Quantum teleportation
between light and matter
Eugene Polzik
Niels Bohr Institute
Copenhagen University
Quantum mechanical wonders
(second wave)
Quantum Information Science
•Quantum memory
•Communications with
absolute security
•Computing with unprecedented
speed
•Teleportation of objects (or at least
of their quantum states)
Teleportation a la Star Trek, what’s the problem?
Problem: Matter cannot be reversibly
converted into light!
Question: If matter if not teleported, then
what is being transmitted?
Answer: information - is what should be transmitted
Problem: electrons, atoms and humans cannot be
described as a set of classical bits
00111010111000010101
The more precisely the position is determined,
the less precisely the momentum is known in this instan
and vice versa.
--Heisenberg 1927
Blegdamsvej 17, Copenhagen
Heisenberg in 1927.
Minimal symmetric
Uncertainty:
1
2
2
Var  x   x  p 
2
Bohr’s
complementarity
principle
Perfect
measurement
of both position
and momentum
is impossible
x  p  12 
Noncommuting operators:
ˆ,P
ˆ ]  i
[X
Challenge of Quantum Teleportation:
transfer two non-commuting operators from one system onto another
(Heisenberg picture)
equivalent to:
Transfer an unknown quantum state from one system onto another
(Schördinger 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)
Teleportation cartoon
Classical communication
Bell
measurement
Ensemble of 1012 atoms
<n> = 0 – 500 photons
Interaction↔entanglement=conservation of energy
momentum
angular momentum
σ+ + σ0
+
-1
Single atom/ion
Ann Arbor
Singlet or e-bit – maximally entangled pair
1

1
2
 1,

  1,  

Ensembles of atoms
-1
1
Harvard, Caltech,
GeorgiaTech
-1
0
Copenhagen, Caltech
Einstein-Podolsky-Rosen (EPR) entanglement
Canonical operators: position/momentum
or real/imaginary parts of the e.-m. field amplitude, etc
EPR paradox 1935
Xˆ 1  Xˆ 2  Const
[ Xˆ , Pˆ ]  i
Pˆ1  Pˆ2  0
• 2 particles entangled in position/momentum
ˆ ,P
ˆ
X
1
1
ˆ ,P
ˆ
X
2
2
• EPR state of light Caltech 1992
• EPR state of atoms Aarhus 2001
 1
Teleportation principle (canonical operators)
[Y , Q]  i, [Y 1  Y 2, Q1  Q 2]  0
L.Vaidman
Yˆ1 , Qˆ1
Yˆ2 , Qˆ 2
YˆV , QˆV
CX CP
CX CP
Yˆ , Qˆ
V
V
Einstein-Podolsky-Rosen entangled state
Y1  Y2  0,
Q1  Q2  0
Canonical operators for light
Yˆ , Qˆ   i
Yˆ 
Qˆ 
1
2
i
2
aˆ
aˆ


Coherent state:


 aˆ 
 aˆ
Q̂
Yˆ
Eˆ  Yˆ cos(t )  Qˆ sin( t )
t
Pulse: YˆL 
T
1
T

ˆ
(
a
 (t )  aˆ (t ))dt
0

Var Yˆ  Var Qˆ  12



1
1
ˆ
A
(
a
 a) 
S 2  4 [( A  aˆ ) ( A  aˆ )  ( A  aˆ ) ( A  aˆ )]  2
-450
l/4
AYˆ
450
Sˆ3 
Polarizing
Beamsplitter 450/-450
x
Polarizing
cube
1
2
Quantum field a -> Y, Q
1
2
AQˆ
Quantum tomography – with many copies of a state
Coherent state
Squeezed single photon state


Var Yˆ  Var Qˆ  12
Q̂
Q̂
Yˆ
Yˆ
5
2.5
0
QUANTOP 2006
-2.5
Wigner function
-5
0.3
0.2
0.1
0
7.5
5
2.5
0
-2.5
Canonical quantum variables for an atomic ensemble:


Jˆ z , Jˆ y  iJ x
x
Xˆ
y
A

, PˆA  i
z
J yJ z 
1
2
F
Jx 
N
2
ˆ
ˆ
J
J
y
Xˆ A  z , PA 
Jx
Jx
6P3 / 2
5
2.5
0
Quantum state
(Wigner function)
-2.5
-5
0.3
0.2
0.1
0
Jz
7.5
5
2.5
0
-2.5
Jy
6S1/ 2 3 4

Light modes and atomic levels
Orthogonally
polarized
Teleported
operators –
of quantum
mode   
Yˆ , Qˆ 
Strong field
3
4


