1. Light-Matter Quantum Interface
Danish Quantum Optics Center University of Aarhus
QuanTOp
Niels Bohr Institute
Copenhagen University
Light-Matter Quantum Interface
Eugene Polzik LECTURE 4
IHP Quantum Information Trimester

2. Quantum memory for light:
criteria
Memory must be able to store independently prepared
states of light
The state of light must be mapped onto the memory with
the fidelity higher than the fidelity of the best
classical recording
The memory must be readable
B. Julsgaard, J. Sherson, J. Fiurášek , I. Cirac, and E. S. Polzik
Nature, 432, 482 (2004); quant-ph/

3. Mapping a Quantum State of Light onto Atomic Ensemble
Spin Squeezed
Atoms
The beginning. Complete absorption
1 >
2 >
Squeezed Light pulse
Proposal:
Kuzmich, Mølmer, EP
PRL 79, 4782 (1997)
0 >
Experiment:
Hald, Sørensen, Schori, EP
PRL 83, 1319 (1999)
Atoms
Very inefficient
lives only nseconds,
but a nice first try…

4. interaction entangles
Our light-atoms interface - the basics
…and feedback
applied
Light pulse – consisting of two modes
Strong
driving
Weak
quantum
Projection
measurement
on light
can be made…
Dipole off-resonant
interaction entangles
light and atoms
or more atomic samples
Passes through one…

5. vertical horizontal Polarization quantum variables – Light x y 45 -45
Polarization – Stokes
parameters
vertical
Propagation direction
Linear polarizations
Circular polarizations
horizontal

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

7. Decoherence from stray Special coating – 104 collisions
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

8. t Pulse: Canonical quantum variables for light
Complementarity : amplitude and phase of
light cannot be measured together t
Pulse:
Various
states

9. Polarization homodyning - measure X (or P)
-450
450
l/4
Polarizing
Beamsplitter 450/-450
Strong field A(t) x
EOM
Polarizing
cube
Quantum field a -> X,P S1

10. Teleportation in the X,P representation
Bell
measurement

11. another idea for (remote) state transfer
Today:
another idea for (remote) state transfer
and its experimental implementation for quantum
memory for light
Projection
measurement X
See also work on quantum cloning:
J. Fiurasek, N. Cerf, and E.S. Polzik,
Phys.Rev.Lett. 93, (2004)

12. Implementation: light-to-matter state transfer
No prior entanglement necessary
squeeze atoms first
= C
- C
F≈80%
F→100%
B. Julsgaard, J. Sherson, J. Fiurášek , I. Cirac, and E. S. Polzik
Nature, 432, 482 (2004); quant-ph/

13. These criteria should be met for memory in:
Quantum computing
with linear operations
Quantum buffer
for light
Quantum Key storage
in quantum cryptography
More
efficient repeaters

14. Classical benchmark fidelity for transfer 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),

15. Preparation of the input state of light
Strong field A(t)
Quantum field - X,P x
EOM
Polarizing
cube S1
Vacuum
Input quantum
field
Coherent P
Squeezed
Polarization
state X

16. Physics behind the Hamiltonian: 1. Polarization rotation of light
-450
450
Polarizing
Beamsplitter 450/-450 x
Polarizing
cube
Quantum field

17. Physics behind the Hamiltonian: 2. Dynamic Stark shift of atoms
Strong field A(t)
Quantum field - a x
EOM
Polarizing
cube y

18. atoms Entanglement XL Quantum memory – Step 1 - interaction
Light rotates atomic spin – Stark shift XL
atoms
Atomic spin rotates polarization
of light – Faraday effect
Output
light PL
Input
light
Entanglement

19. light out atoms c XL Quantum memory – Step 2 - measurement + feedback
Polarization
measurement c
light out PL
Feedback
to spin rotation
atoms
Compare to
the best classical
recording
Fidelity – > 100%
(82% without SS atoms)

20. Experimental realization of quantum memory for light

21. B B Memory in rotating spin states y z 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]

22. B B x Memory in rotating spin states - continued z y
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]

23. Encoding the quantum states in frequency sidebands

24. Memory in atomic Zeeman coherences
Cesium
Rotating frame spin 4 3 2

25. x B B z y

26. Readout Input pulse pulse Magnetic feedback Nature, Nov. 25 (2004)
quant-ph/

27. Light t Stored state versus Input state: mean amplitudes p X plane
read
write t
output
input
Y plane
Magnetic
feedback p
/ 2 - rotation
Xin ~ SZin
Pin ~ SYin
Light

