2. Memory must be able to store independently prepared states of light The state of light must be mapped onto the memory with the fidelity higher than the fidelity of the best classical recording The memory must be readable B. Julsgaard, J. Sherson, J. Fiurášek, I. Cirac, and E. S. Polzik Nature, 432, 482 (2004); quant-ph/0410072.

3. These criteria should be met for memory in: Quantum computing with linear operations Quantum buffer for light More efficient repeaters Quantum Key storage in quantum cryptography

4. Mapping a Quantum State of Light onto Atomic Ensemble Squeezed Light pulse 1 > 2 > Atoms The beginning. Complete absorption 0 > Proposal: Kuzmich, Mølmer, EP PRL 79, 4782 (1997) Experiment: Hald, Sørensen, Schori, EP PRL 83, 1319 (1999) Spin Squeezed Atoms Very inefficient lives only nseconds, but a nice first try…

5. Light pulse – consisting of two modes Strong driving Weak quantum or more atomic samples Dipole off-resonant interaction entangles light and atoms Projection measurement on light can be made… …and feedback applied

6. Teleportation in the X,P representation x,p Bell measurement

7. Today: another idea for (remote) state transfer and its experimental implementation for quantum memory for light Projection measurement X See also work on quantum cloning: J. Fiurasek, N. Cerf, and E.S. Polzik, Phys.Rev.Lett. 93, 180501 (2004)

8. Implementation: light-to-matter state transfer No prior entanglement necessary = C - C squeeze atoms first F≈80% F →100% B. Julsgaard, J. Sherson, J. Fiurášek, I. Cirac, and E. S. Polzik Nature, 432, 482 (2004); quant-ph/0410072. Cesium atoms Feedback magnetic coils

9. 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),

10. Preparation of the input state of light x EOM S1S1 Polarization state Input quantum field Vacuum Coherent Squeezed Strong field A(t) Quantum field - X,P Polarizing cube P X

11. PLPL Quantum memory – Step 1 - interaction Light rotates atomic spin – Stark shift Input light Output light Atomic spin rotates polarization of light – Faraday effect XLXL

12. Quantum memory – Step 2 - measurement + feedback PLPL XLXL Polarization measurement Feedback to spin rotation Compare to the best classical recording c Fidelity – > 100% (82% without SS atoms)

14. Encoding the quantum states in frequency sidebands

15. Memory in atomic Zeeman coherences Cesium 4 3 2 Rotating frame spin

16. 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

17. 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

18. y z x

20. Stored state versus Input state: mean amplitudes X in ~ S Zin P in ~ S Yin Magnetic feedback X plane Y plane read write t outputinput  / 2 - rotation

21. Stored state: variances =1/2 3.0 Absolute quantum/classical border Perfect mapping

22. Fidelity of quantum storage - State overlap averaged over the set of input states F 0.820.840.860.880.9 0.54 0.56 0.58 0.62 0.64 Gain Experiment Best classical mapping Coherent states with 0 < n <8 0.650.70.750.80.850.9 0.56 0.58 0.62 0.64 0.66 0.68 Coherent states with 0 < n <4 Experiment Best classical mapping

23. Quantum memory lifetime

24. Deterministic Atomic Quantum Memory proposed and demonstrated for coherent states with in the range 0 to 10; lifetime=4msec Fidelity up to 70%, markedly higher than best classical mapping