. Felinto, C. W. Chou, J. Laurat, E. W. Schomburg, H. de Riedmatten, & H. J. Kimble, Nature Physics 2, 844 (2006)

19 Real-time control of Two Memories D. Felinto, C. W. Chou, J. Laurat, E. W. Schomburg, H. de Riedmatten, & H. J. Kimble, Nature Physics 2, 844 (2006)

20 First Application : HOM L R Two independent sources of single photons Field 2 Field 2 λ/2 BS V=0.77±0.06 (Integrated data) 28-fold increase in p 1122! (N=23, 12µs) D. Felinto et al., Conditional control of the quantum states of remote atomic memories for Q. networking, Nature Physics 2, 844 (2006)

21 Narrowband, close-to to-transform-limited wavepacket D. Felinto et al., Conditional control of the quantum states of remote atomic memories for Q. networking, Nature Physics 2, 844 (2006)

22 Outline «DLCZ building block» : writing, reading, memory time Syncronization of two single photon sources Number-state entanglement between two ensembles 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)

23 Entanglement between Two Ensembles Atoms entangled Light 50/50 Beam splitter Light Atoms entangled

24 Entanglement between Two Ensembles 1 photon detected 1 atom transferred 50/50 Beam splitter

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

26 Entangling 2 Remote Ensembles C.-W. Chou, H. de Riedmatten, D. Felinto, S. Polyakov, S. Van Enk, H. J. Kimble Nature 438, 828 (2005) L 1 L phase shifter Phase controller 1064 nm Write Fiber BS w 2.8 m Atoms filter Fiber BS nm filters D 1a R 1 R D 1b Atoms filter Data acquisition Write Field 1 Ideal case Entanglement is stored in the ensembles for 1 µs.

27 The Hard Part : Operational Verification C.-W. Chou, H. de Riedmatten, D. Felinto, S. Polyakov, S. Van Enk, H. J. Kimble Nature 438, 828 (2005) Field 2 Read L 2 L atoms L ρ L, R entangled? Map matter state ρ to field state 2 L,2R Field 2 Read R atoms R 2 R Quantum-state tomography on the density matrix for the fields 2,2 L R ρ 2,2 L R

28 A Robust,, Model-Independent Protocol C.-W. Chou, H. de Riedmatten, D. Felinto, S. Polyakov, S. Van Enk, H. J. Kimble Nature 438, 828 (2005) L 2 L Quantum-state tomography ρ L, R atoms L ρ 2,2 L R Black entangled? Box R atoms R 2 R where 2 L 2 L Coherence d Photon statistics p ij 2 R 2 R Concurrence / C > 0 Entanglement of formation E > 0 W. K. Wootters, Phys. Rev. Lett. 80, 2245(1998)

29 ρ L, R L entangled? atoms L What are the issues? C.-W. Chou, H. de Riedmatten, D. Felinto, S. Polyakov, S. Van Enk, H. J. Kimble Nature 438, 828 (2005) ρ 2,2 L R Map matter state to field state 2 L Coherence? Necessary but not sufficient R 2 R atoms R Black Box Consider the unentangled conditional state ( 0 a 1 L) ( 0 a 1 L) unen tan gled Φ 2,2 = + L R L L R R = Ψ entangled 2,2 L R + a L, where ( 1 ) entangled Ψ 2,2 = + a L R L R 2L R L R L 2 R Critically, the distinction between unentangled and entangled states involves higher-order photon statistics

30 Diagonal Elements C.-W. Chou, H. de Riedmatten, D. Felinto, S. Polyakov, S. Van Enk, H. J. Kimble Nature 438, 828 (2005) L 2 L 1064 nm Atoms filter D 2a Read BS R R Atoms filter 2 R 1064 nm filters D 2b Data acquisition Field 2 Read

31 Diagonal Elements C.-W. Chou, H. de Riedmatten, D. Felinto, S. Polyakov, S. Van Enk, H. J. Kimble Nature 438, 828 (2005) Conditional Conditioned on Conditioned on <1, suppression of 2-photon events relative to single-excitation events For non-conditioned events, 0.30 ± ± 0.04

