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

Mar 09, 2023 503 likes •778 views

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

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How to build a quantum repeater.

Wolfgang Tittel Institute for Quantum Science and Technology, and Department of Physics & Astronomy, University of Calgary, Canada

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How to build a quantum repeater. Maybe.

Wolfgang Tittel Institute for Quantum Science and Technology, and Department of Physics & Astronomy, University of Calgary, Canada

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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 E E QM BSM QM E E QM BSM QM E E BSM BSM

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How to build a quantum repeater

  • Photon-echo quantum memory (AFC) in RE crystals
  • Broadband waveguide quantum memory for entangled photon
  • Multi-mode storage and read-out on demand
  • Bell state measurements
  • Putting things together: system performance
  • Discussion and conclusion

needed: Pair ),

BSM E E QM BSM QM E E QM BSM QM E E BSM BSM

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Rare-earth-ion doped crystals

Frequency Absorption

Γhom Γinhom

Inhomogeneous broadening Stress and defects

  • naturally trapped emitters with free atom - like spectra
  • transitions in the visible and at telecom wavelength
  • at 4 K: Γhom ≈ 50 Hz – 100 kHz, T2 up to 4 ms
  • ground state coherence up to 30 s
  • Γinhom ≈ 500 MHz – 300 GHz
  • > capacity for long-term storage over large spectral width
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Photon-echo quantum memory (AFC)

  • 1. Preparation of an atomic frequency comb
  • 2. Absorption of a photon -> fast dephasing
  • 3. Phase matching φ(z) = -2kz enables backwards recall
  • 4. Rephasing at tR =1/νcomb with 2πΔjtR = m 2π
  • 5. Reversible mapping of optical coherence onto spin coherence allows recall on demand

frequency Δ absorption

  • > Reemission of light with unity efficiency and fidelity,

very good broadband and multi-mode storage capacity

frequency absorption

Γhom

Hesselink et al., PRL (1979); Afzelius et al., PRA (2009); De Riedmatten et al., Nature. (2008); Afzelius et al., PRL (2010), Bonarota et al., New J. Phys 2011. νcomb

Ω

ψ = 1 N c je

−i2πΔ j t j =1 N

∑

e

ikz j g1... e j... gN

|g> |e> |a> |s>

Experiments: Geneva, Lund, Paris, Calgary, Barcelona, Hefei

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Ti:Tm:LiNbO3 waveguides

  • N. Sinclair, WT et al., & C. Thiel et al., J. Lumin. (2010); N. Sinclair, WT et al., in preparation

Thulium

  • 795 nm zero-phonon absorption line, Γhom ~200 kHz @3K, Γhom~ 5kHz @ 0.7K
  • polarization and wavelength dependent optical depth (α~2.2/cm @ 3K & 795.5 nm)
  • T1(3H4)=80 µs
  • optical pumping into magnetic ground-state sublevels (T1~sec @ B~100G & T=3K; T1~h @B~100G &T=0.7K)

LiNbO3:

  • “telecommunication” material, waveguide fabrication well mastered

Waveguide

  • large Rabi frequencies
  • simplified integration with fibre optic components and into networks

80 µs 2.4 ms

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Waveguide quantum memory

Currently 20% fibre-to-fibre coupling efficiency (non-optimized mode overlap)

Ti:Tm:LiNbO3 waveguide

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Broadband waveguide quantum memory for entangled photons

challenge: match bandwidth of entangled photons with memory

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Broadband waveguide quantum memory for entangled photons: schematics

Wait 2.2 ms Time Prepare 10 ms Store & Retrieve 40 ms

c

AOM PM Memory Laser 795 nm Cryostat Ti:Tm:LiNbO

T = 3 K B = 570 G

3

b

Beam splitter Switch Filter Coupler Quarter/Half waveplate SPD Monitor detector Fibre Coaxial cable

FD Pump Interferometer Pump Laser 1047 nm 523 nm TDC & PC SPDC Etalon FBG 1532 nm 795 nm 30 m fibre DM Memory Setup

a

±x,y ±z ±x,y ±z

Qubit Analyzer Qubit Analyzer

  • generation of ‘individual’ pairs with
  • spectral filtering results in frequency-uncorrelated photon

pairs (suitable for quantum teleportation)

  • 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 -> ρin, ρout

φ+ = 1 2 e,e + l,l

( )

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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
  • f two, sinusoidal AFC, non-uniform AFC, etc.)
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Storing members of entangled photons

Entanglement Entanglement

  • f f
  • f formation
  • rmation

In Input-Output put-Output Fidelity Fidelity Purity Purity Fidelity with | Fidelity with |φ+> > CHSH-Bell CHSH-Bell parame parameter S er S ρin 0.644±0.042 0.954±0.029 0.757±0.024 0.862±0.015 2.379±0.034 ρout 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 (SLHV≤2)
  • E. Saglamyurek, WT et al., Nature (2011). Clausen et al., Nature (2011)
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Storing members of entangled photons

Entanglement Entanglement

  • f f
  • f formation
  • rmation

In Input-Output put-Output Fidelity Fidelity Purity Purity Fidelity with | Fidelity with |φ+> > CHSH-Bell CHSH-Bell parame parameter S er S ρin 0.644±0.042 0.954±0.029 0.757±0.024 0.862±0.015 2.379±0.034 ρout 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 (SLHV≤2)
  • similar results in the Gisin group
  • E. Saglamyurek, WT et al., Nature (2011). Clausen et al., Nature (2011)

