1. cone@montana.edu wtittel@ucalgary.ca Rufus L. Cone Department for Physics Montana State University Bozeman, Montana, USA Photon-echo type storage of quantum information using rare-earth-ion doped crystals Wolfgang Tittel Institute for Quantum Information Science and Department of Physics & Astronomy University of Calgary Calgary, Alberta, Canada

2. cone@montana.edu wtittel@ucalgary.ca Rare-Earth-Activated Optical Materials Efficient, High-Power, Long-Lived IR, Visible, & UV Lasers –Nd 3+ :YAG and Yb 3+ :YAG lasers for high power –Nd 3+ :YAG doubled for green pointers –Nd 3+ :YVO 4 doubled for watts of green –Ho 3+, Er 3+, Tm 3+, … medical, dental, and industrial devices, … Phosphors, Displays, Hg-Free Lamps, Solid-State Lighting –Red Eu 3+ :Y 2 O 2 S, a critical factor in success of color TV –Blue Eu 2+ phosphors –Green Tb 3+ :(Ln, Ce)PO 4 phosphor –White light by phosphors & diodes –Electroluminescent semiconductors with rare-earth ions Scintillators, Digital X-Ray Imaging, CAT and PET Scans, Particle Physics, and Oil Exploration, … –Lu 3+ provides high density for efficient absorption –Some of the fastest and most efficient scintillator materials such as CeF 3, Ce 3+ :YAlO 3, and Ce 3+ :Lu 2 SiO 5 Spectral Hole Burning Devices –High bandwidth analog signal processing –Lasers stabilized to 2 parts in 10 13 –Stabilized lasers for local oscillator in atomic clock –Optical data storage Quantum Information Devices –Eu 3+ :Y 2 SiO 5, Pr 3+ :Y 2 SiO 5, Er 3+ :Y 2 SiO 5, Tm 3+ :YAG, Tm 3+ :LiNbO 3, Er 3+ :LiNbO 3 –Er-doped optical fiber

3. cone@montana.edu wtittel@ucalgary.ca Photon-echo type storage of quantum information using rare-earth-ion doped crystals - QIP, quantum memory, dream and reality - Two-pulse photon-echo-based storage of light - Photon-echo quantum memory (CRIB & AFC) - Spectroscopic investigations of RE crystals for quantum memory - Quantum state storage in RE crystals - Conclusion WT, M. Afzelius, T. Chanelière, RLC, S. Kröll, S.A. Moiseev, and M. Sellars, Las. Phot. Rev. 2010

4. cone@montana.edu wtittel@ucalgary.ca Quantum information processing Encoding information in quantum states of light allows doing some tasks better (as compared to classical encoding) -Quantum computing -promises solving certain computational tasks in polynomial time -classical computers require exponentially increasing resources -Quantum Communication -promises information-theoretic secure encryption -provides strong forward security (that does not break down in the event of a quantum computer) -QIP requires generation, (transmission), processing and detection of quantum states

5. cone@montana.edu wtittel@ucalgary.ca Quantum memory, a synchronization device for quantum data Lvovsky, Sanders, WT, Nature Photonics (2010); Simon et al., quant-ph (2010) |>|> QM |>|> |>|> |>|> 01010 01000

6. cone@montana.edu wtittel@ucalgary.ca Quantum memory: dream and reality PropertyDesired performance State-of-the-art (quantum & classical memory) Efficiency≈10.69 Fidelity≈10.92* Multi-mode storage capacity high64 modes (>1000) Pulse duration≤ ns700 ps Storage time> sec>2 sec Complexitysimple… Hedges et al., Nature 2010; X.-M. Jin et al., arXiv (2010); Usmani et al., Nature Comm. (2010); Chanelière, ISOMQIS 2010; Tittel et al., ISOMQIS 2010; Longdell et al., PRL (2005) Different storage media and protocols * post selected

7. cone@montana.edu wtittel@ucalgary.ca Storage of light using two-pulse photon-echoes Kopvil’em & Nagibarov, Fiz. Metall. Metalloved. (1963) Kurnit, Abella & Hartmann, Phys. Rev. Lett. (1964), Mossberg, Opt. Lett. (1982)  hom frequency absorption  /2-pulse t electric field amplitude  pulse  u v dephasing =0=0 >0>0 <0<0  -pulse  0 <0<0 rephasing echo-pulse   echo at t=2  u v w allows data storage!

