Cristaux dopés terres rares pour les mémoires quantiques

A. Ferrier , M. Lovric, Ph. Goldner

M.F. Pascual-Winter, R. Cristopher Tongning,

Th. Chanelière et J.-L. Le Gouët

D. Suter

Quantum Memory ?

Storage and retrieval of single photon quantum state

Nj ggg ......1 Nj geg ......1 Nj ggg ......1

Review W. Tittel et al. Laser & Photon. Rev., 1 (2009)

Quantum system

0>

1> Classical system

a0> +

Or 1> 0>

b1>

RE:Crystal

Quantum Memory ?

Storage and retrieval of single photon quantum state

Nj ggg ......1 Nj geg ......1 Nj ggg ......1

Review W. Tittel et al. Laser & Photon. Rev., 1 (2009)

Lambda system

Ground state Nuclear spin states g>

e>

g'>

RE:Crystal

Quantum Memory ?

Storage and retrieval of single photon quantum state

Nj ggg ......1 Nj geg ......1 Nj ggg ......1

Review W. Tittel et al. Laser & Photon. Rev., 1 (2009)

Lambda system

Ground state Nuclear spin states

Optical coherence

g>

e>

g'>

RE:Crystal

Quantum Memory ?

Storage and retrieval of single photon quantum state

Nj ggg ......1 Nj geg ......1 Nj ggg ......1

Review W. Tittel et al. Laser & Photon. Rev., 1 (2009)

Lambda system

Ground state Nuclear spin states g>

e>

g'>

RE:Crystal

Quantum Memory ?

Storage and retrieval of single photon quantum state

Nj ggg ......1 Nj geg ......1 Nj ggg ......1

Review W. Tittel et al. Laser & Photon. Rev., 1 (2009)

Lambda system

Ground state Nuclear spin states

Hyperfine coherence

g>

e>

g'>

RE:Crystal

Quantum Memory ?

Storage and retrieval of single photon quantum state

Nj ggg ......1 Nj geg ......1 Nj ggg ......1

Review W. Tittel et al. Laser & Photon. Rev., 1 (2009)

Lambda system

Ground state Nuclear spin states g>

e>

g'>

RE:Crystal

Quantum Memory ?

Storage and retrieval of single photon quantum state

Nj ggg ......1 Nj geg ......1 Nj ggg ......1

Review W. Tittel et al. Laser & Photon. Rev., 1 (2009)

Lambda system

Ground state Nuclear spin states g>

e>

g'>

RE:Crystal

Storage and retrieval of single photon quantum state

Nj ggg ......1 Nj geg ......1 Nj ggg ......1

Quantum memory requirement:

High Efficiency (>90%) Lambda system Long storage time (ms) = long coherence

time Multimode (increase transmission rate) Large bandwidth (~100 MHz)

Review W. Tittel et al. Laser & Photon. Rev., 1 (2009)

T. Chanelière New Journal of Physics 13 (2011) 013013

69 % Sellars et al. Nature 465 1052 (2011)

3s Sellars PRL 95, 063601 (2005)

1060 modes 1GHz

Best results :

Quantum Memory ?

RE:Crystal

1000 km Transmission in telecom fibers = 10-20

EDFA will not preserve quantum states cannot be used with quantum information

Why Quantum Memory ? Quantum Repeaters

N. Sangourd et al. Rev. Modern Physics 83 33 2011

Spontaneous Parametric Down Conversion

Entangled Photon pair source

Bell Measurement

Beam splitter

Entangled Photon pair source

http://quantumrepeaters.eu/

Quantum Memory Quantum Memory

Quantum Repeaters : extend the maximum distance for secure communication

Quantum Repeaters

Quantum channel

Alice

Bob

QM QM

S S

QM QM

S S

QM QM

S S

Bob Alice

Rare Earth Doped Crystals

Weak interaction with crystal enviroment

Long optical coherence times (T < 4K) 10 µs

Long hyperfine coherence times (T < 4K) 100 µs

Rare earth ions provide a quantum light matter interface through optical transitions

104

10-4

Energy (cm-1)

0 Hyperfine levels

10 µs - 1 ms

100 µs - 10 ms

qubit

Rare Earth Doped Crystals

Weak interaction with crystal enviroment

Long optical coherence times (T < 4K) 10 µs

Long hyperfine coherence times (T < 4K) 100 µs

Rare earth ions provide a quantum light matter interface through optical transitions

