Niels Bohr InstituteCopenhagen University

Quantum teleportation between light and matter

Eugene Polzik

Quantum Information ScienceQuantum Information Science

•Computing with unprecedented speed

•Teleportation of objects (or at least of their quantum states)

•Quantum memory •Communications with

absolute security

Quantum mechanical wonders(second wave)

Teleportation a la Star Trek, what’s the problem?Teleportation a la Star Trek, what’s the problem?

Problem: Matter cannot be reversiblyconverted into light!

Question: If matter if not teleported, thenwhat is being transmitted?

Answer: information - is what should be transmitted

Problem: electrons, atoms and humans cannot bedescribed as a set of classical bits

00111010111000010101

The more precisely the position is determined, the less precisely the momentum is known in this instant, and vice versa.

--Heisenberg 1927 Blegdamsvej 17, Copenhagen

Heisenberg in 1927.

Bohr’s complementarity

principlePerfect

measurementof both position and momentum

is impossible

21 px

iPX ]ˆ,ˆ[

Noncommuting operators:

2

122 pxxVar

Minimal symmetricUncertainty:

Challenge of Quantum Teleportation:

transfer two non-commuting operators from one system onto another(Heisenberg picture)

Teleportation experiments so far:Light onto light: Innsbruck(97), Rome(97), Caltech(98), Geneva, Tokyo, Canberra…

Single ion onto single ion: Boulder (04), Innsbruck (04)

equivalent to:

Transfer an unknown quantum state from one system onto another(Schördinger picture)

Teleportation cartoon

Bellmeasurement

<n> = 0 – 500 photons

Classical communication

Ensemble of 1012 atoms

Interaction↔entanglement=conservation of energymomentum

angular momentum

1-1

0 σ+ σ-+

+Single atom/ion Ann Arbor

Ensembles of atoms

-1 1Harvard, Caltech,GeorgiaTech

-1 0

Copenhagen, Caltech

,1,12

1

Singlet or e-bit – maximally entangled pair

Einstein-Podolsky-Rosen (EPR) entanglement

• 2 particles entangled in position/momentum

11ˆ,ˆ PX 22

ˆ,ˆ PX

0ˆˆˆˆ2121 PPConstXX

• EPR state of light Caltech 1992

• EPR state of atoms Aarhus 2001

Canonical operators: position/momentum or real/imaginary parts of the e.-m. field amplitude, etc

1]ˆ,ˆ[ iPXEPR paradox 1935

Teleportation principle (canonical operators)L.Vaidman

VV QY ˆ,ˆ

22ˆ,ˆ QY11

ˆ,ˆ QY

0,0 2121 QQYYEinstein-Podolsky-Rosen entangled state

XC PC VV QY ˆ,ˆXC PC

0],[,],[ 2121 QQYYiQY

iQY ˆ,ˆ

Y

Q

t

)sin(ˆ)cos(ˆˆ tQtYE

Pulse: T

TdttataY

0

1L ))(ˆ)(ˆ(ˆ

21ˆˆ QVarYVar

Canonical operators for lightCoherent state:

aaQ

aaY

i ˆˆˆ

ˆˆˆ

2

21

xStrong fie

ld A(t)

Quantum field a -> Y, QPolarizing

cube

-450 450

PolarizingBeamsplitter 450/-450

)]ˆ()ˆ( aAaA YAaaA ˆ)(2

121 )ˆ()ˆ[(ˆ

41

2 aAaAS

QAS ˆˆ2

13

-2.50

2.55

7.5

-5

-2.5

0

2.55

0

0.1

0.2

0.3

-2.50

2.55

7.5

-5

-2.5

0

2.55

Wigner function

Y

Q

Squeezed single photon state

QUANTOP 2006

Y

Q

21ˆˆ QVarYVar

Coherent stateQuantum tomography – with many copies of a state

-2.5

02.5

57.5

-5

-2.5

0

2.55

0

0.1

0.2

0.3

-2.50

2.55

7.5

-5

-2.5

0

2.55

Quantum state (Wigner function)

yJzJ

Canonical quantum variables for an atomic ensemble:

y z

x

NF

JJJiJJJ xzyxyz 2ˆ,ˆ

21

x

yA

x

zAAA

J

JP

J

JXiPX

ˆ,

ˆˆˆ,ˆ

2/36P

432/16S

Light modes and atomic levels

43

Strong field

Orthogonallypolarized

QY ˆ,ˆ

Teleported operators – of quantum mode

Extra benefit: homodyne measurements on quantum mode carried at beatnote frequency Ω