8. cone@montana.edu wtittel@ucalgary.ca Photon storage using two-pulse photon-echoes Massar & Popescu, PRL (1995); Ruggiero et al, PRA (2009); Sanguard, WT et al., PRA (in press) u v w -Storage of a weak (single photon) input followed by  pulse inverts the atomic medium - spontaneous emission of photons in random states (polarization, time) adds noise -> decreased fidelity of output with input state P echo = P noise   out = F  in +(1-F)  in F = tr(  in  out ) = 2/3 = F classical (max)

9. cone@montana.edu wtittel@ucalgary.ca Photon-echo quantum memory (CRIB) 1.Preparation of an optically thick, single absorption line 2.Controlled reversible inhomogeneous broadening (CRIB) 3.Absorption of light in arbitrary quantum state -> fast dephasing 4.Reduction of broadening to zero 5.Phase matching:  (z) = -2kz ; E in  e ikz  E out  e -ikz 6.Reestablishment of broadening, with reversed sign frequency absorption (interaction with external electric field) -> Time reversed evolution of atomic system and reemission of light in backward direction with unity efficiency and fidelity  frequency absorption  hom frequency opt. depth Moiseev et al., PRL (2001); Nilsson et al., Opt. Comm. (2005); Kraus, WT et al., PRA(2006); Alexander et al., PRL (2006); Hoseini et al., Nature 2009; Hedges et al., Nature (2010); WT, RLC, et al., Las. Phot. Revs. (2010).  i -> -  i  i  i =  i t

10. cone@montana.edu wtittel@ucalgary.ca Photon-echo quantum memory (AFC) 1.Preparation of an atomic frequency comb 2.Absorption of light in arbitrary quantum state -> fast dephasing and repetitive rephasing at t n = 1/ comb with 2  i t n = n 2  3.Phase matching  (z) = -2kz enables backwards recall 4.Reversible mapping of optical coherence onto spin coherence allows recall on demand frequency absorption -> Reemission of light with unity efficiency and fidelity, very good multi-mode storage capacities frequency absorption  hom Hesselink et al., PRL (1979); Afzelius et al., PRA (2009); De Riedmatten et al., Nature. (2008); Afzelius et al., PRL (2010); Usmani et al., Nature Com. (2010). comb 

11. cone@montana.edu wtittel@ucalgary.ca Why solid state quantum memory? - Compared to atomic vapors, optical centers in solids do not move -> allows for longer storage times -> no laser cooling necessary - Many possibilities (color centers in diamond, RE ions in crystals, quantum dots,..) - More degrees of freedom to explore (and master) -> spectroscopy needed

12. cone@montana.edu wtittel@ucalgary.ca What Makes Rare Earth-Doped Crystals Special? Why Use Solid State Materials for Quantum Memory? Compared to Atomic Vapors, Ions in Solids Do Not Move Allows for longer storage times No laser cooling necessary Only the Transition Elements Form Stable Compounds with Partially Filled Electron Shells Needed for a Resonant Optical Material Transition metals (3d N, 4d N, or 5d N ), Rare earths (4f N ), Actinides (5f N ) Localized electronic transitions & sharp lines Wavelengths range from far-IR to vacuum-ultraviolet Rare-Earth Ions Set Apart from Others 4f electrons remain highly localized within the ion Optical transitions maintain much of an atomic-like character even in a crystalline solid  Atomic-Like Behavior and Strong Localization of the 4f Electrons Many Options for Ions & Crystal Hosts Sharp Contrast to Transition Metal d Electrons d electrons are involved in chemical bonding  strongly affected by host lattice d electrons may show significant delocalization and mixing with electronic states of other ions in the lattice Actinide 5f Electrons Provide an Intermediate Case, Properties Vary Depending on the Material

13. cone@montana.edu wtittel@ucalgary.ca Lanthanide Contraction Mayer (1941)/Meggers (1947) Strong Coulomb potential draws 4f electrons nearer to nucleus due to imperfect shielding of one 4f by another Lowest-energy electrons are not the outermost electrons The 5s 2 5p 6 closed shells “shield” the 4f N electrons from the crystal environment 4f N electrons maintain most of free ion atom-like character in a crystal Also responsible for chemical similarity of rare-earth ions Rare Earth 3+ Ions r (arbitrary units)

