Danmarks Grundforskningsfond - Quantum Optics Center

1. QUANTOP Danmarks Grundforskningsfond - Quantum Optics Center Quantum teleportation between light and matter Niels Bohr Institute Copenhagen University

2. Experiment Niels Bohr Institute Jacob Sherson Hanna Krauter Rasmus Olsson Brian Julsgaard* Theory Max Planck Institute Klemens Hammerer Ignacio Cirac J. Sherson, H. Krauter, R. K. Olsson, B. Julsgaard, K. Hammerer, I. Cirac, and ESP; quant-ph/0605095 , to appear in Nature

3. Challenge of Quantum Teleportation: transfer two non-commuting operators from one system onto another (Heisenberg picture) equivalent to: Transfer an unknown quantum state from one system onto another (Schördinger picture) Teleportation experiments so far: Light onto light:Innsbruck(97), Rome(97), Caltech(98), Geneva, Tokyo, Canberra… Single ion onto siingle ion: Boulder (04), Innsbruck (04)

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

5. Y,Q Bell measurement Atomic cloud N=1012 <n> = 0 – 500 photons Teleportation cartoon

6. t Pulse: Canonical operators for light Coherent state:

7. Vacuum Coherent Single photon Adding a strong field and defining Stokes operators S1 S3 S2 Strong field Quantum field x Polarizing cube

8. Teleported operators - upper sideband mode: Encoding quantum states in frequency sidebands

9. Rotating frame spin Atomic operators Atoms: ground state Caesium Zeeman sublevels 4 3

10. Canonical operators for a spin polarized atomic ensemble: Jx Jz Coherent spin state 4 3 Jy

11. Teleportation of light onto a macroscopic atomic sample

12. Teleportation step 1: entanglement

13. Upper sideband is teleported Light+Atoms: entangling Hamiltonian Off-resonant interaction entangles light and atoms D = 800 MHz 6P3/2 W = 0.3 MHz 6S1/2 + magnetic field

14. Addition of amagnetic fieldcouples light to rotating spin states B y z Atomic Quantum Noise 2,4 2,2 2,0 1,8 1,6 1,4 1,2 Atomic noise power [arb. units] 1,0 0,8 0,6 0,4 0,2 0,0 0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4 1,6 1,8 2,0 Atomic density [arb. units]

15. Entanglement of light and atoms Entanglement criterion (Duan et al, 2000): E.g., for k = 2 and similar for K. Hammerer, E.S.P., J.I. Cirac. Phys. Rev. A72, 052313 (2005).

16. Geometrical picture of the light-atoms entangled state Jx S1 Jz S3 Jy S2 Atoms Light

17. Teleportation step 2: Bell measurement

18. q y

19. Teleportation step 3: classical communication

20. 322 kHz RF field Magnetic shields

21. Teleportation experiment Teleported operators:

22. Teleportation step 4: verification

23. Mean values of operators Variances

24. Teleportation of coherent state n ≈ 500

25. Teleported state readout determines atomic variance Input state readout Teleportation of a vacuum state of light

26. Teleportation of a coherent state, n ≈ 5

27. Atomic variances are below a critical value Mean values of operators are transferred

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

29. Raw data: atomic state for <n>=5 input photonic state Reconstructed teleported state, F=0.58±0.02

30. Experimental quantum fidelity versus best classical case Upper bound on <n> ≈ 1000 – due to gain instability F quantum F classical = Anticipated qubit fidelity: Fqubit =72% (with feasible imperfections) Optimal gain

32. Summary: • Teleportation between two mesoscopic objects of different nature – • a photonic pulse and an atomic ensemble demonstrated • Distance 0.5 meter, can be increased (limited mainly • by propagation losses) • Extention to qubit teleportation possible • Fidelity can approach 100% with more sophisticated measurement • procedure plus using squeezed light as a probe J. Sherson, H. Krauter, R. K. Olsson, B. Julsgaard, K. Hammerer, I. Cirac, and ESP; quant-ph/0605095 , accepted by Nature

33. Odd-number Fock state source compatible with atomic memories J. S. Neergaard-Nielsen, B. Melholt Nielsen, C. Hettich , K. Mølmer, E. S. P. To appear in Phys.Rev.Lett. quant-ph/0602198. Other sources of single photons compatible with atoms: Cavity QED: Kimble, Rempe Atomic ensembles: Lukin, Kimble, Kuzmich Similar results with a fsec source Grangier et al, Science 2006

34. delay line Squeezed state: Atoms homodyning Photon subtracted squeezed vacuum Squeezed cavity mode T=0.03 filter OPO APD After photon subtraction pulse Low gain: shaper Higher gain:

36. Tomography of the photon subtracted squeezed vacuum

37. Low squeezing Higher squeezing Theory • Frequency bandwidth ≈ 10 MHz • Perfect Gaussian spatial mode • Tunable to Cs resonance

38. Summary: • Teleportation between two mesoscopic objects of different nature – • a photonic pulse and an atomic ensemble demonstrated • Distance 0.5 meter, can be increased (limited by propagation losses) • Extention to qubit teleportation possible • Fidelity can approach 100% with more sophisticated measurement • procedure plus using squeezed light as a probe