Cristaux dopés terres rares pour les mémoires quantiques

Cristaux dopés terres rares pour les mémoires quantiques A. Ferrier, M. Lovric, Ph. Goldner D. Suter M.F. Pascual-Winter, R. Cristopher Tongning, Th. Chanelière et J.-L. Le Gouët

Quantum Memory? Storage and retrieval of single photon quantum state RE:Crystal Review W. Tittel et al. Laser & Photon. Rev., 1 (2009) g... g j... g N g... e j... g g... 1 g j... g 1 1 N N 1> Classical system 0> Or 1> Quantum system 0> a 0> + b 1>

Quantum Memory? Storage and retrieval of single photon quantum state RE:Crystal Review W. Tittel et al. Laser & Photon. Rev., 1 (2009) g... g j... g N g... e j... g g... 1 g j... g 1 1 N N Lambda system e> g> g'> Ground state Nuclear spin states

Quantum Memory? Storage and retrieval of single photon quantum state RE:Crystal Review W. Tittel et al. Laser & Photon. Rev., 1 (2009) g... g j... g N g... e j... g g... 1 g j... g 1 1 N N Optical coherence Lambda system e> g> g'> Ground state Nuclear spin states

Quantum Memory? Storage and retrieval of single photon quantum state RE:Crystal g... g j... g N g... e j... g g... 1 g j... g 1 1 N N Review W. Tittel et al. Laser & Photon. Rev., 1 (2009) Quantum memory requirement: High Efficiency (>90%) Lambda system Long storage time (ms) = long coherence time Multimode (increase transmission rate) Large bandwidth (~100 MHz) 69 % Sellars et al. Nature 465 1052 (2011) 3s Sellars PRL 95, 063601 (2005) 1060 modes 1GHz Best results : T. Chanelière New Journal of Physics 13 (2011) 013013

Why Quantum Memory? Quantum Repeaters 1000 km Transmission in telecom fibers = 10-20 EDFA will not preserve quantum states cannot be used with quantum information Quantum Repeaters : extend the maximum distance for secure communication Quantum Memory Bell Measurement Quantum Memory Spontaneous Parametric Down Conversion Entangled Photon pair source Beam splitter Entangled Photon pair source http://quantumrepeaters.eu/ N. Sangourd et al. Rev. Modern Physics 83 33 2011

Quantum Repeaters Bob Alice QM QM QM QM QM QM S S S S S S Bob Alice Quantum channel

Rare Earth Doped Crystals Rare earth ions provide a quantum light matter interface through optical transitions Weak interaction with crystal enviroment Long optical coherence times (T < 4K) 10 µs Energy (cm -1 ) 10 4 10 µs - 1 ms Long hyperfine coherence times (T < 4K) 100 µs 100 µs - 10 ms 10-4 0 Hyperfine levels qubit

Absorption Rare Earth Doped Crystals Rare earth ions provide a quantum light matter interface through optical transitions Weak interaction with crystal enviroment Long optical coherence times (T < 4K) 10 µs Long hyperfine coherence times (T < 4K) 100 µs Large inhomogeneous broadening 100 MHz 10 GHz GHz Y 2 SiO 5 : 0.1 Eu % 1.7 GHz (0.019 nm) Frequency

Rare Earth Doped Crystals Rare earth ions provide a quantum light matter interface through optical transitions Weak interaction with crystal enviroment Long optical coherence times (T < 4K) 10 µs Long hyperfine coherence times (T < 4K) 100 µs Large inhomogeneous broadening 100 MHz 10 GHz Several systems l (nm) = 606 880 580 1550 790 Y 2 SiO 5 YVO 4 Y 2 SiO 5 Y 2 SiO 5 Y 3 Al 5 O 12 Y 2 SiO 5 La 2 (WO 4 ) 3 Y 3 Al 5 O 12 LiNbO 3 :Ti

How to extend the hyperfine T 2? Dynamical decoupling in Pr:LaWO

Two Pulse Photon Echo Excitation of an inhomogeneously broadened line Rephasing Echo : coherent collective emission separated from laser pulses T 2 determination Basic storage scheme /2 1> z z z Time z z y /2 y y y 0> x x x x

Why µs range for the hyperfine T 2? Pr : LaWO Fluctuation of the spin bath = Relaxation c n x c c : correlation time of fluctuation : standard deviation