14. cone@montana.edu wtittel@ucalgary.ca Summary of Special Rare Earth Properties 4f N to 4f N Optical Transitions of Rare Earths in Solids Can  Be long lived; optical T 1 ~ 10 ms observed  Have high fluorescence quantum efficiency ~100%  Have exceptional coherence properties:  Optical T 2 ~ 4 ms observed  Spin coherence up to 30 s  Be surprisingly sharp;  h ~ 75 Hz observed  Vary slowly in frequency from material to material  Can be “compositionally” tuned These properties can be achieved at number densities of 10 18 /cm 3 or more.

15. cone@montana.edu wtittel@ucalgary.ca Principal Transitions for Spectral Hole Burning and Lasers Echo, Hole Burning, and QIP Commercial Solid State Lasers

16. cone@montana.edu wtittel@ucalgary.ca Optical Linewidths of Ions in Crystals Room temperature Lines are homogeneously broadened by phonons  h = 60 – 1000 GHz 2 – 30 cm -1 Crossover to inhomogeneous broadening occurs ~ 77 K Strain and inhomogeneity Narrowest homogeneous transitions occur for Lowest component of Ground multiplet to lowest component of an Excited multiplet Low temperatures ~1.5 to 10 K (cryocoolers or helium)  inh = 1 - 30 GHz, or more depending on ion concentration  inh > 200 – 300 GHz with disorder  h = 15 Hz to a few kHz, in favorable cases that are lifetime-limited ~ 75 Hz observed in several crystal systems in our laboratory Er 3+ :Y 2 SiO 5 and Eu 3+ :Y 2 SiO 5 Provides TREMENDOUS ratio:  inh /  h ~ 10 5... 10 8

17. cone@montana.edu wtittel@ucalgary.ca Excite a subset of ions with a narrow-band laser Excited ions are temporarily or permanently removed from the absorbing population  inh : 10’s to 100’s of GHz  h : as low as ~ 50 Hz  inh /  h ~ 10 5... 10 8 Persistent Holes Weeks to indefinite Transient Holes 10 ms lifetimes absorption frequency Spectral hole  inh hh f Laser Spectral Hole Burning … and Spectral Recording

18. cone@montana.edu wtittel@ucalgary.ca Spectral hole burning allows tailoring the line shape for Quantum Memory Protocols such as CRIB & AFC  inh : 10’s to 100’s of GHz  h : as low as ~ 50 Hz  inh /  h ~ 10 5... 10 8 Persistent Holes Weeks to indefinite Transient Holes 10 ms lifetimes absorption frequency Spectral hole  inh hh f Laser Spectral Hole Burning … and Spectral Recording

19. cone@montana.edu wtittel@ucalgary.ca Spectral Hole Burning Mechanisms & Lifetimes Two-level saturation Population storage in the excited state (ms to ns or less) Er 3+ :Y 2 SiO 5 with lifetime T 1 = 11 ms  h = 75 Hz – several kHz possible Optical pumping of hyperfine levels in Eu 3+ :Y 2 SiO 5  h = 120 Hz to several kHz Hole lifetime > 2 weeks in our lab Local ion rearrangement Tm 3+ :CaF 2 :D - and Er 3+ :CaF 2 :D - where interstitial D - moves Hole lifetime appears indefinite based on activation energy Gated spectral hole burning – ideal case Two-photon photoionization UV Photoemission used to explore options

20. cone@montana.edu wtittel@ucalgary.ca Applications of Spectral Hole Burning Spatial-Spectral Holography – “S2” or “4 - d Holography” Time- and space-domain holography Synthesis of Spectral hole burning Spatial holography and Fourier optics Optical Signal Processing High bandwidth spectrum analysis Radar signal processing beyond electronic bandwidths Correlation and Convolution of optical pulse trains True-time delay for phased arrays Optical Storage Spectral holes = bits Buffers at 1.5 microns, etc. Laser Frequency Stabilization to Ultra-Narrow Spectral Holes