32 Off-Diagonal element d C.-W. Chou, H. de Riedmatten, D. Felinto, S. Polyakov, S. Van Enk, H. J. Kimble Nature 438, 828 (2005) L 2 L Phase shifter controlling ϕ Phase controller 1064 nm Atoms filter D 2a Read BS R BS nm filters R 2 R D 2b Atoms filter Data acquisition Field 2 Read

33 Entanglement creation L 1 L Off-Diagonal element d C.-W. Chou, H. de Riedmatten, D. Felinto, S. Polyakov, S. Van Enk, H. J. Kimble Nature 438, 828 (2005) Atomsfilter BS 1 D 1a R Atoms filter L 1 R Entanglement verification ϕ 2 L D 1b Data acquisition ϕ Atomsfilter BS 2 D 2a R Atoms 2 R filter D 2b Data acquisition

34 Off-Diagonal element d C.-W. Chou, H. de Riedmatten, D. Felinto, S. Polyakov, S. Van Enk, H. J. Kimble Nature 438, 828 (2005) L 1 L Atomsfilter BS 1 D 1a R Atoms L 1 R filter 2 L ϕ D 1b Data acquisition Atomsfilter BS 2 D 2a R Atoms 2 R filter D 2b Data acquisition

35 Off-Diagonal element d C.-W. Chou, H. de Riedmatten, D. Felinto, S. Polyakov, S. Van Enk, H. J. Kimble Nature 438, 828 (2005) L 1 L Atomsfilter BS 1 D 1a R Atoms L 1 R filter 2 L ϕ D 1b Data acquisition Atomsfilter BS 2 D 2a R Atoms 2 R filter D 2b Data acquisition

36 Concurrence Estimation C.-W. Chou, H. de Riedmatten, D. Felinto, S. Polyakov, S. Van Enk, H. J. Kimble Nature 438, 828 (2005) / Fields 2 L and 2 R C > 0 entanglement of formation E > 0 Fields 2 L and 2 R are entangled Ensembles L and R are entangled Local operations at L, R cannot increase entanglement. C (atomic state) > C (field state)>0 Low concurrence because : - Loss+ low retrieval efficiency (q c ~ 10%) (limits the ability to infer the entanglement in the atoms) ( - No post-selection)

37 Field Entanglement along the Pathway from Ensembles to Detections Retrieval efficiency q c ~ 10% High concurrence C between ensembles

38 Back to entanglement between Two Ensembles 50/50 Beam splitter Now 2 ensembles in the same MOT just 1 mm apart

39 Experimental Density Matrix Populations 2 L 2 R Coherence 2 L 2 R D1c D1b <1, suppression of 2-photon events relative to single-excitation events p= Hz preparation rate J. Laurat et al., Heralded Entanglement between Atomic Ensembles: Preparation, Decoherence, and Scaling, arxiv:

40 Outline «DLCZ building block» : writing, reading, memory time Syncronization of two single photon sources Number-state entanglement between two ensembles Polarization entanglement between two nodes (4 ensembles) 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)

41 How Having one Click on Each Side? 3 m Node L Entangled! Node R ϕ L 2 LU 2 RU ϕ R D La BS 2 LD LU Entangled! RU 2 RD BS D Ra D Lb LD RD D Rb Effective state giving one click on each side

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

43 Results : Preparation and Bell Violation 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) Preparation x 35 Asynchronous Preparation p 11 : Probability of both pairs are prepared in an entangled state Duration that the first entanged pair is stored before retrieval

44 Results : Preparation and Bell Violation 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) 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)

45 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 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) Duration that the first entanged pair is stored before retrieval

46 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) 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

47 In a Nutshell Q. Repeaters, DLCZ et Building Block Photon pair : α<1% Efficient retrieval : 50% Memory time ~ 10 µs Entanglement Heralded Without postselection, C~0.1 Write Writing Field 1 Reading Field 2 Read Conditional Control Asynchronous preparation Polarisation Entanglement 2 nodes, 4 ensembles Bell violation Node L 3m Node R 2 L 2 R LU LD RU RD

48 The End