How to extend the hyperfine T 2? Pr : LaWO Fluctuation of the spin bath c n x c c : correlation time of fluctuation : standard deviation Control of the decoherence : Application of an external magnetic field Dynamical decoupling 1s storage with EIT (Longdell PRL 2005 )

How to extend the hyperfine T 2? /2 Dynamical Decoupling : Bang Bang Phase Time Time

How to extend the hyperfine T 2? Dynamical Decoupling : Bang Bang /2 Phase Time Time

How to extend the hyperfine T 2? Dynamical Decoupling : Bang Bang /2 Phase Time Phase cor Time Time

How to extend the hyperfine T 2? /2 Phase Dynamical Decoupling : Bang Bang Time Phase cor Time Phase Time Time

How to extend the hyperfine T 2? Dynamical Decoupling : Bang Bang /2 Phase Time Time A sequence of -pulses refocuses the coupling to the environment. What happens with photon echo based protocols and larger bandwidths? Optimal RF sequence?

How to extend the hyperfine T 2? Dynamical decoupling in Pr:LaWO

La 2 (WO4) 3 :Pr 3+ I=5/2 (100 % abundance) Low site symmetry Ground state hyperfine transitions: T1 = 16 s T2 (hyperfin) = 250 µs EIT, Spin Hamiltonian, ZEFOZ effect shown/determined P. Goldner et al. PRB 2007, 2009, 2011, PRA 2009, J.Phys. B 2012 25

Photon Echo Memory Extending storage time in the ms range Excitation pulse Rephasing pulse Photon echo Excitation pulse Transfer pulses Time Rephasing pulse Photon echo Dynamical decoupling Time RF rephasing pulses 26

RF Sequences? Compensate for slow changes in the environment z z z Series of π pulses CP sequence y y y Pulse errors x x z z z x Series of π-δ pulses loss of coherence y y y x x x z z z Series of ±(π-δ) pulses coherence preserved CPMG2 sequence y y y x x x 27

Studied RF Sequences 2 RF pulses sequence: τ/2 - π - τ - π - τ/2 CP sequence: [τ/2 - π - τ - π - τ/2] N CPMG2 sequence: [τ/2 - π - τ - (-π) - τ/2] N Preserving arbitrary initial phases KDD sequence: [KDD 0 KDD π/2 - KDD 0 - KDD π/2 ] N KDD φ = [τ/2 - π π/6+ φ - τ - π φ - τ - π π/2+φ - τ - π φ - τ - π π/6+ φ - τ/2 ] 28 Souza et al, PRL 2011

Optical to Spin Transfer in Pr 3+ :La2(WO4)3 Input: 500 ns Transfer: 1 µs RF pulses: 5 µs Rephasing RF pulses Output Rephasing Input Transfer Transfer Detection gate 29

Storage Times 30 µs Retrieval efficiency 30 10-1 10-2 10-3 10-4 Storage time CPMG2 T2 = 8.8 ms KDD T2 = 1.3 ms 2 RF T2 = 250 µs 0 2 4 6 8 10 12 14 16 18 20 Storage time (ms)

Coherent Raman Scattering Initial coherence created by a RF pulse 31

Relative Optical Phase 1 CP 3ms 1 a 1 b T T T RF rephasing pulses Time 32 M. Lovric et al arxiv:1302.3358

Relative Optical Phase 1 1 a +2 b 2 CP 3ms 2 1b a T T T Time RF rephasing pulses 33 M. Lovric et al arxiv:1302.3358

Relative Optical Phase 1 1 a +2 b 2 CP 3ms 2 1b a T T T Time RF rephasing pulses Relative optical phase (degrees) 34 M. Lovric et al arxiv:1302.3358

Conclusion Extension of hyperfine T 2 by Dynamical Decoupling on two different systems Tm : YAG (B 0) Dynamical decoupling increase spin coherence lifetime from 1.1ms up to 230 ms nearly 220 times Model with good agreement with experiment Pr: LAWO (B=0) 20 ms storage time achieved on a 2 MHz absorption line Dynamical decoupling increases storage time by nearly 40 times Relative optical phases preserved 35

Thank you for your attention! LAC LCMCP Funding: ANR (RAMACO), EU (QUREP, CIPRIS) 36