21. cone@montana.edu wtittel@ucalgary.ca Applications of Spectral Hole Burning Spatial-Spectral Holography – “S2” or “4 - d Holography” Time- and space-domain holography Synthesis of Spectral hole burning Spatial holography and Fourier optics Optical Signal Processing High bandwidth spectrum analysis Radar signal processing beyond electronic bandwidths Correlation and Convolution of optical pulse trains True-time delay for phased arrays Optical Storage Spectral holes = bits Buffers at 1.5 microns, etc. Laser Frequency Stabilization to Ultra-Narrow Spectral Holes That Work Led Naturally to Quantum Information & Slow Light

22. cone@montana.edu wtittel@ucalgary.ca Rare Earth Ion Hamiltonian Free ion (Slater-Racah) ‑ Full rotation symmetry 1. Central field splits configurations ~ 10 5 cm -1 (10 eV) 2. Within lowest configuration 4f N Non-central field~ 10 4 cm -l (1 eV) Spin-orbit coupling ~ 10 3 cm -l (0.1 eV) 3. Eigenfunctions of form: built up from products of single-electron basis states Weak crystal field (Bethe) ‑ Local site symmetry 1. Free ion levels split ~ 100 - 200 cm -1 (10 - 20 meV) 2. Eigenfunctions of form (Sometimes, summation over J is important) Hyperfine and superhyperfine splittings – kHz to GHz Orbit-lattice interaction – Non-radiative relaxation, thermal line shifts, etc.

23. cone@montana.edu wtittel@ucalgary.ca Free ion (Slater-Racah) ‑ Full rotation symmetry 1. Central field splits configurations ~ 10 5 cm -1 (10 eV) 2. Within lowest configuration 4f N Non-central field~ 10 4 cm -l (1 eV) Spin-orbit coupling ~ 10 3 cm -l (0.1 eV) 3. Eigenfunctions of form: built up from products of single-electron basis states Weak crystal field (Bethe) ‑ Local site symmetry 1. Free ion levels split ~ 100 - 200 cm -1 (10 - 20 meV) 2. Eigenfunctions of form (Sometimes, summation over J is important) Hyperfine and superhyperfine splittings – kHz to GHz Orbit-lattice interaction – Non-radiative relaxation, thermal line shifts, etc. Rare Earth Ion Hamiltonian Important for QIS

24. cone@montana.edu wtittel@ucalgary.ca Role of Symmetry in Choice of Host Material Free ion (Slater-Racah) ‑ Full rotation symmetry Eigenfunctions of form: Weak crystal field (Bethe) ‑ Local site symmetry 1. Free ion levels split ~ 100 - 200 cm -1 (10 - 20 meV) 2. Eigenfunctions of form Local point symmetry often forbids optical transitions from lowest component of Ground multiplet to lowest component of Excited multiplet - but those are the ones we need ! Branching ratio among hyperfine levels for optical and RF transitions also depends on symmetry (and direction of applied fields) and is critical for state preparation and other aspects.

25. cone@montana.edu wtittel@ucalgary.ca Material Design and Characterization Tasks Active Ions & Transitions Operating wavelength range Lowest to lowest transition allowed Dynamical properties Gap to next lower multiplet Magnetic g factors Storage times (optical & hyperfine) Host Materials Specific wavelengths & compositional tuning Bandwidth by control of disorder Low nuclear magnetism Phonons impact decoherence Spectral Coverage Absorption spectrum lamp absorption for big picture of ion’s energy level structure laser absorption for precision watch out for hole burning distortions watch out for optical density distortions watch out for leakage around sample Photon echo-excitation spectrum Decoherence and Bandwidth Photon echoes Spectral diffusion by stimulated photon echoes Time-resolved spectral hole burning Large parameter space concentration magnetic field magnitude magnetic field direction temperature light direction light polarization electric field effects ODNMR, ODEPR, PENDOR, etc. Crystal Growth Material Optimization Device Demonstrations Large Scope & Critical Part of System Design for QIS & SSH

