Verifying Entanglement between Atomic Ensembles

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Verifying Entanglementbetween Atomic Ensembles
S.J. van Enk Bell Labs, Lucent
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Verifying Entanglementbetween Atomic Ensembles
S.J. van Enk Bell Labs, Alcatel
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Overview

• Entanglement between atomic ensembles
• Theory behind an experiment (Chou et al., Nature
  238, 828(2005))
• Some new data
• Progress!
• Verifying entanglement is harder than creating it

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Entanglement Stored in Remote Atomic Ensembles
Sergey Polyakov Jeff Kimble SJvE
Hugues de Riedmatten
Daniel Felinto
James Chou
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The DLCZ Protocol

• Describes how to entangle 2 atomic ensembles
• Entanglement is generated probabilistically
• but heralded
• Many errors are eliminated automatically
• built-in purification
• Shows how to use the entanglement for
  teleportation etc.
• Many experiments Kuzmich, Lukin, Polzik,..

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Physical Ingredients of DLCZ

• Uses collective enhancement (twice!)
• Heralding of success by photons eliminates many
  errors

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Entangling 2 Ensembles
Entanglement is stored in the ensembles for 1 ms.
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How to Verify Entanglement?

• Violate Bell or CSHS inequality
• Measure entanglement witness W
• Measure appropriate uncertainty relations of
  joint observables
• Do quantum state tomography

• Is quantitative
• Not the Wigner function, but density matrix

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Verification of Entanglement
Quantum state tomography
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Diagonal Elements
L
2L
Atoms
1064 nm
D2a
filter
BSR
1064 nm filters
Read
R
2R
D2b
Data acquisition
Atoms
filter
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Results
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Off-diagonal Elements
Phase shifter controlling ?
L
2L
Phase controller
Atoms
1064 nm
D2a
filter
BSR
BS2
1064 nm filters
Read
R
2R
D2b
Data acquisition
Atoms
filter
Read
Field 2
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L
1L
D1a
Atoms
filter
BS1
R
1R
D1b
Atoms
Data acquisition
filter
?
L
?
2L
D2a
Atoms
filter
BS2
R
2R
D2b
Atoms
Data acquisition
filter
14
L
1L
D1a
Atoms
filter
BS1
R
1R
D1b
Atoms
Data acquisition
filter
L
?
2L
D2a
Atoms
filter
BS2
R
2R
D2b
Atoms
Data acquisition
filter
15
L
1L
D1a
Atoms
filter
BS1
R
1R
D1b
Atoms
Data acquisition
filter
L
?
2L
D2a
Atoms
filter
BS2
R
2R
D2b
Atoms
Data acquisition
filter
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Result

• For the two different entangled states find

• Entanglement may seem small, BUT
• Compared to Bell inequality tests we took into
  account all
• null results
• Used measurements without any corrections for
  losses

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L
2L
Atoms
D2a
filter
R
2R
D2b
Atoms
Data acquisition
filter
z0
z1
z2
Inferred entanglement as function of location
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New data
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Three Worries

• We restricted our attention to states of the form

• What about 2 photons? (P(11)P(20)P(02)!)
• What about all those 0s off the diagonal?
• What about other modes?

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LOCC

• Filtering out more than 2 photons is a local
  operation, hence

measured

• Suppose one applies equal but random phase shifts
  to both fields,
• and subsequently forgets what phase was applied
• This is LOCC, and sets off-diagonal elements
  between states
• with different numbers of photons to zero

• Suppose one checks the color of photons, and
  subsequently
• forgets what color it was (does not give info
  about state!)
• This is LOCC, too hence ok!

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Postselection?

• Most experiments using entangled photons use
  only data
• where photons were detected
• But this does not work for detecting entanglement
  in

Why not??
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Beware of Postselection

• Take the unentangled state

• Data where photons are detected consistent with

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Beware of Postselection 2

• Keeping results with 1 photon in total detected
  is a nonlocal filter
• Keeping results with 1 photon on each side is a
  local filter
• used in Bell inequality tests on
  polarization-entangled state

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Conclusions

• Verifying entanglement is harder than making it
• Made verified entanglement between ensembles
  2.8 m apart
• Should be close to ideal state inside ensembles
• There are subtle issues lurking in the background
• Local filtering is ok
• Postselection is not ok
• Phase
• Need a reference to define it

• Some claim, wrongly, that 0gt1gt1gt0gt is not
  entangled
• But dont get me started on that