QM QM QM QM QM QM S S S S S S

Quantum Memories Requirements High fidelity released photon quantum state identical to stored one decoherence, added noise High efficiency probability of releasing a photon after storage 1 reabsorption Long storage time 1 10 ms (only secret key transmission: 1 b/s) Large bandwidth high rate photon pair sources (100 MHz) Multimode storage storing and measuring many photons improves data rate

Spectral Tailoring Long population lifetimes for hyperfine levels (16 s) "permanent" structure Signal absorption 2 MHz 41

Transfer efficiency OTSS 97.5% compared to TPPE OTSS 0.45 % compared to input pulse 42

Storage Times 30 µs Storage time CPMG2 T2 = 8.8 ms CP T2 = 8.8 ms KDD T2 = 1.3 ms 2 RF T2 = 250 µs 45

Dynamical Decoupling, Theory Vs Experiment CPMG

Minimize ihn? Magnetic Field M.F. Pascual-Winter et al. PHYSICAL REVIEW B 86, 184301 (2012) Spin sublevel splitting per Tesla Maximum or minimum?

Minimize ihn? Magnetic Field Spin sublevel splitting Rabi frequency Vs B [100] =54.8 et =45

Minimize ihn? Magnetic Field =54.8 et =45 Bext = 1T Expected : Γ Inh spin ~15kHz Γ Inh spin ~100kHz

c c Transmission I max 50 % I max 0 t M.F. Pascual-Winter et al. PHYSICAL REVIEW B 86, 184301 (2012)

c c Transmission Pompage optique I max 50 % I max 0 M.F. Pascual-Winter et al. PHYSICAL REVIEW B 86, 184301 (2012)

c c Transmission I max 50 % I max Pulse RF 0 /2 M.F. Pascual-Winter et al. PHYSICAL REVIEW B 86, 184301 (201

c c Transmission Population probe I max 50 % I max 0 Pulse RF /2 /2 M.F. Pascual-Winter et al. PHYSICAL REVIEW B 86, 184301 (201

Dynamical decoupling in Tm:YAG 3 H 4 (0) m I =1/2 m I =-1/2 Large oscillator strength Well known crystal growth 793 nm 27 Al 3+ nuclear spin 3.64 3 H 6 (0) B=0 B 0 m I =1/2 m I =-1/2 large anisotropy of magnetic gyromagnetic tensor xx = zz =20 MHz/T yy = 400Mhz/T Γ Inh spin ~500kHz M.F. Pascual-Winter et al. PHYSICAL REVIEW B 86, 184301 (2012)

Spin echo RF Pulse /2 /2 Theoritical model c t >> c c = 172 µs = 3 khz T 2 =1.01ms

How to extend the hyperfine T 2? Dynamical decoupling in Pr:LaWO Dynamical decoupling in Tm:YAG

Dynamical decoupling in Tm:YAG M.F. Pascual-Winter et al. PHYSICAL REVIEW B 86, 184301 (2012) CPMG T 2 =230 ms 220 time increase T 2 =1.01 ms

Long optical storage in a rare earth doped crystal using dynamical decoupling Marko Lovrić 1, Dieter Suter 1, Alban Ferrier 2, Philippe Goldner 2 1 Technische Universität Dortmund Fachbereich Physik Dortmund, Germany 2 Condensed Matter Chemistry Laboratory Chimie-Paristech CNRS UPMC Paris, France LPHYS 2012, 23-27 July 2012, Calgary, Canada

Rare Earth Doped Crystals Energy (cm -1 ) 10 4 10-4 0 10 µs - 1 ms 100 µs - 10 ms Hyperfine levels Rare earth ions provide a quantum light matter interface through optical transitions Optical coherence can be transferred to nuclear spins (I 0 - hyperfine levels) Hyperfine T2 longer Long storage time for quantum memories 61

Storage times of Optical Memories Pr 3+ :Y2SiO5 EIT: several seconds!! (Longdell et al, PRL 2005, G. Heinze et al. CIPRIS meeting 2012: 7.5 s) Hyperfine T2: 500 µs Spins decoupled by magnetic field (static) + RF pulses (dynamic) Low bandwidth (10 khz) AFC: 20 µs (M. Afzelius et al. PRL 2010) No hyperfine rephasing Larger bandwidth (2 MHz) What happens with photon echo based protocols allowing larger bandwidths? Optimal dynamical decoupling? 62