26. cone@montana.edu wtittel@ucalgary.ca Specialized Requirements (& Tradeoffs) No material currently solves all problems for all protocols Protocols evolve, too Long decoherence times T 2 – optical and magnetic sublevel Hosts, fields, & potentially magic angles (Pr 3+ :Y 2 SiO 5 ) Controlling spectral diffusion Inhomogeneous broadening Narrow 1-10 MHz for CRIB Broad for AFC protocols Hyperfine structure with long decoherence time Permanent ground state electric dipoles for CRIB – symmetry Nice to have optically-resolved hyperfine structure (very rare) Large oscillator strengths for relevant optical transitions Need better understanding of mechanisms of inhomogeneous broadening Crystal growth, strain, defects – defect chemistry, growth chemistry, …

27. cone@montana.edu wtittel@ucalgary.ca Magnetic Hyperfine Interactions – Odd Electron Case Hamiltonian H hfs =  J I  J where  J is an atomic constant Er 3+  162 (0.14%), 164 (28.2%), 166 (33.6%), 168 (26.8%), 170 (14.9%) All I = 0  No HFS  167 (22.94%) I = 7/2  1st Order HFS Kramers Degeneracy of Electronic States  All Levels Are Magnetic

28. cone@montana.edu wtittel@ucalgary.ca Electric Hyperfine Interactions – Even Electron Case Hamiltonian for Electric Quadrupole & Pseudo-Quadrupole Interactions H eq = P [(I Z 2 - I(I+1)/3) +  (I X 2 – I Y 2 )/3] + h  N I  (1 -  )  B Flurin Könz, Y. Sun, C. W. Thiel, R. L. Cone, R. W. Equall, R. L. Hutcheson, and R. M. Macfarlane, Phys. Rev. B. 68, 085109 (2003) 151 Eu 3+ : 151 Eu 3+ : Y 2 SiO 5 I = 5/2 Hole Burning Spectrum R. W. Equall, R. L. Cone, and R. M. Macfarlane, Phys. Rev. B 52, 3963 (1995). 141 Pr 3+ : Y 2 SiO 5 - 100% I = 5/2 C 1 Symmetry Site – Singlet Lowest  No Electronic Moment, Only Pseudo-Quadrupole Crystal field levels & Hyperfine splittings

29. cone@montana.edu wtittel@ucalgary.ca Investigated: 0.001%, 0.005%, 0.02%, 0.1% Er 3+ concentrations and also co-doped with 1% and 2% Eu 3+ to induce weak disorder Grown by: of Bozeman, MT Active ion is Er 3+ Er 3+ replaces Y 3+ on sites of C 1 symmetry Transient hole burning by population storage gives hole lifetime: T 1 ~ 11 ms T ~ 1.5 – 5 K to minimize phonon & spin- flip broadening Site 1 4 I 13/2 4 I 15/2 T 1 ~ 11 ms 1.53614  m 41 cm -1 91 cm -1 0 cm -1 39 cm -1 84 cm -1 102 cm -1 0 cm -1 Basic Spectroscopic Properties of Er 3+ :Y 2 SiO 5 Opt. Lett. 22, 871-873 (1997) J. Lumin. 94-95, 565-568 (2001) Proceedings of SPIE Vol. 4988, 51-61 (2003) Physical Review B 73, 075101 (2006) Physical Review B 74, 075107(2006)

30. cone@montana.edu wtittel@ucalgary.ca Broadening Er 3+ :Y 2 SiO 5 for Increased Processing Bandwidth by Introduction of Eu 3+ Site 1, D2 Polarization Highlighted Below * Coherent integration of 0.5 GHz spectral holograms at 1536 nm using dynamic bi-phase codes, Appl. Phys. Lett. 81, 3525-3527 (2002) Controlled compositional disorder in Er 3+ :Y 2 SiO 5 for wide bandwidth hole burning material at 1.5  m, Böttger, Thiel, Cone, and Sun, Phys. Rev. B 77, 155125 (2008). 0.005%Er 3+ :Y 2 SiO 5 * Er conc  inh abs. coeff. 0.005% 0.5 GHz 7 cm -1 0.02%Er 3+ :1%Eu:Y 2 SiO 5 Er conc  inh abs. coeff. 0.02% 12.5 GHz 1.14 cm -1 0.02%Er 3+ :2%Eu:Y 2 SiO 5 Er conc  inh abs. coeff. 0.02% 21.5 GHz 0.6 cm -1

