a photon echo-based quantum memory using double...

2012-12-06

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A Photon Echo-Based Quantum Memory

Using Double Rephasing and Optical Locking

Byoung S. Ham

Inha University, S. Korea

Asia Pacific Conf. & Workshop in Quantum Information Science

Pullman Lakeside, Putrajaya, Malaysia

Dec. 3~7, 2012

Experiments were performed by J. Hahn.

PIP CenterInha University, S. Korea

2012-12-06

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Motivation: Quantum memories1. For scalable quantum nodes in quantum networks2. For quantum repeaters in long-distance quantum communications

D bl h i

Physics: Coherent control of collective atom phases1. Quantum mapping between optical and spin states2. Double rephasing and optical locking

Optical locking: -BS Ham, Nature Photon. 3, 518 (2009)

Double rephasing: -BS Ham, PRA 85, 031402R (2012)


1.Background2. Photon echoes3. Modified photon echo protocols4 Double rephasing & Optical locking4. Double rephasing & Optical locking


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Functional Quantum Nodes: 1. Single photon generation, transmission/reception, and storage2. Long-time storage for long-distance entanglement creation3. Scalable

Remote Quantum Node Entanglement Creation:Remote Quantum Node Entanglement Creation: 1. Trapped single ion in an optical cavity: Nature 484, 195 (2012)2. Bulk solids: Nature Photon 6, 234 (2012)

Constraint of Storage Time: -Phase (spin) decay time: ~ms

To increase coherence (storage) time,-Purely grown Isotopes: single spin (2012)


Purely grown Isotopes: single spin (2012)1. NV color center (13C nuclear spin): 1.4 sec2. 28Si (nuclear spin): 180 sec

Trade-off: storage time vs. efficiency

-Definition: Random quantum state storage and retrieval in a reversible manner

-History: Ensemble-based-Early 2000s: Single mode

Trade-off: Efficient interface vs. Long-time storage

I. Quantum Memory

-Early 2000s: Single mode1. Slow light: Hau/Harris, Scully/Lukin, Hemmer/Ham, etc.2. Raman: Polzik (2004)

-Late 2000s: Multimode; Modified Photon echo, Spin echo1. AFC:Gisin group2. Gradient Echo: ANU group3. Optically locked photon echo: Ham group4. Spin echo in NV: Harvard/Stuttgart group

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- For distributed quantum networking- For Long-distance quantum communications using quantum repeaters

II. Why ultralong quantum memories?


RMP 83, 33 (2011): Fig. 18 (DLCZ)

1. Background

2.Photon echoes3. Modified photon echo protocols4. Double rephasing & Optical locking


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Two-Pulse Photon Echoes (2PE): Hahn Echoes

T2opt (1/)

D R

|3>

TD TR TE|1>

Abs

orpt

ion

D R

Echo

tim

e

R

Im

Time Detuning

• Coherent transient process


Im13

Bloch Vector Model


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Problem I: Echo reabsorption ~1%

I0exp(l)

photons

eegg

1

D: R

0 L

Length

Mag

nitu

de

eg

x100

=1

|g>

|e>

P

D

R

E

0 T 2T

Storage vs. Retrival


Backward photon echo:Theory:- Moiseev & Kroll, PRL (2001)Exp:- Ham, NJP (2011)


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Problem 2: Population inversion

- Spontaneous emission: negligible!- Stimulated echo gain: violation to ‘no cloning’

R|g>

|e>

gg

gg

ee

echo

D E

0 T 2T

Echo

ee

Time


For a 0.1 ns data pulse,spontaneously emitted photons in 0.05 at. % Pr doped YSO: 0.03

N=VN0~5x1011.T/T ~ 6x10-7

S

Spontaneous emission: negligible!

S=4f2 ~103

A=D2 ~10-4

f=10 cm f

D=10-2 cm

T/T1~ 6x10 7. NeN=3x105. A/S=10-7.

NfNeVN0~ 0.03

A

Pr3+ d=10-3 cm

L=0.1 cmV=Ld2 ~10-7 [Ham, JOSAB 29, 463 (2011)]


[Atom width: ~10 GHz]

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Stimulated emission

|e>

|g>

|e>

N identical photons Quantum Noise!

Violation to ‘no cloning’ theorem!


1. Background2. Photon echoes

3.Modified photon echo protocols4. Double rephasing & Optical locking


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Solution for the population inversion:p p-Deshelving: Atomic Frequency Comb (AFC)-Linear Stark: Gradient echo-Double Rephasing


A. With a single pulse:- Wide pop excitation!

|e>

1. Spontaneous Deshelving: AFC

time0

spin << opt; spin >> opt

|g>

|aux>

opt

spin

0

B. With delayed pulses by :- Modulation spectrum!

spin opt; spin opt

In 1970’s, -To extend 2PE storage time!

