- Quantum Storage of Photonic Entanglement in Nd:Y 2 SiO 5 - Towards a complete AFC quantum memory in Eu:Y 2 SiO 5 Imam Usmani, Christoph Clausen, Félix Bussières, Björn Lauritzen, Nuala Timoney, Mikael Afzelius, Hugues de Riedmatten, Nicolas Sangouard, Nicolas Gisin Group of Applied Physics, University of Geneva - Switzerland

 Coherent and reversible mapping of entanglement between photons (flying qubits) and atoms (stationary qubits)  Enables entanglement of remote material systems  A resource for future quantum repeaters/quantum networks  Solid-state resources could provide a scalable and affordable solution Light-matter interfaces For Quantum Networks Quantum Channel Quantum Channel Quantum Node Quantum Node Genève Bern Zurich

Photon Emissive quantum memory ‣Single atoms/ions: Blinov et al, Nature 428, 153 (2004) Volz et al, PRL 96, (2006) H. P. Specht, doi: /nature09997 ‣NV centers: Togan et al, Nature 466, 730 (2010) ‣Atomic ensembles (DLCZ): Matsukevich et al, PRL 95, (2005) de Riedmatten et al, PRL 97, (2006) Continous variables quantum memory J. Sherson et al., Nature 443, 557 (2006) SPDC + quantum memory ‣Single ions: Piro et. al., Nature Phys. 7, (2011) ‣Atomic ensembles: Jin et al, arXiv: (2010) + No atom trapping + One telecom photon Light-matter entanglement in quantum information science

Building a Quantum Memory with an Atomic Ensemble Collective interference  Collective enhancement factor N Before absorption After re-emission All atoms in ground state1 photon in optical mode k After absorption Huge superposition state! Macroscopic number N= Spatial phase imprinted onto the atomic ensemble K. Hammerer, A.S. Sorensen, E.S. Polzik, RMP 82, 1041 (2010) A. I. Lvovsky, B. C. Sanders, W. Tittel, Nature Photonics 3, 706 (2009)

Properties of RE-doped crystals  Weak interaction with crystal enviroment - "atom" like energy structure for 4f-4f transitions - "frozen gas" of ions, no motional decoherence  High number of stationary ions ( ) - strong light-matter coupling  Long optical coherence times (T < 4K), T 2 opt = 1  s – 1 ms (  h = 300 kHz – 300 Hz)  Long hyperfine coherence times (T < 4K), T 2 hyp = 1 ms – 1 s  Large inhomogeneous broadenings 100 MHz – 10 GHz Inhomogeneous ensemble (eg. RE-crystals) Non-directional, spontaneous re- emission at random time Absorption Frequency GHz dephasing! Self-rephasing using spectral tailoring? Quantum Memory in an Rare-earth Ensemble (nm) = REVIEW: W. Tittel, M. Afzelius, T. Chanelière, R. L. Cone, S. Kröll, S. A. Moiseev, and M. Sellars, Laser & Photon. Rev., 1 (2009) Y 2 SiO 5 Crystal Low Nuclear Spin Density

Inhomogeneous ensemble (eg. RE-crystals) Absorption Frequency GHz Non-directional, spontaneous re-emission at random time dephasing! How to rephase the coherence? Quantum Memory in an Rare-earth Ensemble (nm) =

AFC preparation Photon Signal Time Preparation Photon Echo Control Echo 2 levels: preprogrammed delay (AFC echo) 3 levels: on-demand re- emission (spin wave storage) M. Afzelius et al. PRA 79, (2009) Periodic! Atomic Frequency Comb (AFC) Quantum Memory Multimode !

Detector noise Counts [/200s] Phase [rad] Nature 456, 773 (2008) Nature Comm. 1, 12, 2010 Recent AFC/CRIB progress at UNIGE Telecom Memory

Entanglement source : Photon pair source by Spontaneous Parametric down Conversion (SPDC) A light matter interface : Quantum Memory in a Nd3+ doped crystal Entanglement measurement : Energy-time entanglement Franson experiment This experiment: Light-Matter Entanglement Ingredients:

45 MHz 1.5 THz Storing a single photon generated by SPDC : technical challenges ‣Strong filtering to match the 100 MHz bandwidth of our quantum memory : from 1.5 THz to 45 MHz! ‣Lock pump’s wavelength to satisfy energy conservation A Narrowband SPDC source of Energy-time entangled photons ~ 6 GHz ~100 MHz

A bit more complicated in reality… &

Crystal Cold finger 3 K Frequency  Storage of a heralded photon in Nd 3+ :Y 2 SiO 5 Experimental comb Optimal AFC efficiency using square peaks M. Bonarota et al., Phys. Rev. A 81, (2010)

Signal-Idler cross-correlation vs. storage time C. Clausen, I.Usmani, F. Bussières, M Afzelius, N. Sangouard, H. de Riedmatten and N. Gisin, Nature 469, 508 (2011)

Energy-time entanglement : Photons created simultaneously within  c Creation is uncertain (in a quantum sense) to within the coherence time of pump  p Thus their creation time are entangled! Energy-time entanglement from a SPDC source CW PUMPED SPDC SOURCE

fiber interferometer Franson interferometer Energy-time entanglement : Photons created simultaneously within  c Creation is uncertain (in a quantum sense) to within the coherence time of pump  p Thus their creation time are entangled! Interference short-short long-long Interference short-short long-long Energy-time entanglement from a SPDC source