Large inhomogeneous broadening 100 MHz – 10 GHz

Ab

so

rptio

n

Frequency

GHz Y2SiO5 : 0.1 Eu % 1.7 GHz (0.019 nm)

Rare Earth Doped Crystals

Weak interaction with crystal enviroment

Long optical coherence times (T < 4K) 10 µs

Long hyperfine coherence times (T < 4K) 100 µs

Rare earth ions provide a quantum light matter interface through optical transitions

Large inhomogeneous broadening 100 MHz – 10 GHz

l (nm) = 606 880 580 1550 790

Several systems

Y3Al5O12

LiNbO 3:Ti Y2SiO5

La2(WO4)3

Y2SiO5

YVO4

Y2SiO5 Y2SiO5

Y3Al5O12

Dynamical decoupling in Pr:LaWO

How to extend the hyperfine T2 ?

Two Pulse Photon Echo Excitation of an inhomogeneously broadened line

Rephasing

Echo : coherent collective emission separated from laser pulses

T2 determination

Basic storage scheme

Time

/2

z

x

y

z

x

y

/2

z

x

y

z

x

y

x

y

z

0>

1>

Why µs range for the hyperfine T2 ? Fluctuation of the spin bath = Relaxation

c

…

n x c

Pr : LaWO

c : correlation time of fluctuation

: standard deviation

How to extend the hyperfine T2 ? Fluctuation of the spin bath

c

…

Control of the decoherence : Application of an external magnetic field

n x c

Dynamical decoupling

Pr : LaWO

c : correlation time of fluctuation

: standard deviation

1s storage with EIT (Longdell PRL 2005 )

How to extend the hyperfine T2 ? Dynamical Decoupling : Bang Bang

Time

/2

Phase

Time

How to extend the hyperfine T2 ? Dynamical Decoupling : Bang Bang

Time

/2

Phase

Time

How to extend the hyperfine T2 ? Dynamical Decoupling : Bang Bang

Time

/2

cor

Phase

Phase Time

Time

How to extend the hyperfine T2 ?

Dynamical Decoupling : Bang Bang

Time

/2

cor

Phase

Phase Time

Time Phase

Time

How to extend the hyperfine T2 ?

• What happens with photon echo based protocols and

larger bandwidths ?

• Optimal RF sequence ?

Dynamical Decoupling : Bang Bang

Time

/2

Phase

Time

A sequence of -pulses refocuses the coupling to the environment.

Dynamical decoupling in Pr:LaWO

How to extend the hyperfine T2 ?

25

La2(WO4)3:Pr3+

• 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

26

Photon Echo Memory

Time

Excitation pulse Rephasing pulse

Photon echo

Time

• Extending storage time in the ms range

Excitation pulse Rephasing pulse

Photon echo

RF rephasing pulses

Transfer pulses

Dynamical decoupling

27

RF Sequences ? • Compensate for slow changes in the environment

z z z

x

y

x

y

x

y

z z z

x

y

x

y

x

y

z z z

x

y

x

y

x

y

Series of π pulses

CP sequence

Series of π-δ pulses

⇒ loss of coherence

Series of ±(π-δ) pulses

⇒ coherence preserved

CPMG2 sequence

• Pulse errors

28

Studied RF Sequences

CP sequence: [τ/2 - π - τ - π - τ/2]N

KDD sequence: [KDD0 – KDDπ/2 - KDD0 - KDDπ/2 ]

N KDDφ = [τ/2 - ππ/6+ φ - τ - π φ - τ - π π/2+φ - τ - π φ - τ - π π/6+ φ - τ/2 ]

2 RF pulses sequence: τ/2 - π - τ - π - τ/2

CPMG2 sequence: [τ/2 - π - τ - (-π) - τ/2]N

• Preserving arbitrary initial phases

Souza et al, PRL 2011

29

Optical to Spin Transfer in Pr3+:La2(WO4)3

Rephasing RF pulses

Input Transfer Transfer

Output

Rephasing

Input: 500 ns

Transfer: 1 µs

RF pulses: 5 µs

Detection gate

0 2 4 6 8 10 12 14 16 18 2010

-4

10-3

10-2

10-1

R

etr

ieval effic

iency

Storage time (ms)

30

Storage Times

Storage time

KDD T2 = 1.3 ms

2 RF T2 = 250 µs

CPMG2 T2 = 8.8 ms

30 µs

31

Coherent Raman Scattering • Initial coherence created by a RF pulse

32

Relative Optical Phase

M. Lovric et al arXiv:1302.3358

1 1a 1b

T T T

CP 3ms

Time RF rephasing pulses

33

Relative Optical Phase

M. Lovric et al arXiv:1302.3358

1 1a+2b

1b

T T T

CP 3ms 2 2a

Time RF rephasing pulses

34

Relative Optical Phase

Relative optical phase (degrees)

M. Lovric et al arXiv:1302.3358

1 1a+2b

1b

T T T

CP 3ms 2 2a

Time RF rephasing pulses

35

Conclusion Extension of hyperfine T2 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

36

Thank you for your attention !