Photon-Crystal CHSH = 2.64

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Multi-mode storage and read-out on demand

BSM QM E E QM BSM QM E E QM BSM QM E E BSM BSM

info info info info

frequency Δ absorption νcomb

Ω

|g> |e> |a> |s>

  • AFC QM allows read-out on demand in the

temporal domain via coherence transfer

  • additional benefit: long storage times
  • feasible, but challenging

Afzelius et al., PRL (2010); N. Timoney et al., arXiv (2013)

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Multi-mode quantum repeater: temporal versus frequency modes

τ1 τ2 τ0 τ0 same frequency, but arrival times synchronize arrival times

info info

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Multi-mode quantum repeater: temporal versus frequency modes

τ τ Δν1 Δν2 ν0 ν0

ν

τ1 τ2 τ0 τ0 same frequency, but arrival times synchronize arrival times same arrival time, but different frequencies match frequencies

info info info info

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  • AFC quantum memory in

Tm:LiNbO3 is perfectly suited for frequency multiplexing (Γinh~300 GHz!)

  • (potential) storage time of ~50 µsec
  • > TBP ~ 25 x 106
  • allows frequency-multiplexed

storage by creating many neighboring AFCs 10 GHz wide AFC tR= 1/νcomb = 6ns Detuning (GHz)

Tm:LiNbO3: a high-bandwidth storage material suitable for frequency multiplexing

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Quantum memory: AFC in Ti:Tm:LiNbO3 waveguide @ 3 K Frequency shiL: Serrodyne modulaOon of phase‐modulator Frequency filtering: Monolithic Fabry‐Perot cavity MulOplexed Time‐bin qubits:

Ome

Experimental setup

AOM AOM Memory preparation qubit preparation Interferometer stabilization

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0.5 photons/qubit on average

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 around zero detuning)

Results

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  • simultaneousl preparaOon of qubits in 5 frequency bins:

(sufficient to invesOgate cross‐talk)

  • Assessment of fidelity for |ψ>∈[|e>,|l>,|e>±|l>]

QuanOficaOon of storage fidelity of arbitrary qubits

750 1050 1350 1650 1950 (detuning in MHz)

Favg = 0.97(4) > 0.67 (classical memory) Decoy state method known from QKD allows finding a lower bound on single‐photon fidelity:

Decoy states: X. Ma et al.,Phys. Rev. A 72 01236 (2005)

0.5 photons/qubit 0.1 photons/qubit single photon/qubit

Results

  • N. Sinclair, WT et al., arXiv (2013).
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Real-world Bell-state measurement

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  • requires photons to be indistinguishable -> feedback

systems (polarization, spectrum, arrival time)

  • performed in the context of MDI-QKD
  • visibility close to theoretical maximum
  • J. Jin, WT et al., Nature Comm. (2013)
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Real-world Bell-state measurement

BSM QM E E QM BSM QM E E QM BSM QM E E BSM BSM

  • requires photons to be indistinguishable -> feedback

systems (polarization, spectrum, arrival time)

  • performed in the context of MDI-QKD
  • visibility close to theoretical maximum
  • also: HOM interference and BSM with attenuated

laser pulses (qubits) after recall from two AFC QMs

  • A. Rubenok, WT et al., PRL (2013), Y. Liu et al. PRL (2013), J. Jin, WT et al., Nature Comm. (2013)
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System performance - assumptions

  • N. Sinclair, WT et al., arXiv (2013)

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info info info info info info

  • Frequency multiplexed photon pair sources with fibre coupling efficiency per

photon of 90 %

  • Fibre loss of 0.2 dB/km
  • Quantum memories with 90% efficiency, Γinh = 300 GHz (-> Rclock= f(# of bins),

and ~500 µsec storage time

  • Detectors with 90% efficiency
  • Bell state measurements with 50 (75)% efficiency
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System performance - results

  • N. Sinclair, WT et al., arXiv (2013)

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  • for given number of

elementary links, rate remains constant as total distance increases until

  • Pelem. drops below 1
  • adding another

elementary link decreases rate, reflecting BSM efficiency Psuccess=(Pelem.)n x (Pconnect)n-1; R = Rclock x Psuccess

a) 10 GHz source (direct transmission) b) Perfect pair source, 100 bins, 50% BSM c) Perfect pair source, 1000 bins, 50% BSM d) Perfect pair source, 1000 bins, 75% BSM e) SPDC source, 1000 bins, 50% BSM

a) b) c) d) e)

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Conclusion

  • Demonstration of
  • entanglement storage

entanglement storage

  • multi-mode storage & recall on demand

multi-mode storage & recall on demand in frequency domain

  • two-photon interference after storage & real-world Bell-state measurement

two-photon interference after storage & real-world Bell-state measurement

  • Still a lot of work to meet requirements of memory for quantum repeaters, but there is a
  • path. Relaxed requirements for linear-optics quantum computer.
  • Bell-state measurements (frequency-multiplexed)
  • Detectors
  • Ideal, frequency-multiplexed photon pair sources

Average Average

❍

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Thank you !

MSc, PhD and PDF positions available

Collaboration with group of Prof. Wolfgang Sohler, University of Paderborn/Germany