28. Atoms Light Stored state: variances Absolute quantum/classical border
3.0
Absolute quantum/classical border
Perfect mapping
Atoms
<P2mem >
<X2mem>
<X2in> =1/2
<P2in >=1/2
Light

29. Fidelity of quantum storage
State overlap averaged over
the set of input states
0.65
0.7
0.75
0.8
0.85
0.9
0.56
0.58
0.62
0.64
0.66
0.68
Coherent states with 0 < n <4
Experiment
Best classical mapping F
0.82
0.84
0.86
0.88
0.9
0.54
0.56
0.58
0.62
0.64
Gain
Experiment
Best classical mapping
Coherent states with 0 < n <8

30. Quantum memory lifetime

31. Decoherence Limitations
Typical estimate of linewidth:
G[Hz] = *q[deg] + 1.0*P[mW] + 0.5*P[mW]*q[deg]
1-2Hz
3-6Hz
25-40Hz
Dominating
Working values:
Important for entanglement:
Atomic/shot ratio
(T is time, typical 2ms)
Decoherence
(retaining the dominating term)
up to around 0.5
Theoretical entanglement
with no decoherence:
Need k2 large and
h low, impossible.

32. Realized by an extra QND
Deterministic quantum memory for a light Qubit
Initial state of atoms
Initial state of atoms
coherent
squeezed
State overlap
Input state
63%
Fidelity 100% for
a qubit input state
78%
90%
Realized by an extra QND
measurement pulse
Qubit fidelity
A. Sørensen, NBI

33. Quantum Memory for Light demonstrated
Deterministic Atomic Quantum Memory proposed and
demonstrated for coherent states with <n> in
the range 0 to 10; lifetime=4msec
Fidelity up to 70%, markedly higher than best
classical mapping

34. Spatial array of memory cells Detector array
Scalability – an array of dipole traps or
solid state implementation – quantum holograms
Detector
array
Spatial
array of memory
cells
I. Sokolov and EP, to be submitted

35. Future: Inverse Mapping Atoms Light
Detector
Proposals: Kuzmich, EP ; Kraus, Giedke, Cirac 2001 Y
l/4 wave plate
Recent advanced proposals:
K. Hammerer, K. Mølmer, EP, J.I. Cirac. Phys.Rev. A., 70, (2004).
J. Sherson, K. Mølmer, A.Sørensen, J. Fiurasek, and EP
quant-ph/
Atoms Y
Light pulse

36. z x y z y Quantum memory read-out: single pulse in squeezed state
Step 1
Exchange y and z components:
pass light through l/4 plate and
probe along spin-y axis y z
Step 2

37. Light-Atoms Q-interface with cold atoms6P
Cesium clock levels
F=4
F=3
D. Oblak
C. Alzar,
P. Petrov

38. Memory Summary New state transfer protocol → quantum memory for light
Experimental demonstration for coherent states
Nature, 432, 482 (2004)
Prediction for a qubit state – bridging dicrete and
continuous variables
State retrieval protocols

39. Criteria for light-ensemble interface
2-level stable state with long coherence time
Initialization: collective coherent spin state (CSS)
Coupling of the CSS to light corresponding to
high optical density
Figure of merit
Probe depumping
parameter:

40. Entangled atoms + Entangled light Light/atoms QI exchange
Atomic
teleportation
3-party
entanglement/
Secret sharing
Scaling/
solid state
implementation
Entangled
atoms +
Entangled light
Light/atoms
QI exchange
Quantum
memory
for light
Color code
hard
“easy”
Distillation
by local
operations
Multi-atom
Cat states
Continuous
variable
logic
Discrete
variable
logic

41. cavity enhanced interaction
enhanced phase shift
power build-up inside cavity
compensate with smaller photon number
cold atomic cloud
T: mirror transmission
a: absorption

42. Coupling strength of the interfacex y z
Initial coherent spin state:
results in distribution
Measurement on light
Spin squeezed state Z
degree of squeezing in Jz
Figure of merit for the
quantum interface
Duan, Cirac, Zoller, EP
PRL (2000)

43. Figure of merit for the quantum interface
Probe scattering
parameter:

44. + h Spontaneous emission – the fundamental limit 0.3 10 30 50
Single pass interaction
degree of entanglement
Figure of merit for the
quantum interface
+ h
Spontaneous emission
probability
K. Hamerrer, K. Mølmer, E. S. Polzik, J. I. Cirac.
PRA 2004, quant-ph/