Memory must be able to store independently prepared states of light The state of light must be mapped onto the memory with the fidelity higher than the.

• Memory must be able to store independently prepared states of light

• The state of light must be mapped onto the memory with the fidelity higher than the fidelity of the best

classical recording

• The memory must be readable

B. Julsgaard, J. Sherson, J. Fiurášek , I. Cirac, and E. S. PolzikNature, 432, 482 (2004); quant-ph/0410072.

These criteria should be met for memory in:

Quantum computingwith linear operations

Quantum bufferfor light

More efficient repeaters

Quantum Key storage in quantum cryptography

Mapping a Quantum State of Light onto Atomic Ensemble

Squeezed Light pulse

1 > 2 >

Atoms

The beginning. Complete absorption

0 >

Proposal:Kuzmich, Mølmer, EP PRL 79, 4782 (1997)

Experiment:Hald, Sørensen, Schori, EP PRL 83, 1319 (1999)

Spin SqueezedAtoms

Very inefficientlives only nseconds,but a nice first try…

Light pulse – consisting of two modes

Strong driving

Weak quantum

or more atomic samples

Dipole off-resonant interaction entangles

light and atoms

Projectionmeasurement

on lightcan be made…

…and feedbackapplied

Teleportation in the X,P representation

x,p

Bellmeasurement

Today: another idea for (remote) state transferand its experimental implementation for quantummemory for light

Projectionmeasurement

X

AL XPH ˆˆˆ See also work on quantum cloning:J. Fiurasek, N. Cerf, and E.S. Polzik,

Phys.Rev.Lett. 93, 180501 (2004)

Implementation: light-to-matter state transfer

ALz PPJSaH ˆˆˆˆˆ3 No prior entanglement necessary

inL

inA

memA PXX ˆˆˆ

inA

memA PP ˆˆ

= C

- C inLX

squeeze atoms first

F≈80%F→100%

B. Julsgaard, J. Sherson, J. Fiurášek , I. Cirac, and E. S. PolzikNature, 432, 482 (2004); quant-ph/0410072.

inA

inL

outL PXX ˆˆˆ

Cesium atoms

Feedback magnetic coils

Classical benchmark fidelity for transfer of coherent states

)ˆˆ(ˆ2

1 aaX

)ˆˆ(ˆ2

aaP i

Atoms

Best classical fidelity 50%

e.-m. vacuum

K. Hammerer, M.M. Wolf, E.S. Polzik, J.I. Cirac, Phys. Rev. Lett. 94,150503 (2005),

Preparation of the input state of lightPreparation of the input state of light

x

EOM

S1

Polarizationstate

X

P

Input quantumfield

VacuumCoherentSqueezed

Strong fie

ld A(t)

Quantum field - X,P

Polarizingcube

P

X

PL

Quantum memory – Step 1 - interaction

Light rotates atomic spin – Stark shift

LmemA PX in

AX ˆˆ ˆ

121

A

nNk photatoms

Inputlight

Outputlight

Atomic spin rotates polarization of light – Faraday effect

AinL

outL PXX ˆˆˆ

ALz PPJSaH ˆˆˆˆˆ3

AXAP

xJ

XL

Quantum memory – Step 2 - measurement + feedback

AXAP

xJ

PL XL

cPXX AinL

outL ˆˆˆ Polarization

measurement

Feedback

to spin ro

tation

inLA

memoryA XcPP ˆˆˆ

Compare tothe best classical

recording

c

Fidelity – > 100% (82% without SS atoms)

Encoding the quantum states in frequency sidebands

dttSPdttSXT

inzTSL

TinyTSL

xx cosˆˆ;cosˆˆ

0

2

0

2

Memory in atomic Zeeman coherences

Cesium2/36P

2/16S 432

tJtJJ

tJtJJ

Labz

Labyz

Labz

Labyy

cosˆsinˆˆ

sinˆcosˆˆ

Rotating frame spin

0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4 1,6 1,8 2,0

0,0

0,2

0,4

0,6

0,8

1,0

1,2

1,4

1,6

1,8

2,0

2,2

2,4 Atomic Quantum Noise

Ato

mic

noi

se p

ower

[ar

b. u

nits

]

