How to build a quantum repeater. Wolfgang Tittel Institute for - PowerPoint PPT Presentation

How to build a quantum repeater. Wolfgang Tittel Institute for Quantum Science and Technology, and Department of Physics & Astronomy, University of Calgary, Canada BSM BSM BSM BSM BSM E E E E E E QM QM QM QM Q 2 Lab Q 2 C C Lab

How to build a quantum repeater. Maybe. Wolfgang Tittel Institute for Quantum Science and Technology, and Department of Physics & Astronomy, University of Calgary, Canada BSM BSM BSM BSM BSM E E E E E E QM QM QM QM Q 2 Lab Q 2 C C Lab

How to build a quantum repeater. (But not within a year.) Wolfgang Tittel Institute for Quantum Science and Technology, and Department of Physics & Astronomy, University of Calgary, Canada BSM BSM BSM BSM BSM E E E E E E QM QM QM QM Q 2 Lab Q 2 C C Lab

How to build a quantum repeater - Photon-echo quantum memory (AFC) in RE crystals - Broadband waveguide quantum memory for entangled photon needed: Pair - Multi-mode storage and read-out on demand ), - Bell state measurements - Putting things together: system performance - Discussion and conclusion BSM BSM BSM BSM BSM E E E E E E QM QM QM QM Q 2 Lab Q 2 C C Lab

Rare-earth-ion doped crystals Absorption Γ inhom Γ hom Frequency Stress and defects Inhomogeneous broadening - naturally trapped emitters with free atom - like spectra - transitions in the visible and at telecom wavelength - at 4 K: Γ hom ≈ 50 Hz – 100 kHz, T 2 up to 4 ms - ground state coherence up to 30 s - Γ inhom ≈ 500 MHz – 300 GHz -> capacity for long-term storage over large spectral width Q 2 Lab Q 2 C C Lab

Photon-echo quantum memory (AFC) 1. Preparation of an atomic frequency comb ν comb |e> Γ hom absorption absorption Ω |a> |s> |g> frequency frequency Δ 2. Absorption of a photon -> fast dephasing N 1 ikz j g 1 ... e j ... g N ∑ − i 2 π Δ j t c j e e ψ = Experiments: Geneva, N j = 1 Lund, Paris, Calgary, Barcelona, Hefei 3. Phase matching φ (z) = - 2kz enables backwards recall 4. Rephasing at t R =1/ ν comb with 2 πΔ j t R = m 2 π 5. Reversible mapping of optical coherence onto spin coherence allows recall on demand -> Reemission of light with unity efficiency and fidelity, very good broadband and multi-mode storage capacity Hesselink et al ., PRL (1979); Afzelius et al. , PRA (2009); De Riedmatten et al ., Nature. (2008); Q 2 Q 2 Lab C C Lab Afzelius et al ., PRL (2010), Bonarota et al. , New J. Phys 2011.

Ti:Tm:LiNbO 3 waveguides 80 µ s 2.4 ms Thulium - 795 nm zero-phonon absorption line, Γ hom ~200 kHz @3K, Γ hom ~ 5kHz @ 0.7K - polarization and wavelength dependent optical depth ( α ~2.2/cm @ 3K & 795.5 nm) - T 1 ( 3 H 4 )=80 µ s - optical pumping into magnetic ground-state sublevels (T 1 ~sec @ B~100G & T=3K; T 1 ~h @B~100G &T=0.7K) LiNbO 3 : - “telecommunication” material, waveguide fabrication well mastered Waveguide - large Rabi frequencies - simplified integration with fibre optic components and into networks Q 2 Lab Q 2 C C Lab N. Sinclair, WT et al ., & C. Thiel et al ., J. Lumin. (2010); N. Sinclair, WT et al ., in preparation

Waveguide quantum memory Ti:Tm:LiNbO 3 waveguide Currently 20% fibre-to-fibre coupling efficiency (non-optimized mode overlap) Q 2 Q 2 Lab C C Lab

Broadband waveguide quantum memory for entangled photons BSM BSM BSM BSM BSM E E E E E E QM QM QM QM QM challenge: match bandwidth of entangled photons with memory Q 2 Lab Q 2 C C Lab

Broadband waveguide quantum memory for entangled photons: schematics a 1047 nm 523 nm 1532 nm Qubit Analyzer ± � x,y DM ± � z FBG 30 m Pump Laser FD SPDC Pump Interferometer fibre Beam splitter Switch Etalon Filter Coupler 795 nm Quarter/Half waveplate TDC SPD Monitor detector & Fibre Coaxial cable PC φ + = 1 c Store & - generation of ‘individual’ pairs with b ( ) e , e + l , l 795 nm Qubit Analyzer Prepare Wait Retrieve Cryostat 2 ± � x,y AOM PM - spectral filtering results in frequency-uncorrelated photon 10 ms 2.2 ms 40 ms Memory Ti:Tm:LiNbO 3 Setup pairs (suitable for quantum teleportation) ± � z Memory T = 3 K B = 570 G Time Laser - photon wavelengths coincide with transmission windows of free-space and telecom fibres - qubit analyzers allow projections onto superpositions of |e> and |l> - measurement without and with memory -> ρ in , ρ out Q 2 Lab Q 2 C C Lab