C. Clausen, I.Usmani, F. Bussières, M Afzelius, N. Sangouard, H. de Riedmatten and N. Gisin, Nature 469, 508 (2011) Alice’s analyser (fibered interferometer) Entanglement verification by violation of Bell inequality Bob’s analyser ("interferometer" in the crystal) Crystal Quantum Memory Light-matter entanglement

Bob’s measurement choice (phase) C. Clausen, I.Usmani, F. Bussières, M Afzelius, N. Sangouard, H. de Riedmatten and N. Gisin, Nature 469, 508 (2011) Entanglement verification by violation of Bell inequality Coincidences in central peak Violation of Bell-CHSH inequality Witness of light-matter entanglement Light-matter entanglement

Similar experiment by the group of Wolfgang Tittel (U. of Calgary) E. Saglamyurek, N. Sinclair, J. Jin, J. A. Slater, D. Oblak, F. Bussières, M. George, R. Ricken, W. Sohler & W. Tittel. Nature 469, 512 (2011). Tm 3+ :LiNbO 3 Waveguide - 5 GHz - 7 ns storage Light-matter entanglement

OUTLOOK Entangling excitation stored in two crystals Single photon Single photon Heralded entangled state of two crystal QMs Memory A Memory B PREVIOUS WORK: K. S. Choi, H. Deng, J. Laurat & H. J. Kimble, Nature 452, 67 (2008) J. Laurat, K. S. Choi, H. Deng, C. W. Chou, and H. J. Kimble, Phys. Rev. Lett. 99, (2007)

CONCLUSIONS NEODYMIUM PART Development of frequency stabilized narrowband SPDC source Storage of a heralded single photon in Nd:Y 2 SiO 5 crystal Demonstration of entanglement between a telecom photon and a stored excitation

Quantum Communication (QC) Alice Bob Photon source   qubit Genève Neuchâtel High-speed Quantum Cryptography Field Experiment Fiber length: L ~150km Losses: 43 dB (0.29dB/km) Base Freq: >300 Mbits/s Secret bit key rate: 2.5 bits/s (average value over 3 h !) Damien Stucki et al., arXiv:

1 click Initial state Pump Memory SPDC source A SPDC source B A more concrete example!! Conditional state (one click!) Heralded entangled state of remote QM

Long-distance QC - Quantum Repeater A Z The average time to establish entanglement between A and Z is polynomial in the time to create the entanglement in one link, eg. AB. H.J. Briegel W.Dur, J.I. Cirac, P.Zoller, PRL 81, 5932 (1998) L.M. Duan, M.D. Lukin, J.I. Cirac, P.Zoller, Nature 414, 413 (2001) Requires heralded creation, storage and swapping of entanglement. B Entanglement swapping CD AD A Z Create entanglement independently for each link. Extend by swapping.

Ensemble based Quantum Memory Quantum Physical system: Must preserve the quantum state of the photon Quantum memory Typically: Coherent atoms Two important properties: - Efficiency - Conditional fidelity F=1 means an output photon with the same state as the input photon WRITE The goal of the quantum memory is to temporarily store the quantum state of a photon READ

Atomic density Atomic detuning  Output mode Input mode State after absorption Atomic Frequency Comb (AFC) Quantum Memory Ensemble of inhomogeneously broadened atoms Intensity Time Input mode Output mode Control fields Storage state Dephasing Periodic structure => Rephasing after a time Collective emission in the forward mode. Photon echo like emission Intensity Time Input mode Output mode  (superradiant Dicke state) M. Afzelius, C. Simon, H. de Riedmatten and N. Gisin, Phys Rev A 79, (2009)

  Atomic detuning  Finesse dd Efficiency vs optical depth (theory) M. Afzelius et al. PRA 79, (2009)

Efficient Storage of multiple temporal modes N pulses, total duration T p QM   Atomic density Atomic detuning  pp  Number of modes limited by minimal  and maximal  Does not depend on d AFC

Input mode Output mode Control fields  1/2  3/2  5/2  1/2  3/2  5/ MHz 606 nm 3H43H4 1D21D2 AFC storage experiment in Pr 3+ :Y 2 SiO 5 Output M. Afzelius et al (2009) Up to 20 microseconds storage time Longer possible using spin echo control (up to 1 seconds)!

Stabilized ring dye-laser at 606 nm with 1-kHz bandwidth Optical cryostat with Pr:Y 2 SiO 5 crystal

Multi-mode storage in Nd 3+ :Y 2 SiO 5 Storage efficiency as a function of storage time (one mode) Weak coherent input states  n  < 1

Multi-mode storage in Nd 3+ :Y 2 SiO 5 Mapping 64 input modes onto one crystal  n  < 1 per mode 64 time modes can be used to code 32 time-bin qubits! Largest qubit memory achieved so far.

Multi-mode storage in Nd 3+ :Y 2 SiO 5 Multimode (11 modes) interference experiment to check coherence! Consecutive modes are interfering with a different phase difference:

Numerical example of efficient multi-mode storage in Eu 3+ :Y 2 SiO 5 Optical transition at 580 nm Optical homogenenous linewidth = 122 Hz Spin coherence time = 36 ms Optical depth d = 4 cm -1 Eu 3+ :Y 2 SiO 5 properties: AFC numerical simulation: Peak width = 2 kHz Peak separation = 20 kHz Finesse = 10 Total AFC bandwidth = 12 MHz d=40 Efficient (90%) storage of 100 modes in ONE memory (30 shown below)

Cavity-enhanced Quantum Memory The idea…. Takes a 1% efficient QM to >90%