Atomic density [arb. units]

21

21

ˆcosˆ

ˆsinˆ

yinzxy

zinzxz

JtSJJ

JtSJJ

)ˆˆ(ˆˆ21

Labz

Labz

iny

outy JJSS

]sin)ˆˆ(cos)ˆˆ[(ˆˆ1121 tJJtJJSSS yyzzx

iny

outy

J

yz )(ˆ tS y

xS

Memory in rotating spin states

J

0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4 1,6 1,8 2,0

0,0

0,2

0,4

0,6

0,8

1,0

1,2

1,4

1,6

1,8

2,0

2,2

2,4 Atomic Quantum Noise

Ato

mic

noi

se p

ower

[ar

b. u

nits

]

Atomic density [arb. units]

2121ˆcosˆˆsinˆ

yinzxyz

inzxz JtSJJJtSJJ

]sin)ˆˆ(cos)ˆˆ[(ˆˆ1121 tJJtJJSSS yyzzx

iny

outy

y z)(ˆ tS yxS

Memory in rotating spin states - continuedx

)ˆˆ(sinˆsinˆ212

00

yyTS

Tiny

Touty JJdttSdttS x

dttSJJJJJ

JJtSJJJT

inzx

inz

inz

outz

outz

yyinzxzz

0

2121

2121

sin2ˆˆˆˆ

0ˆˆsin2ˆˆ

y z)(ˆ tS yxS

x

inL

inA

inLxx

inA

Tinzx

inz

inzJ

outz

outzJ

outA

yyJA

PXPTJSX

dttSJJJJJX

ConstJJP

xx

x

ˆˆˆˆ

sin2)ˆˆ()ˆˆ(ˆ

)ˆˆ(ˆ

0

2121

2121

2121

inA

inL

yyTS

TinyTS

ToutyTS

outL

PX

JJdttSdttSX x

xx

ˆˆ

)ˆˆ(sinˆsinˆˆ212

0

2

0

2

-10 -8 -6 -4 -2 0 2 4 6 8 10

-8

-6

-4

-2

0

2

4

6

8Gain plot for S

y and S

z modulation.

gF = 0.797

gBA

= 0.836

Ato

mic

mea

n va

lue

[xp-

units

]

Mean(Sy or S

z) [xp-units]

Sy modulated

Sz modulated

y = 0.797*x y = 0.836*x

Stored state versus Input state: mean amplitudes

Xin ~ SZin

Pin ~ SYin

Magneticfeedback

X plane

Y plane

read write

toutput input

/ 2 - rotation

Stored state: variances

<X2in> =1/2

<P2in >=1/2

<P2mem >

<X2mem>

3.0

-10 -8 -6 -4 -2 0 2 4 6 8 10

0,0

0,2

0,4

0,6

0,8

1,0

1,2

1,4

1,6

1,8

2,0

2,2

2,4

PN level

Mean value Sy or S

z [xp-units]

1+2g2 = 2.31 (classically best for n <= 8)

BA

2 = 1.818(75)*PN

F

2 = 1.643(67)*PNAt

omic

noi

se [P

N u

nits

]

Absolute quantum/classical border

Perfect mapping

Fidelity of quantum storage

ininoutinin dPF - State overlap averaged over the set of input states

F

0.820.840.860.88 0.9

0.54

0.56

0.58

0.62

0.64

Gain

Experiment

Best classical mapping

Coherent states with 0 < n <8

0.650.70.750.80.850.9

0.56

0.58

0.62

0.64

0.66

0.68

Coherent states with 0 < n <4

Experiment

Best classical mapping

0 2 4 6 8 10

40

45

50

55

60

65

Classical limit

16-06-2004/mapping.opj

Fidelity versus delay.Calculated for <n> <= 10.

Fid

elity

[%

]

Pulse delay [ms]

Quiet data Extrapolated

Quantum memory lifetime

•Deterministic Atomic Quantum Memory proposed and demonstrated for coherent states with <n> in the range 0 to 10; lifetime=4msec

•Fidelity up to 70%, markedly higher than bestclassical mapping