2. Niels Bohr Institute Copenhagen University Eugene PolzikLECTURE 5

3. Light – to – light Entanglement resource – parametric downconversion process Atoms – to – atoms Entanglement resource – measurement induced entanglement of two atomic ensembles Light – atoms, etc

4. Parametric Hamiltonian, no dissipation: Equations of motion for field operators: Hamiltonian commutes with the photon number difference operator: In photon number basis: Workhorse of photon entanglement experiments!

5. Parameter: More accurate description : field modes in an optical resonator Entangled cavity modes

6.   Parametric downconversion in a resonator (Optical Parametric Oscillator below threshold) 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+

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

8. 2 0123456 -6 -4 -2 0 2 4 6 8  (X + -X - ) 2 [dB(2 SQL)] Phase [  Radians] Entangled cavity modes Narrowband tunable entangled beams Sorensen, Schori, Polzik PRA, 2002 Necessary and sufficient condition for entanglement Degree of entanglement 0.8 – observed

9. Teleportation principle (canonical variables) L.Vaidman Einstein-Podolsky-Rosen entangled state Demonstrated experimentally for light variables by Furusawa, Sørensen, Fuchs, Braunstein Kimble, Polzik. Science 1998

10. Classical benchmark fidelity for transfer of coherent states Atoms Best classical fidelity 50% e.-m. vacuum K. Hammerer, M.M. Wolf, E.S. Polzik, J.I. Cirac, Phys. Rev. Lett. 94,150503 (2005),

11. Alice |v in  LO p _ LO x DxDx DpDp Victor _ LO V DVDV MpMp MxMx Bob m Bob  out ipip Out In Victor _ _ ixix c vacuum X P Classical teleportation

12. Alice OPO Pump 2 Pump 1 |v in  LO p _ LO x DxDx DpDp Victor _ LO V DVDV MpMp MxMx Bob m Bob  out EP R bea ms a b i ii Classical Information ipip Out In Victor __ ixix c

13. Furusawa et al, Science, Vol 282, Issue 5389, 706-709, 23 October 1998 2 units of Vacuum = 4.8 dB Quantum teleportation

14. Classical boundary

15. conditional rotation detection of light Communication networks based on continuous spin variables Continuous variables: polarization state of light spin state of atoms Input-Output interaction: free space off-resonant dipole interaction Memory Alice EPR pulses Memory Bob EPR spins Quantum channel Memory Alice Memory Bob EPR spin Alice EPR spin Bob Classical channel Coherent pulse Symbols : Operations: Light-atom teleportation Operation: Teleportation of atoms

16. Light-to-Atoms Teleportation z x y k=1 Kuzmich, EP 2000

17. Light pulse Detector Atoms 1 Atoms 2 entangled Proposals: Duan, Cirac, Zoller, EP 2000 Kuzmich, EP. 2000 Atoms X Classical signal Teleported Teleportation of atomic states

18. 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 Atomic Quantum Noise Atomic noise power [arb. units] Atomic density [arb. units] y z Memory in rotating spin states - continued x

19. Teleportation of an entangled atomic state 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 entanglement onto cell 1 and cell 4: rotate spin 4 by A+B+C:

20. Tripartite entanglement Fan HY, Jiang NQ, Lu HL Lance AM, Symul T, Bowen WP, et al. Van Look et al For atomic ensembles via quantum measurement: simple step from 2 to 3 N atoms, spins up N/2 atoms, spins down N/2 atoms, spins down

21. N and S condition for 3-party pairwise entanglement: 1 2 3

22. Coupling strength of the interface Z x y z Initial coherent spin state: degree of squeezing in J z Figure of merit for the quantum interface Duan, Cirac, Zoller, EP PRL (2000) results in distribution Measurement on light Spin squeezed state

23. Figure of merit for the quantum interface Probe scattering parameter:

24. Spontaneous emission – the fundamental limit degree of entanglement Figure of merit for the quantum interface K. Hamerrer, K. Mølmer, E. S. Polzik, J. I. Cirac. PRA 2004, quant-ph/0312156 +  Spontaneous emission probability 0.3 10 3050 Single pass interaction

25. cavity enhanced interaction  enhanced phase shift  power build-up inside cavity compensate with smaller photon number cold atomic cloud T: mirror transmission  : absorption