Extra benefit: homodyne measurements
on quantum mode carried at beatnote frequency Ω
Atoms: ground state Caesium Zeeman subleve
6P3 / 2
Rotating frame spin
Jˆ zLab  Jˆ y cos t  Jˆ z sin t
Jˆ yLab   Jˆ y sin t  Jˆ z cos t
6S1/ 2
Atomic operators
lab

ˆ
ˆ
ˆ
J z  N 3, 4   4,3 
J
lab
x
3
4
lab

ˆ
ˆ
ˆ
J y  iN 3, 4   4,3 
 N ˆ 4, 4  ˆ 3,3   N

Object – gas of spin polarized atoms at room temperature
Optical pumping with circular
polarized light
3
4
Decoherence from stray
magnetic fields
Magnetic Shields
Special coating – 104 collisions
without spin flips
J z  N
Quantum Noise of Atomic Spin – Var
N
Classical benchmark fidelity
for teleportation of coherent states
Qˆ 
i
2
(aˆ   aˆ )
Yˆ 
1
2
(aˆ   aˆ )
e.-m. vacuum
Best classical fidelity 50%
K. Hammerer, M.M. Wolf, E.S. Polzik, J.I. Cirac,
Phys. Rev. Lett. 94,150503 (2005),
Atoms
October 5, 2006
J.Sherson, H.Krauter,
R.Olsson, B.Julsgaard,
K.Hammerer, I.Cirac, and
E.Polzik,
Nature 443, 557 (2006).
?
Teleportation of light onto a macroscopic atomic sample

E
Atoms – target object
of teleportation
Pulse
to be
teleported
<n>=0–200
photons

E
Off-resonant
interaction entangles
light and atoms
6P3/2
D  800 MHz
Upper sideband
is teleported
YˆL , Qˆ L
6S1/2
  0.3 MHz
Hˆ  Sˆ3 Jˆ z   Qˆ L Xˆ A
+ magnetic field

  2a1
N ph N at   0  50  0.02  1
AD
Entanglement via forward scattering of light
4
Atoms

Addition of a magnetic field couples light to rotating spin states
̂
J
S1
y
Sˆ2 (t )
z
Atomic Quantum Noise
2,4

Jˆ zlab (t )  Jˆ ylab (t )
2,2
2,0

ˆ (t )
Jˆ ylab (t )  Jˆ zlab (t )   S
3
Atomic noise power [arb. units]
1,8
1,6
1,4
1,2
ˆ out  S
ˆ in   J
ˆ Lab
S
2
2
z
1,0
0,8
0,6
0,4
Sˆ2out (t )  Sˆ2in (t )   [ Jˆ z cos(t )  Jˆ y sin( t )]
0,2
0,0
0,0
0,2
0,4
0,6
0,8
Atomic density [arb. units]
1,0
1,2
1,4
1,6
1,8
2,0
Sˆ2 
1
2
AYˆ
-450
l/4
450
Sˆ3 
Polarizing
Beamsplitter 450/-450
1
2
AQˆ
yˆ s  qˆc 
1
2
( yˆ
out
s
 qˆ )  Yˆ
out
c
q
y
Yˆ , Qˆ
yˆ c  qˆ s 
1
2
( yˆ
out
c
 qˆ )  Qˆ
out
s
yˆ s  qˆc
yˆ c  qˆ s
322 kHz
RF field
Magnetic
shields
Teleportation experiment
Teleported
ˆ  Xˆ , Pˆ
operators: Yˆ , Q
A
A
pulse sequence
feedback
pump
4ms
2ms
entangling+ verifying
Bell measurement
Sˆ2out (t )  Sˆ2in (t )   [ Jˆ z cos(t )  Jˆ y sin( t )]
ycver
y sver
XA=Jz
Mean values of operators
are transferred
X A  YL , PA  QL
PA=Jy
Atomic variances are below a critical value
 X2 , P  1.22  0.03 
3
2
Teleportation of coherent state n ≈ 500
tele
X atoms
Y
in
photons
 1.00  0.02
Teleportation of a vacuum state of light
Teleported state
ŷ c readout
determines
atomic
variance
Input state
Yˆ
readout
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
Upper bound on <n>
≈ 1000 – due to gain instability
F quantum
n 1
F classical =
n 2
Anticipated qubit fidelity:
Optimal gain
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 mainly
by 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
Outlook June 2001
Scientists teleport two different objects
POSTED: 1113 GMT (1913 HKT), October 5, 2006
First Teleportation Between Light and Matter
J. Sherson, H. Krauter, R. K. Olsson, B. Julsgaard,
K. Hammerer, I. Cirac, and ESP;
quant-ph/0605095 , Nature, October 5, 2006
Wed Oct 4, 1:06 PM ET LONDON (Reuters)
Quantum information teleported from light to matter
NBI - QUANTOP 2006