2. Copenhagen interpretation

3. Entanglement - qubits 2 quantum coins 2 spins ( spin “up” or spin “down”) Entangled state many qubits: Entangled state:

4. 2 ensembles of quantum coins Entanglement – collective variables 3 heads, 3 tails 4 heads, 2 tails

5. Now, imagine 10 12 spins in each ensemble… 2 gas samples Only interactions/measurements of the collective spin of each ensemble are necessary Atoms are indistinguishable - high symmetry of the system – - robustness against losses of spins No free lunch: limited capabilities compared to ideal maximal entanglement

6. Outline Continuous quantum variables Atoms: Collective spin of the sample Light: Stokes parameters of the pulse Hald, Sorensen, Schori, Polzik PRL 83, 1319 (1999) Entangling atoms via interaction with light Theory Kuzmich, Polzik PRL 85, 5639 (2000) Duan,Cirac, Zoller, Polzik PRL 85, 5643 (2000) Experiment: entangled state of two Cs gas samples – two macroscopic entangled objects Julsgaard, Kozhekin, Polzik Nature 413, 400 (2001). Quantum communication protocols with entangled atomic samples Proposals Kuzmich, Polzik PRL 85, 5639 (2000) Duan,Cirac, Zoller, Polzik PRL 85, 5643 (2000)

7. t Quantum limits on the communication rate n photons, frequency  duration  t     frequency multiplexing Quantum memory

8. Quantum State (information) Processing Quantum memory for light: Write in the memory: map polarization state of light onto atomic spin Entangled ensembles Unknown quantum state of light Rotations of spin memory Teleportation of atoms: Entangled ensembles Spin rotations target Light pulse Ensemble to be teleported Memory read-out: map atomic spin state onto polarization of light Entangled light Polarization rotations Output beam memory Teleportation of light Innsbruck Rome Caltech-Aarhus

9. Why use ensembles of atoms? Quantum information processing often requires efficient interaction between light and atoms Entangled (squeezed) states of atomic ensembles are required in applications such as frequency standards Basic light - matter interaction: Must belarge Increase with cavity:E A photon gets many chances to interact with the atom. Caltech (H. J. Kimble) Munich (G. Rempe),... 1 And increase dipole moment d: Atoms in Rydberg states n=50, 51 are large and easy to hit with a photon Paris ( S. Haroche et al) 2 Use ensemble of atoms: 3 Aarhus, since 1997

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12. Spin memory with Coherent Spin States Quasi-continuous encoding 0 180 90 270 Indistinguishable coherent states Densely coded states are impossible to read but possible to transfer via teleportation

13. Entangled or inseparable continuous variable systems EPR example 1935 2 particles entangled in position/momentum Perfect EPR state Simon PRL (2000) Duan, Giedke, Cirac, Zoller PRL (2000) Necessary and sufficient condition for entanglement EPR state of light Ou, Pereira, Kimble 1992

14. Along x: all tails Along y,z: random misbalance between heads and tails Coherent state of spin-½ atoms y z j=1/2 y z ++ = = N/2 JxJx  J z,y 2 =J x /2=N/4 x Uncorrelated atoms

15. EPR state of two macro-spin systems [J z,J y ] = iJ x N and S condition for entanglement: x y z J1J1 y z J2J2 Along x: all tails Along y,z: ideally no misbalance between heads and tails of the two ensembles, or, at least, less than random misbalance

16. yz y z Two samples oppositely polarized Two entangled samples -x x

17. Total z and y components of two ensembles with equal and opposite macroscopic spins can be determined simulteneously with arbitrary accuracy xx y z z Therefore entangled state with Can be created by measurement

18. How to measure the total spin projections? Send off-resonant light through two atomic samples Measure polarization of light (Faraday effect)

20. Continuous variables Bell measurement Light / Atom - Interaction Lu-Ming Duan, J. I. Cirac,P. Zoller, E. S. Polzik, Phys. Rev. Lett., 85, 5643 (2000) A. Kuzmich and E. S. Polzik, Phys. Rev. Lett., 85, 5639 (2000) Faraday effect: Atomic spins rotate polarization of light z x y  6S, F=4 1/2 6P 3/2 Cesium Back action: Light rotates spins of atoms z x y