31. cone@montana.edu wtittel@ucalgary.ca Suppress and manage spin-flip broadening using: Er 3+ dopant concentration (range dependent interactions) Temperature (thermal population) Magnetic field (maximize level splitting) Magnetic field direction (maximize level splitting) Er 3+ -Er 3+ Interaction Dynamics and Spectral Diffusion Successfully modeled Physical Review B 73, 075101 (2006)

32. cone@montana.edu wtittel@ucalgary.ca 12 3 stimulated photon echo photon echo step t 12 T time Stimulated Echo t 12 - Decay

33. cone@montana.edu wtittel@ucalgary.ca Magnetic field suppresses spectral diffusion J. Lumin. 94-95, 55 (2001)  h   Initial linewidth  SD   Saturated linewidth R – Rate of perturbations T – Waiting time Spectral Diffusion: Magnetic Field Dependence

34. cone@montana.edu wtittel@ucalgary.ca B D1D1 D2D2 b k step t 12 Angle Dependent g-Factors and Linewidth  h

35. cone@montana.edu wtittel@ucalgary.ca Achieving 30 sec Hyperfine Coherence for Pr 3+ & Eu 3+ Controlling spectral diffusion No first-order magnetic moment for electronic singlet states (unlike Er 3+ ) Local field fluctuations arise from ligand nuclear moments Nuclear Zeeman splittings too small to allow “freezing out” spin fluctuations Solution is to find magnetic fields and field directions where hyperfine Zeeman splittings are “stationary” Dynamic decoherence control of a solid-state nuclear-quadrupole qubit, E. Fraval, M. J. Sellars, J. J. Longdell, Phys. Rev. Lett. 95, 030506 (2005). Method of extending hyperfine coherence times in Pr 3+ :Y 2 SiO 5, E. Fraval, M. J. Sellars, J. J. Longdell, Phys. Rev. Lett. 92, 077601 (2004). Hyperfine interaction in ground and excited states of praseodymium-doped yttrium orthosilicate, J. J. Longdell, M. J. Sellars, N. B. Manson, Phys. Rev. B 66, 035101 (2002).

36. cone@montana.edu wtittel@ucalgary.ca Er 3+ :LiNbO 3 & Tm 3+ :LiNbO 3 Papers J. Lumin. 130, 1603-1609 & 1598-1602 (2010)  Large energy splittings—Er 3+ :LiNbO 3 has a Favorable Energy Level Structure  Oscillator strength concentrated in desired 4 I 15/2 (1) to 4 I 13/2 (1) transition Er 3+ :LiNbO 3 Energy Levels Er 3+ :LiNbO 3 4 I 13/2 4 I 15/2 1.532  m 62 cm -1 87 cm -1 0 cm -1 63 cm -1 132 cm -1 156 cm -1 0 cm -1 Crystal Field Splittings

37. cone@montana.edu wtittel@ucalgary.ca Photon echo spectroscopy is a powerful probe of optical decoherence, spectral diffusion, and superhyperfine interactions Optical Decoherence Measurements Distribution A: approved for public release; distribution unlimited  Decays are non-exponential— Indicates presence of strong spectral diffusion over timescale of measurement  Echo modulation observed for timescales of a few  s—Indicates strong superhyperfine coupling to 93 Nb and 7 Li nuclei in host and large inhomogeneity  Some motional narrowing can be observed at longest timescales when t ~ 1/R

38. cone@montana.edu wtittel@ucalgary.ca Stimulated photon echo techniques provide an exceptionally powerful tool to characterize time-dependent broadening and probe spectral diffusion dynamics Time Evolution of Linewidth  Use stimulated echo decays to measure the effective linewidth over a wide range of timescales  Spectral diffusion causes echo decay shapes and decoherence rates to evolve over time  Use spectral diffusion model to fit decays and extrapolate to linewidth at t 12 =0 —allows us to probe broadening independent of decoherence during t 12 Distribution A: approved for public release; distribution unlimited

