memory must be able to store independently prepared states of light the state of light must be...
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• 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.
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These criteria should be met for memory in:
Quantum computingwith linear operations
Quantum bufferfor light
More efficient repeaters
Quantum Key storage in quantum cryptography
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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…
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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
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Teleportation in the X,P representation
x,p
Bellmeasurement
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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)
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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
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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),
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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
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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
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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)
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Encoding the quantum states in frequency sidebands
dttSPdttSXT
inzTSL
TinyTSL
xx cosˆˆ;cosˆˆ
0
2
0
2
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Memory in atomic Zeeman coherences
Cesium2/36P
2/16S 432
tJtJJ
tJtJJ
Labz
Labyz
Labz
Labyy
cosˆsinˆˆ
sinˆcosˆˆ
Rotating frame spin
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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
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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
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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
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-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
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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
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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
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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
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•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