0

Population Grating 3PEAFC

time0


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Time (s)

Abs

orpt

ion

Im 1

3

Time (s)

Am

plit

ude

(rad

)

INP

UT

(a) (b)

AFC vs. 3PE

AFC problem: - Lower retrieval efficiency- Short storage time: < 0.01 ms

Pop

ulat

ion 1

1

Time (s) Time (s)

Abs

orpt

ion

Im 1

3

Time (s) Spectral detuning (MHz)

(c) (d)

(e) (f)

AFC


Abs

orpt

ion

Im 1

3

Time (s) Spectral detuning (MHz)

Pop

ulat

ion 1

1

( ) ( )

“1” “2”

Conventional Stimulated Echo (3PE)

[Ham, JOSAB 28, 775 (2011]

2. Linear Stark Effect: Gradient Echo

[Hosseini et al., Nature (2012)][Hetet et al, PRL (2008)]


Storage time: limited by T2opt

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3. Double Rephasing (with optical locking)

1. No population inversion2. Storage time extension

BS Ham, arXiv:1101.5480 (2011) J-L Gouet et al, arXiv:1104.4875 (2011)

J-L Gouet et al, NJP (2011)

No storage time extension!g


1. Background2. Photon echoes3. Modified photon echo protocols

4 Double rephasing & Optical locking4.Double rephasing & Optical locking


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1. Storage time extension: Optical locking

B1B2|3>

D

R

Coherence conversion into spin states

T

ΦB1 = (4n − 3)π

ΦB2 = (4n −1) π

|1>|2>

|1>

D/R

D

Optical coherence Spin coherence

[Ham, Opt. Exp. 18, 1704 (2010)][Ham, NJP 13, 093011 (2011)]


[Optical locking: Ham, Nature Photon. 3, 518 (2009)]

[Ham, Opt. Exp. 18, 1704 (2010)]

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[B. S. Ham, Opt. Exp. 18, 1704 (2010)]


APD1

B2Lens

(b)M

Iris

D1)

R1)

2) 2)

T

(a)

E1)

Experimental Scheme

APD2

Pr:YSO

532 nm

Ring-Dye(606 nm)D/R

LensTD TR TB1 TB2

T

TimeTE

D/R

EB2

Pr:YSO

B1AOM

(606 nm)

MBSM1 mm

D/R

EB1


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Boxcar

OSC

GPIB

Freq. Synthesizer

Digital Delay Generator

AWG module Cryogenic system

APD

Laser controller

APD


Pr3+(0.05 at.%):YSO

10 mm


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Pr3+(0.05 at.%):YSO

Inha University, S. Korea

Optical depth: 1~30

PIP Center

Ham, OE 16, 16723 (2008)

D

B1 B2E

Pr:YSO

s

T2opt

2PE

Backward echo scheme:- echo enhancement: x15

Length: 1 mm 3 mm s

Extended time: spin dephasing!

gEnhancement: x15 x50

[Ham, NJP 13, 093011 (2011)]


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2. Three-pulse photon echo (3PE): population grating

t=TW

D W R W

D

E

t=TR

Im

Im

Coh

eren

ce

Im

R

D


Coherence Mapping:Phase (2PE) Population (3PE)

T2opt ~ T1

opt

However, no practical benefit: R: exp(it) exp(-it)

pulse

Ree >> gg

3. 3PE with optical locking

Atom Phase Locking: inherent property of 3PE

|3>

|2>|1>

D/W/R B1/B2

Active Optical Deshelving: Optical/spin coherence conversion

Topt2

T1spin

vs.

[3PE with optical locking]

B1 B2

T

T1opt

Topt2

[3PE]

T

TD TW TR TE

~100 % (T<<Topt2)


Efficiency

Storage time T1spin (>sec)

TD TW TR TE

< 50% (33>>11)

T1opt (<<ms)

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T1spin (2 sec)

[Ham, NJP 14, 013003 (2012)]


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Problem: -Population inversion!


T T TR

C1 C2D W R RR

T1spin

TRR

4. Double Rephasing

TD TWTR TRR

[Ham, PRA 85, 031402(R) (2012)]


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DW RC1 C2 RR

a ce gi k

|1>|2>

|3>

C1/C2D/W/R/RR

Optical phase grating Spin pop. grating


[Ham, PRA 85, 031402(R) (2012)]

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Conclusion

• Presented double rephaisng via controlled deshelving to remove spontaneous emission noise or echo gain, and to extend photon storage time longer than a second.to extend photon storage time longer than a second.

Acknowledgment: Supported by 1. CRI program, MOST/NRF, S. Korea2. Korea Communications Commission

http://photon.re.kr

Thank you for your attention!


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