39. cone@montana.edu wtittel@ucalgary.ca Ion - Ion Interactions Rare Earth - Rare Earth Interactions 1.Electronic exchange 2.Magnetic dipole-dipole 3.Electric multipole-multipole (includes electric dipole-dipole) 4.Virtual phonon exchange Pair Symmetry Typically Not Unique Laser-Induced “Instantaneous Spectral Diffusion” G. K. Liu and R. L. Cone, Phys. Rev. B 41, 6193-6200 (1990). References on Rare Earth - Rare Earth Interactions  R. L. Cone and R. S. Meltzer, Ion-Ion Interactions and Exciton Effects in Rare Earth Insulators, Chapter 8 in Spectroscopy of Crystals Containing Rare-Earth Ions, Ed. by A. A. Kaplyanskii and R. M. Mafarlane (North Holland, 1987).  S. Hufner, Optical Spectroscopy of Lanthanides in Crystal Matrix, Ch. 8 in Systematics and the Properties of the Lanthanides, Ed. S. P. Sinha, (D. Reidel Publ. Co., Dordrecht, 1982).  S. Hufner, Optical Spectra of Transparent Rare Earth Insulators (Academic Press, New York, 1978).  R. L. Cone and W. P. Wolf, Phys. Rev. B 17, 4162 (1978).  W. P. Wolf, J. Phys. (Paris) 32, C1 ‑ 26 (1971).  J. M. Baker, Rep. Prog. Phys. 34, 109 (1971).  W. P. Wolf and R.J. Birgeneau, Phys. Rev. 166, 376 (1968). Hz level to 10 cm -1 (300 GHz)

40. cone@montana.edu wtittel@ucalgary.ca Experimental demonstrations - storage of sub-nanosecond qubits using AFC - time-variable storage (of classical data) in spin states using AFC - 69% efficiency quantum storage with CRIB WT et al., ISOMQIS (2010); Afzelius et al., PRL (2010); Hedges et al., Nature (2010).

41. cone@montana.edu wtittel@ucalgary.ca Ti:Tm:LiNbO 3 waveguides N. Sinclair, WT et al., J. Lumin. (2010), C. Thiel, RLC et al., J. Lumin. (2010) Thulium - 795 nm zero phonon absorption line,  hom ~200 kHz @3K - large, polarization and wavelength dependent optical depth (  min ~2.2/cm @ 3K & 795.5 nm) - T 1 ( 3 H 4 )=80  s - optical pumping into magnetic ground-state sublevels (T 1 ~sec @ B=150G & T=3K) LiNbO 3 : - no inversion symmetry -> Stark shifting of resonance lines - “telecommunication” material, waveguide fabrication well mastered Waveguide - large Rabi frequencies - fast switching of large electric fields using closely spaced electrodes - simplified integration with fibre optic components and into networks 80  s 2.4 ms

42. cone@montana.edu wtittel@ucalgary.ca The setup T=2.9K B=133 G Oscilloscope LaserAOMpol. mod.PBS Detector Ti:Tm:LiNbO 3 waveguide fibre-to-fibre coupling loss ~10dB - prepare AFC (2 ms long pulse sequences) - wait 1.5 ms (19 T 1 ) - send data to be stored - register transmitted and recalled data - prepare AFC (2 ms long pulse sequences) - wait 1.5 ms (19 T 1 ) - send data to be stored - register transmitted and recalled data P ll timefrequency 795.5 nm  ≥300 ps Width ~1/  80  s 2.4 ms

43. cone@montana.edu wtittel@ucalgary.ca Storage of classical data – 20 ns long pulses  internal  ≈ 1.25 % 0.00 0.02 0.04 0.06 0.08 0.10 opt. power (au) Time (ns) Transmitted light Recalled light -1000100200 Frequency comb d0d0 d1d1   F=2, d 0 ~1.1, d 1 ~1.6 ->  ~ 1.6 % F=  De Riedmatten et al., Nature (2008)

44. cone@montana.edu wtittel@ucalgary.ca Storage of sub-ns time-bin qubits - AFC preparation using 300 ps long pulses -> GHz-width AFC - 0.4 photons/qubit before cryostat, 500 ps duration of each temporal mode - 30 to 60 ns storage time T=2.9K B=133 G TDC LaserAOMpol. mod.PBS Si- APD Ti:Tm:LiNbO 3 waveguide 795.5 nm Start Stop |  >=  |t 0 >+  ei  |t 1 > x x0x0 x1x1 pxpx   Time-bin qubit

45. cone@montana.edu wtittel@ucalgary.ca Storage of sub-nanosecond time-bin qubits - 700 ps duration output pulses - internal efficiency 4.5 % -  out = F  in +(1-F)  in F = P correct /(P wrong + P correct ) = 0.989/0.994 > F classical (max) = 2/3 |  >=  |t 0 >+  ei  |t 1 >