Funding: ANR (RAMACO), EU (QUREP, CIPRIS)

LCMCP LAC

QM QM

S S

QM QM

S S

QM QM

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

41

Spectral Tailoring

Long population lifetimes for hyperfine levels (16 s) "permanent" structure

Signal absorption ≈ 2 MHz

42

Transfer efficiency

OTSS 97.5% compared to TPPE OTSS 0.45 % compared to input pulse

45

Storage Times

Storage time

KDD T2 = 1.3 ms

2 RF T2 = 250 µs

CPMG2 T2 = 8.8 ms

CP T2 = 8.8 ms

30 µs

Dynamical Decoupling , Theory Vs Experiment

CPMG

Minimize ihn ? Magnetic Field

Spin sublevel splitting per Tesla

Maximum or minimum ?

M.F. Pascual-Winter et al. PHYSICAL REVIEW B 86, 184301 (2012)

Minimize ihn ? Magnetic Field

=54.8° et =45°

Spin sublevel splitting Rabi frequency Vs B

[100]

Minimize ihn ? Magnetic Field

=54.8° et =45° Bext = 1T

𝚪𝐈𝐧𝐡𝐬𝐩𝐢𝐧~𝟏𝟎𝟎𝐤𝐇𝐳

Expected :

𝚪𝐈𝐧𝐡𝐬𝐩𝐢𝐧~𝟏𝟓𝐤𝐇𝐳

M.F. Pascual-Winter et al. PHYSICAL REVIEW B 86, 184301 (2012)

c c …

t 0

50 % Imax

Imax

Transmission

M.F. Pascual-Winter et al. PHYSICAL REVIEW B 86, 184301 (2012)

c c …

Pompage optique

0

50 % Imax

Imax

Transmission

M.F. Pascual-Winter et al. PHYSICAL REVIEW B 86, 184301 (2012)

c c …

0

50 % Imax

Imax

/2 Pulse RF

Transmission

M.F. Pascual-Winter et al. PHYSICAL REVIEW B 86, 184301 (2012)

c c …

0

50 % Imax

Imax

/2 Pulse RF

Transmission

M.F. Pascual-Winter et al. PHYSICAL REVIEW B 86, 184301 (2012)

c c …

Transmission

0

50 % Imax

Imax

/2 Pulse RF

/2

Population probe

3H4(0)

3H6(0)

B=0 B0

mI=1/2

mI=-1/2

mI=-1/2

mI=1/2

793 nm

Large oscillator strength Well known crystal growth 27Al3+ nuclear spin 3.64 large anisotropy of magnetic gyromagnetic tensor xx= zz=20 MHz/T yy= 400Mhz/T

𝚪𝐈𝐧𝐡

𝐬𝐩𝐢𝐧~𝟓𝟎𝟎𝐤𝐇𝐳

Dynamical decoupling in Tm:YAG

M.F. Pascual-Winter et al. PHYSICAL REVIEW B 86, 184301 (2012)

c= 172 µs = 3 kHz

c

Spin echo

t >> c

T2 =1.01ms

/2

/2 RF Pulse Theoritical model

Dynamical decoupling in Tm:YAG

Dynamical decoupling in Pr:LaWO

How to extend the hyperfine T2 ?

T2 =230 ms

220 time increase

Dynamical decoupling in Tm:YAG M.F. Pascual-Winter et al. PHYSICAL REVIEW B 86, 184301 (2012)

CPMG

T2 =1.01 ms

Long optical storage in a rare earth doped crystal

using dynamical decoupling

• Marko Lovrić1, Dieter Suter1, Alban Ferrier2, Philippe

Goldner2

• 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

61

Rare Earth Doped Crystals

• 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

104

10-4

Energy (cm-1)

0 Hyperfine levels

10 µs - 1 ms

100 µs - 10 ms

62

Storage times of Optical Memories • 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 ?

Pr3+:Y2SiO5