niels bohr institute copenhagen university quantum memory and teleportation with atomic ensembles...
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Niels Bohr InstituteCopenhagen University
Quantum memory and teleportation with atomic ensembles
Eugene Polzik
•Interface matter-light as quantum channel
We concentrate on: deterministic high fidelity* state
transferFidelity of quantum transfer
ininoutinin dPF - State overlap averaged over the set of input states
*) Fidelity higher than any classical measure-recreate protocol can achieve
Light – matter quantum interface
Probabilistic entanglement distribution (DLCZ and the like)
Deterministic transfer of
quantum statesbetween
light and matter
Photon counting – based protocolstypical efficiency 10-50%
Homodyning – basedprotocols (99% detectors)
Hybrid approaches(Schrödinger cats and the like)
K. Hammerer, A. Sørensen, E.P.Reviews of Modern Physics, 2010 arXiv:0807.3358
Quantum interface – basic interactions
† † †ˆ ˆˆ ˆ . .Par BSH a b ab h c
X-type = double Λ interaction
a
b
b
a
† †ˆˆ . .H a b h c
Light-Atoms Entanglement
Innsbruck, Copenhagen, GIT,Caltech, Harvard, Heidelberg
b
a
†ˆˆ . .H ab h c
Light-to-Atoms mapping (memory)
Aarhus, Harvard, Caltech, GIT
Rochester, Copenhagen, Caltech, Garching, Arisona…
ˆ ˆ2 ,L A Par BSP P if
Quantum memory beyond classical benchmark
Atoms
Fidelity of quantum storage
ininoutinin dPF - State overlap averaged over the set of input states
Classical benchmark fidelity for state transfer for different classes of states:
Coherent states (2005)
N-dimentional Qubits (1982-2003)
NEW! Displaced squeezed states (2008)
Fidelity exceeds the classical benchmark
memory preserves entanglement
Classical benchmark fidelity for state transfer is known for the classes of states:
Best classical fidelity forcoherent states is 50%
1. Coherent states
3. Displaced squeezed states:M.Owari, M.Plenio, E.P., A.Serafini, M.M.Wolf New J. of Physics (2008); Adesso, Chiribella (2008)
X
P
2. QubitsBest classical fidelity 2/3
Experimental demonstration:Ion to ion teleportation NIST’04; Innsbruck’04 F=78%
Experimentaldemonstrations of F>FCl:Light to light teleportation Caltech’98 F=58%Light to matter teleportationCopenhagen’06 F=58%
x
Quantum field: EPR entangled Polarizing
cube
-450 450
PolarizingBeamsplitter 450/-450
Stokes operators and canonical variables
ˆ i t i ta a e a e
1; 1Var X X Var P P
12 2
3 2
11 2
ˆ ˆ
ˆ ˆ
ˆ
L
iL
S nX
S nP
S n
S2 measurement
Atom-compatible EPR state
Atomic memory compatiblesqueezed light sourceBo Metholt Nielsen, JonasNeergaard
- 6 dB
X
P
two mode squeezed = EPR entangled light
60.8 0,0 0.48 1,1 0.29 2,2 0.18 3,3 ...
dB
ˆ ˆ,X P i
Spin polarized ensemble as T=00 Harmonic oscillator
† †12 2
ˆˆˆ ˆˆ ˆ ˆ, ( ) , ( ) yz i
A A A A
x x
JJX P i X b b P b b
J J
Jy~P
Jz~X
Jx
xyz iJJJ ˆ,ˆ
1
N
ii
J j
F=4
F=3
6P3/2
6S1/2
Cesium
mF=3 mF=4
X
P
Harmonic oscillatorin the ground stateat room temperature
1012 Room Temperature atoms Cesium
2/36P
2/16S
432
99.8%initialization toground state
Harmonic oscillatorin a ground state
320kHz
1GHz
x Quantum field
Polarizingcube
-450 450
PolarizingBeamsplitter 450/-450
Quantum nondemolition interaction: 1. Polarization rotation of light
a
Polarizationof light
22 2 1
1
ˆˆ ˆ ˆ ˆˆ
inout in
z z
SS S S J J
S A
ˆ ˆ ˆ
ˆ ˆ ˆ
L A
out inL L A
H P P
X X P
xStrong fie
ld A(t)
Quantum field - a
Polarizingcube
Atoms
21
21
aiA ˆ2
1 aiA ˆ2
1
y
Quantum nondemolition interaction: 2. Dynamic Stark shift of atoms 2
1 21
ie
Atomicspin
rotation
3 3
ˆˆ ˆˆ ˆ ˆ
inyout in
y y xx
JJ J J S S
J A
ˆ ˆ ˆout inA A LX X P
Z
Z-quantization
Atom
s IN
Stronger coupling:atom-photon state swap plus squeezing
1
1
out in out inA L A L
out in out inL A L A
X P P X
X P P X
W. Wasilewski et al, Optics Express 2009
Photons IN
Atoms
OUT
PhotonsOUT
† † †ˆ ˆˆ ˆ . .H a b ab h c 1 2
2ˆ ˆ ˆ ˆ( )L A L Ak P P X X
Quantum feedback onto atoms
L
B
cosRF RF LB b t
BRF
RFb t Its just a ~π/√N pulse
Goal: rotate atomic spin ~ to measured photonic operator value
2 Detectors1
K. Jensen, W. Wasilewski, H. Krauter, T. Fernholz, B. M. Nielsen, M. Owari, M. B. Plenio, A. Serafini, M. M. Wolf, and E. S. Polzik. Nature Physics 7 (1), pp.13-16 (2011)
Displaced two-mode squeezed (EPR) states
iPXaaPaaX i ˆ,ˆ)ˆˆ(ˆ),ˆˆ(ˆ22
1 X
P
2 2 1/ 2X P
Coherent
X
P
EPR entangled = two-mode squeezed
1; 1Var X X Var P P
a
aX
P
a
aDisplaced two-mode squeezed
Memory in atomic Zeeman coherences
Cesium2/36P
2/16S
43
+ +1
2 23
8 2
3
1 30 2 4 ...