46. cone@montana.edu wtittel@ucalgary.ca Two-path interferometer/projection onto qubit states   h D 1 1 0 Interference data - comb spacing determines moment of recall - two superposed combs -> two recalls - difference between minima and maxima determines fidelity with target state

47. cone@montana.edu wtittel@ucalgary.ca Two-path interferometer/projection onto qubit states  Double grating read-out F mean =(1+V mean )/2 = 0.985 > 2/3

48. cone@montana.edu wtittel@ucalgary.ca AFC memory with variable storage time time output control fields Intensity input Afzelius et al., PRL (2010) - Material: Pr:YSO, 3 H 4 1 D 2 transition @ 606 nm - AFC determines storage time (in opt. coherence) of 4  sec - Transfer to ground state coherence -> variable storage time 17 MHz 10 MHz 4.8 MHz 4.6 MHz input control fields output ±1/2 ±3/2 ±5/2 ±1/2 ±3/2 ±5/2

49. cone@montana.edu wtittel@ucalgary.ca AFC memory with variable storage time Total storage time T M =9.6 µs T M =11.6 µs T M =14.6 µs T M =19.6 µs Output pulses time output control fields Intensity input Afzelius et al., PRL (2010) Storage time limited by inhomogeneous broadening of spin transition

50. cone@montana.edu wtittel@ucalgary.ca Efficient CRIB-type quantum memory 140 KHz wide spectral feature 140 dB tall longitudinal broadening (gradient echo) to 1.6 MHz, 15 dB tall Hedges et al, Nature (2010), Slide stolen from Mathew Sellars and modified

51. cone@montana.edu wtittel@ucalgary.ca Gradient Echo efficiency Input pulse duration: 600 ns First: 69  2% (switched 1.4  s) Second: 45  2% (switched at 2.1  s) Noise analysis proves quantum nature Hedges et al, Nature (2010), Slide stolen from Mathew Sellars and modified

52. cone@montana.edu wtittel@ucalgary.ca Conclusion - Building on the past 50 years, CRIB & AFC photon-echo quantum memory in RE crystals becomes competitive with other approaches - RE crystals also suitable for other protocols (slow light, DLCZ,..) - Photon-echo quantum memory feasible in gases -Still much to be done, protocols, materials, and material knowledge has to improve in parallel -Workable quantum memory may soon exist

53. cone@montana.edu wtittel@ucalgary.ca Thank you Montana State University, Bozeman, MT C. W. Thiel, R. M. Macfarlane, Y. Sun, T. Böttger, M. J. M. Leask, R. W. Equall, and W. R. Babbitt Air Force Office of Scientific Research National Science Foundation Scientific Materials Corporation, Bozeman, MT Ralph Hutcheson & R. W. Equall University of Calgary, Calgary, AB E. Saglamyurek, N. Sinclair, C. La Mela, J. Slater NSERC, GDC, iCORE University of Paderborn, Paderborn, Germany M. George, R. Ricken, W. Sohler

54. cone@montana.edu wtittel@ucalgary.ca Quantum memory -A synchronization de vice for quantum data - A key ingredie nt for a quantum repeater Lvovsky, Sanders, WT, Nature Photonics (2010); Simon et al., quant-ph (2010) |>|> QM BSM QM EE BSM QM EE BSM QM EE BSM

55. cone@montana.edu wtittel@ucalgary.ca Photon storage using two-pulse photon-echoes Massar & Popescu, PRL (1995); Ruggiero et al, PRA (2009); Sanguard, WT et al., PRA (in oress) u v w -Time-bin qubit (single photon) input: spontaneous emission adds significant noise - P echo = P noise    out = F  in +(1-F)  in F = tr(  in  out ) = (P echo + P noise )/(P echo + 2P noise ) = 2/3 = F classical (max) P(x) x x |  >=  |0>+  ei  |1>

56. cone@montana.edu wtittel@ucalgary.ca Storage of classical data- 500 ps long pulses 550 ps opt. power (au)  internal  ≈ 4.5 % 710 ps AFC preparation using 300 ps long pulses -> AFC spectral width > GHz