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

Two-mode squeezed = EPR entangled mode

OPO2SHG

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

CV entangled states stored with F > Fclassical

X

P

X

P

X

P

Thomas Fernholz

Hanna Krauter

Kasper Jensen

Lars Madsen

WojtekWasilewski

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

Photonic state

F=4

6S1/2

mF=3 mF=4

Growing material cats

N>>>1

│0.3> -│3.0>

PRL 2010

Outlook – scalable quantum network