2 2 8 2dB
Example: 3 dB (factor of 2) spin squeezed state
1012 Cs atoms at RTin a ”magic” cell
MF = 4
MF = 3
MF = -3
MF = -4
MF = 5,4,3
~ 1000 MHz
320 kHz
Storing ± Ω modes in superpositions of atomic Zeeman coherences
- 320 kHz
60.8 0,0 0.48 1,1 0.29 2,2 0.18 3,3 ...
dB
1 2 1 2 3
0
1 2 1 2
1 2
1 2
ˆ ˆ ˆ ˆ 2 cos
( )
ˆ ˆ 0
Tout out in in inz z z z x
out out in in in inA A A A L L
y y
A A
J J J J J S t dt
X X X X P P
J J
P P Const
1
2 2 1 220 0
1 2
ˆ ˆ ˆ ˆsin sin ( )
( )
T TS Tout in
y y
out out in in in inL L L L A A
S t dt S t dt J J
X X X X P P
a a
Cell 1 Cell 2
Two halves of entangled mode of light are stored in two atomic memories
Squeezed states – classical benchmark fidelity:M.Owari et al New J. Phys. 2008
X
P
1F
ξ-1 – squeezed variance
ξ-1
Best classical fidelity vs degree ofsqueezing for arbitrary displacedstates
ξ-1
Optical pumpingand squeezingof atomic state
Inputpulse
Readoutpulse
Rf feedback Π-pulse
Squeezedlight source
Strong field
X
PAlphabet of input states, 6 dB squeezed and displaced
3.8 7.60
Vacuum state variances = 0.5
Imperfections:Transmission from the source to memory 0.8Transmission through the memory input window 0.9Detection efficiency 0.79
Memory added noise: 0.47(6) in XA , 0.38(11) in PA Ideally should be: 0.36 in XA and 0 in PA
1012 spins in each ensemble
y z
x
y z
xSpins which are “more parallel” than that
are entangled
Entanglement of two macroscopic
objects.
21
~ N
Nature, 413, 400 (2001)
1 2 1 2ˆ ˆ ˆ ˆ/ 2 / 2 1z z x y y xVar J J J Var J J J
2)()( 2121 PPVarXXVar
Einstein-Podolsky-Rosen (EPR) entanglement
Driving
field
Entanglement generated by dissipation and steady state
entanglement of two macroscopic ensembles
1012 atoms at RT
H. Krauter, C. Muschik, K. Jensen, W. Wasilewski, J. Pedersen, I. Cirac, E. S. Polzik, PRL, August 17, 2011arXiv:1006.4344
1012 atoms at RT
Driving
field
† †1 2 2 1ˆ ˆ ˆ ˆˆ ˆ ˆ ˆ( . .)H d a b a b a b a b h c
Collective dissipation: forward scattering
MF = 4
MF = 3
MF = 5,4,3~ 1000 MHz
320 kHz MF = -3MF = -41b 2b
† †1 2 2 1ˆ ˆ ˆ ˆˆ ˆ ˆ ˆ . .H a b a b a b a b h c
Standard form of Lindblad equation for dissipationLindblad equation for dissipative dynamics of atoms
† †1 2 2 1ˆ ˆ ˆ ˆA b b B b b
MF = 4
MF = 3
MF = 5,4,3~ 1000 MHz
320 kHz MF = -3MF = -41b 2b
Trace overnon-observed
fields
Pushing entanglement towards steady state
Entangling drive
t
Spin noiseprobe
1b
Optical pumping
50 msec!
Optical pumping
timePump, repump,drive and continuous measurement
Steady state entanglement generated by dissipation and continuous measurement
We use the continuousmeasurement (blue time function) togenerate continuousentangled statePure
dissipation
Macroscopic spin
Variance of the yellowmeasurement conditionedon the result of theblue measurement
Steady stateentanglementkept for hours
Entanglement maintained for 1 hour
Steady state entanglement generated by dissipation and continuous measurement
Quantum teleportation between distant atomic memories
1
2
H.Krauter, J. M. Petersen, T. Fernholz, D.Salart C.MuschikI.Cirac
B
Bell measurement
320 kHz MF = -3MF = -4
2b
MF = -3
H=a-†b†+
Atoms 1 – photonsentanglement
generation
H=a+b†+…
Atoms 2 – photonsbeamsplitter
Bell measurement
Classicalcommunication
Quantum benchmark for storage and transmission of coherent states. K. Hammerer, M.M. Wolf, E.S. Polzik, J.I. Cirac, Phys. Rev. Lett. 94,150503 (2005).
Classical feedback gain
Variance of the teleported atomic state
Process tomographywith coherent states
Deterministicunconditional and broadband teleportation
Rate of teleportation 100HzSuccess probability 100%
Classicalbound