Atoms: ground state Caesium Zeeman sublevels

2/36P

2/16S 43

tJtJJ

tJtJJ

zyLaby

zyLabz

cosˆsinˆˆ

sinˆcosˆˆ

Rotating frame spin

NNJ

iNJNJlabx

laby

labz

3,34,4

3,44,33,44,3

ˆˆ

ˆˆˆˆˆˆ

Atomic operators

Magnetic Shields

Special coating – 104 collisionswithout spin flips

Decoherence from straymagnetic fields

Object – gas of spin polarized atoms at room temperature

Optical pumping with circularpolarized light

3 4

Quantum Noise of Atomic Spin –

N

NJVar z

Classical benchmark fidelity for teleportation of coherent states

)ˆˆ(ˆ2

1 aaY

)ˆˆ(ˆ2

aaQ 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),

J.Sherson, H.Krauter, R.Olsson, B.Julsgaard, K.Hammerer, I.Cirac, and E.Polzik, Nature 443, 557 (2006).

October 5, 2006

?

Teleportation of light onto a macroscopic atomic sample

Pulseto be

teleported<n>=0–200

photons

E

E

Atoms – target objectof teleportation

Off-resonant interaction entangles

light and atoms

ALz XQJSH ˆˆˆˆˆ3 + magnetic field

800 MHz

0.3 MHz6S1/2

6P3/2

102.0502 01

atph NNA

a

Upper sidebandis teleported

LL QY ˆ,ˆ

Entanglement via forward scattering of light

Atoms

4

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]

)(ˆ)(ˆ)(ˆ

)(ˆ)(ˆ

3 tStJtJ

tJtJ

labz

laby

laby

labz

Labz

inout JSS ˆˆˆ22

)]sin(ˆ)cos(ˆ[)(ˆ)(ˆ22 tJtJtStS yzinout

J

yz )(ˆ

2 tS1S

Addition of a magnetic field couples light to rotating spin states

-450 450

PolarizingBeamsplitter 450/-450

YAS ˆˆ2

12

QAS ˆˆ2

13

q

QY ˆ,ˆ

Yqyqy outc

outscs

ˆ)ˆˆ(ˆˆ2

1

Qqyqy outs

outcsc

ˆ)ˆˆ(ˆˆ2

1

y

Magneticshields

cs qy ˆˆ

sc qy ˆˆ 322 kHzRF field

AA PXQY ˆ,ˆˆ,ˆ

Teleportation experimentTeleported operators:

pump

entangling+Bell measurement

verifying

feedback

4ms 2ms

pulse sequence

)]sin(ˆ)cos(ˆ[)(ˆ)(ˆ22 tJtJtStS yzinout

vercy ver

sy

LALA QPYX ,

Mean values of operatorsare transferred

2

303.022.12

, PXAtomic variances are below a critical value

XA=Jz

PA=Jy

Teleportation of coherent state n ≈ 500

02.000.1 inphotons

teleatoms

Y

X

Teleportation of a vacuum state of light

Input state readout Y

Teleported state readout cydetermines

atomic variance

Teleportation of a coherent state, n ≈ 5

Raw data: atomic state for <n>=5 input photonic state

Reconstructed teleported state, F=0.58±0.02

Experimental quantum fidelity versus best classical case

F quantum

F classical =

Optimal gain

2

1

n

n

Upper bound on <n>≈ 1000 – due to gain instability

Anticipated qubit fidelity:

Fqubit =72% (with feasible imperfections)

•Teleportation between two mesoscopic objects of different nature – a photonic pulse and an atomic ensemble demonstrated

•Distance 0.5 meter, can be increased (limited mainlyby propagation losses)

•Extention to qubit teleportation possible

•Fidelity can approach 100% with more sophisticated measurement procedure plus using squeezed light as a probe

J. Sherson, H. Krauter, R. K. Olsson, B. Julsgaard, K. Hammerer, I. Cirac, and ESP; quant-ph/0605095 , Nature, October 5, 2006

Scientists teleport two different objectsPOSTED: 1113 GMT (1913 HKT), October 5, 2006

First Teleportation Between Light and Matter

Wed Oct 4, 1:06 PM ET LONDON (Reuters)Quantum information teleported from light to matter

J. Sherson, H. Krauter, R. K. Olsson, B. Julsgaard, K. Hammerer, I. Cirac, and ESP; quant-ph/0605095 , Nature, October 5, 2006

Outlook June 2001

NBI - QUANTOP 2006