1. Quantum teleportation between light and matter
Danmarks Grundforskningsfond - Quantum Optics Center
QUANTOP
Quantum teleportation
between light and matter
Eugene Polzik
Niels Bohr Institute
Copenhagen University

2. Quantum mechanical wonders
(second wave)
Quantum objects
cannot be measured
cannot be copied
exist in superposition
and entangled states
Quantum Information Science
Quantum memory
Communications with
absolute security
Computing with unprecedented speed
Teleportation of objects (or at least of their quantum states)

3. what is being transmitted?
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

4. described as a set of classical bits
Problem: electrons, atoms and humans cannot be
described as a set of classical bits

5. Noncommuting operators:
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
Bohr’s
complementarity
principle
Perfect
measurement
of both position
and momentum
is impossible
Noncommuting operators:
Heisenberg in 1927.
Minimal symmetric
Uncertainty:

6. 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)

7. entangled objects done! Teleportation cartoon Bell measurement
Ensemble of 1012 atoms
Classical communication
Bell
measurement
entangled objects
done!
<n> = 0 – 500 photons

8. Physics of entanglement
Interaction↔entanglement=conservation of energy
momentum
angular momentum σ- + σ+
Singlet or e-bit – maximally entangled pair -1 1
Single atom/ion
Ann Arbor
Ensembles of atoms -1
Copenhagen, Caltech -1 1
Harvard, Caltech,
GeorgiaTech

9. Einstein-Podolsky-Rosen (EPR) entanglement
Canonical operators: position/momentum
or real/imaginary parts of the e.-m. field amplitude, etc
EPR paradox 1935
2 particles entangled in position/momentum
EPR state of light Caltech 1992
EPR state of atoms Aarhus 2001

10. Teleportation principle (canonical operators)
L.Vaidman
Einstein-Podolsky-Rosen entangled state

11. Canonical operators for light
Coherent state: t
Pulse:

12. Canonical operators of light Y, Q can be efficiently measured
-450
450
l/4
Polarizing
Beamsplitter 450/-450
Strong field A(t) x
Quantum field a -> Y, Q
Polarizing
cube

13. Squeezed single photon state
Quantum tomography – with many copies of a state
Coherent state
Squeezed single photon state
QUANTOP 2006
Wigner function

14. 4 3 Canonical quantum variables for an atomic ensemble: y z x
Quantum state
(Wigner function) 3 4

15. 4 3 Light modes and atomic levels Teleported operators – of quantum
Orthogonally
polarized
Teleported
operators –
of quantum
mode
Strong field 4 3
Extra benefit: homodyne measurements
on quantum mode carried at beatnote frequency Ω

16. Atomic operators Rotating frame spin 4 3
Atoms: ground state Caesium Zeeman sublevels
Rotating frame spin 4
Atomic operators 3

17. Optical pumping with circular
Object – gas of spin polarized atoms at room temperature
Optical pumping with circular
polarized light
Decoherence from stray
magnetic fields
Magnetic Shields
Special coating – 104 collisions
without spin flips

18. Quantum Noise of Atomic Spin –

19. Classical benchmark fidelity for teleportation of coherent states
e.-m. vacuum
Atoms
Best classical fidelity 50%
K. Hammerer, M.M. Wolf, E.S. Polzik, J.I. Cirac,
Phys. Rev. Lett. 94, (2005),

20. Nature 443, 557 (2006). J.Sherson, H.Krauter, R.Olsson, B.Julsgaard,
October 5, 2006
J.Sherson, H.Krauter,
R.Olsson, B.Julsgaard,
K.Hammerer, I.Cirac, and E.Polzik,
Nature 443, 557 (2006).

21. ?

22. Teleportation of light onto a macroscopic atomic sample
Pulse
to be
teleported
<n>=0–200
photons
Atoms – target object
of teleportation

23. Teleportation
step 1: entanglement

24. interaction entangles
Light+Atoms: entangling Hamiltonian
Off-resonant
interaction entangles
light and atoms
D = 800 MHz
6P3/2
Upper sideband
is teleported
6S1/2
W = 0.3 MHz
+ magnetic field

25. Entanglement via forward scattering of light4
Atoms

26. B Addition of a magnetic field couples light to rotating spin states yz B
Atomic Quantum Noise
2,4
2,2
2,0
1,8
1,6
1,4
1,2
Atomic noise power [arb. units]
1,0
0,8
0,6
0,4
0,2
0,0
0,0
0,2
0,4
0,6
0,8
1,0
1,2
1,4
1,6
1,8
2,0
Atomic density [arb. units]

27. step 2: Bell measurement
Teleportation
step 2: Bell measurement

28. Polarization homodyning - measure Y (or Q)
-450
450
l/4
Polarizing
Beamsplitter 450/-450

29. q y

30. step 3: classical communication
Teleportation
step 3: classical communication

31. 322 kHz
RF field
Magnetic
shields

32. Teleportation experiment Teleported operators:
pulse sequence
feedback
Teleported
operators:
pump
4ms
2ms
entangling+
verifying
Bell measurement

33. Teleportation
step 4: verification

34. Mean values of operators
verification
XA=Jz
Mean values of operators
are transferred
PA=Jy
Atomic variances are below a critical value

35. Teleportation of coherent state n ≈ 500

36. Teleportation of a vacuum state of light
Teleported state readout
determines
atomic variance
Input state readout

37. Teleportation of a coherent state, n ≈ 5

38. Raw data: atomic state for <n>=5
input photonic state
Reconstructed
teleported state, F=0.58±0.02

39. Fqubit =72% Experimental quantum fidelity versus best classical case
Upper bound on <n>
≈ 1000 – due to gain instability
F quantum
F classical =
Anticipated qubit fidelity:
Fqubit =72%
(with feasible imperfections)
Optimal gain

41. Summary:
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/ , Nature, October 5, 2006

42. J. Sherson, H. Krauter, R. K. Olsson, B. Julsgaard,
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/ , Nature, October 5, 2006
Wed Oct 4, 1:06 PM ET LONDON (Reuters)
Quantum information teleported from light to matter

43. NBI - QUANTOP 2006