The memory setup - 5 GHz broad grating, generated via laser sideband chirping - 146 MHz tooth separation -> 7 ns storage time - total system efficiency 0.2% (coupling loss, Finesse of two, sinusoidal AFC, non-uniform AFC, etc.) Q 2 Q 2 Lab C C Lab

Storing members of entangled photons Entanglement Entanglement Input-Output In put-Output Purity Purity Fidelity with | Fidelity with | φ + > > CHSH-Bell CHSH-Bell of formation of f ormation Fidelity Fidelity parame parameter S er S 0.644±0.042 0.757±0.024 0.862±0.015 2.379 ± 0.034 ρ in 0.954±0.029 ρ out 0.65±0.11 0.763±0.059 0.866±0.039 2.25 ± 0.06 - no measurable degradation of (post-selected) entanglement during storage - a small unitary transformation - initial (and recalled) state have limited purity and fidelity with target - experimental violation of CHSH Bell inequality (S LHV ≤ 2) Q 2 Q 2 Lab C C Lab E. Saglamyurek, WT et al. , Nature (2011). Clausen et al. , Nature (2011)

Storing members of entangled photons Entanglement Entanglement In Input-Output put-Output Purity Purity Fidelity with | φ + > Fidelity with | > CHSH-Bell CHSH-Bell of f of formation ormation Fidelity Fidelity parameter S parame er S 0.644±0.042 0.757±0.024 0.862±0.015 2.379 ± 0.034 ρ in 0.954±0.029 ρ out 0.65±0.11 0.763±0.059 0.866±0.039 2.25 ± 0.06 - no measurable degradation of (post-selected) entanglement during storage - a small unitary transformation - initial (and recalled) state have limited purity and fidelity with target - experimental violation of CHSH Bell inequality (S LHV ≤ 2) - similar results in the Gisin group Photon-Crystal CHSH = 2.64 Q 2 Lab Q 2 C C Lab E. Saglamyurek, WT et al. , Nature (2011). Clausen et al. , Nature (2011)

Multi-mode storage and read-out on demand BSM BSM BSM BSM BSM E E E E E E QM QM QM QM QM info info info info ν comb |e> - AFC QM allows read-out on demand in the absorption temporal domain via coherence transfer Ω |a> |s> - additional benefit: long storage times |g> frequency Δ - feasible, but challenging Q 2 Q 2 Lab C C Lab Afzelius et al ., PRL (2010); N. Timoney et al ., arXiv (2013)

Multi-mode quantum repeater: temporal versus frequency modes same frequency, but synchronize arrival times arrival times τ 1 τ 2 τ 0 τ 0 info info Q 2 Q 2 Lab C C Lab

Multi-mode quantum repeater: temporal versus frequency modes same frequency, but synchronize arrival times arrival times τ 1 τ 2 τ 0 τ 0 info info same arrival time, but match frequencies different frequencies ν Δν 1 τ τ Δν 2 ν 0 ν 0 info info Q 2 Lab Q 2 C C Lab

Tm:LiNbO 3 : a high-bandwidth storage material suitable for frequency multiplexing - AFC quantum memory in Tm:LiNbO 3 is perfectly suited for frequency multiplexing ( Γ inh ~300 GHz!) - (potential) storage time of ~50 µ sec -> TBP ~ 25 x 10 6 - allows frequency-multiplexed storage by creating many 10 GHz wide AFC neighboring AFCs t R = 1/ ν comb = 6ns Detuning (GHz) Q 2 Lab Q 2 C C Lab

Experimental setup Memory preparation AOM qubit preparation Interferometer stabilization AOM Quantum memory: AFC in Ti:Tm:LiNbO 3 waveguide @ 3 K Frequency shiL: Serrodyne modulaOon of phase‐modulator Frequency filtering: Monolithic Fabry‐Perot cavity MulOplexed Time‐bin qubits: Ome Q 2 Lab Q 2 C C Lab

Results Simultaneous storage and selecOve recall of 26 qubits encoded into different frequency bins: | ψ > ∈ [|e>, |l>] 26, 100 MHz wide AFCs each separated by 200 MHz gap (except 0.5 photons/qubit on average around zero detuning) Q 2 Q 2 Lab C C Lab

Results QuanOficaOon of storage fidelity of arbitrary qubits • simultaneousl preparaOon of qubits in 5 frequency bins: (sufficient to invesOgate cross‐talk) 750 1050 1350 1650 1950 (detuning in MHz) • Assessment of fidelity for | ψ > ∈ [|e>,|l>,|e>±|l>] 0.5 photons/qubit 0.1 photons/qubit single photon/qubit Decoy state method known from QKD allows finding a lower bound on single‐photon fidelity: F avg = 0.97(4) > 0.67 (classical memory) Q 2 Q 2 Lab C C Lab N. Sinclair, WT et al ., arXiv (2013). Decoy states: X. Ma et al.,Phys. Rev. A 72 01236 (2005)

Real-world Bell-state measurement BSM BSM BSM BSM BSM E E E E E E QM QM QM QM QM - requires photons to be indistinguishable -> feedback systems (polarization, spectrum, arrival time) - performed in the context of MDI-QKD - visibility close to theoretical maximum Q 2 Q 2 Lab C C Lab J. Jin, WT et al ., Nature Comm. (2013)