21.   pump   pump X Y Z Z Y Entangling beam Polarization detection Entangled state of 2 macroscopic objects J1J1 J2J2

22. 300000310000320000330000340000 0,0000 0,0002 0,0004 0,0006 0,0008 0,00,20,40,60,81,01,21,41,61,82,0 0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4 1,6 1,8 2,0 2,2 2,4 Shot noise level Noise power [arb. units] Frequency (Hz) Density [arb. units] ---------------------------------- 1.00±0.02 0.56±0.01 0.21±0.01 Atomic Quantum Noise Atomic noise power [arb. units] Atomic density [arb. units], Probe polarization noise spectrum Larmor frequency  320kHz Detecting quantum fluctuations of the spin Atomic density (a.u.) 1.0 0.5 0.2 RF frequency z B probe y

23. B-field PBS Time Verifying pulse Entangling pulse 0.5 ms m=4 700MHz 6S 6P Entangling and verifying beams S Entangling and verifying pulses F=3 F=4  = 325kHz m=4 1/2 3/2 y out x2 Optical pumping Pumping beams J  x1 + J  -

25. " P r o b a b i l i t y " Distribution of CCS Distribution of the created entangled state after 0.5ms Uncertainty of the verifying pulse   Entangled spin state 2) Create entangled state and measure the state variance CSS 2F x S y (1pulse) Light (1pulse) Atoms 0246 0.0 0.5 1.0 1.5 2.0

27. Quantum memory Quantum communication protocols with entangled atomic samples and tunable EPR light Entangled atomic samples Entangled (EPR) light source Protocols (proposals) : Teleportation of atomic states Light-to-atoms teleportation Atom-to-light teleportation

28.   Parametric downconversion in a resonator (OPO) P=Im(E)=i( a + - a) E+E+ E-E- X = Re(E)= a + + a When the two fields are separated correlations – entanglement are observed: X-X- X+X+ P-P- P+P+

29. Frequency tunable entangled and squeezed light around 860nm 800MHz AOM LO - LO + - - Cavity modes 10 7 photons per mode { Classical field

30. 0123456 -6 -4 -2 0 2 4 6 8  (X + -X - ) 2 [dB(2 SQL)] Phase [  Radians] 1 { OR Degree of entanglement 0.6 – observed 0.65 – corrected for detector noise (1- perfect )

31. Quantum state of light stored in long lived spins Light with Controlled X and P – controlled quantum state

32. + - AxAx EPR source x p AxAx EbEb EaEa ApAp Actuators EbEb ApAp in Classical channels Quantum channel Furusawa et al Science, 1998 Caltech-Aarhus-Bangor Quantum Teleportation of Light

33. Teleportation of an entangled atomic state 1 2 3 4 Pulse 1 Pulse 1 * Pulse 2 Every measurement changes the single cell spin, BUT does not change the measured sum Every pulse measures both y and z components of the sum – entanglement is created To complete teleportation of Spin 1 to cell 4: rotate spin 4 by A+B+C:

34. EPR spin Alice EPR spin Bob Coherent pulse Operation: Teleportation of atoms Classical channel Memory Bob Distance limitations: Losses of light – fiber (3 dB): 1 km at 850 nm 10 km at 1500 nm space: 100 km (diffraction) OR (Life time of ERP atoms)x(speed of their transport) Currently: (0.001sec)x(Boeing 747) = 30 cm With 1 hour storage = 1000 km Memory Alice

35. Communication networks based on continuous spin variables Continuous variables: polarization state of light spin state of atoms Operation: Storage of light and read-out from atomic memory Memory Alice EPR pulses EPR spins Memory Bob Light - Quantum channel polarization rotation detection of light Symbols : Input-Output interaction: free space off-resonant dipole interaction

36. Brian Julsgaard Christian Schori