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Entanglement of Collective Quantum Entanglement of Collective Quantum Variables for Quantum Memory and Variables for Quantum Memory and
TeleportationTeleportation
N. P. Bigelow
The Center for Quantum Information
The University of Rochester
ΨUR
CQI
A Tall Pole Item in QIA Tall Pole Item in QI
How to Realize Robust, Long- Lived
Entanglement of Many Particles for
Quantum Information Storage and Processing
ΨUR
CQI
We performed the first experimental demonstration of We performed the first experimental demonstration of
long-lived entanglementlong-lived entanglement of the spins of 10 of the spins of 101212 neutral, neutral,
ground-state atoms in a simple atomic vapor cell ground-state atoms in a simple atomic vapor cell
by using the interaction of the atomic sample by using the interaction of the atomic sample
with polarized laser lightwith polarized laser light
Accomplishments to Date
ΨUR
Simple, Long-lived On-Demand Entanglement Simple, Long-lived On-Demand Entanglement is Required for Practical Quantum Information Networks:is Required for Practical Quantum Information Networks:Quantum Memory, Teleportation and Quantum RepeatersQuantum Memory, Teleportation and Quantum Repeaters
Objectives–to create entanglement of a macroscopic sample of matter – a collection of trillions of atoms–to create entangled samples separated by large distances–to teleport the quantum state of massive particles – a sample of atoms–To develop quantum devices for purification and transmission of entanglement over long distancesRelevanceExtensible entanglement is an enabling technology for QI toolbox: information storage and transmittal
Present Status–We have demonstrated the entanglement of more than 1012 atoms using coherent laser light
Milestones for Future Work–Create entangled atomic samples that are widely separated in space–Teleport the quantum state of massive matter–Quantum repeaters
Approach–To couple light to the collective quantum variables of a macroscopic sample –To create on-demand entanglement using interaction of the atoms with laser light–To use measurements of quantum “noise” as an entanglement detector
There is a beneficial synergy with other CQI projectsThere is a beneficial synergy with other CQI projects
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ΨUR
CQI
Important Quantum Information Protocols: Important Quantum Information Protocols: Entanglement Purification and Quantum RepeatersEntanglement Purification and Quantum Repeaters
Issue and Objective: • Optical states (photonic channels) are ideal for transferring information
as light is the best long distance carrier of information. • To date, the majority of quantum communications experiments on
entanglement involve entangled states of light. • Unfortunately, entanglement is degraded exponentially with distance due
to losses and channel noise. • Solutions protocols have been devised evoking concepts of
entanglement purification and quantum repeaters strategies that avoid entanglement degradation while increasing the
communication time only polynomially with distance.
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Requirements for implementing these QI Devices:• Long lived entanglement - quantum memory
• Generation of entanglement between distant qubits
What platform to use? What tool in our toolbox?
Quantum Information Processing: Quantum Information Processing: Light and/or Atoms?Light and/or Atoms?
Light as the Quantum System
To date, the majority of quantum communications experiments on
entanglement involve entangled states of light
Entanglement of discrete photonic variables (spin-1/2) and continuous
variables (quadrature phases) has been demonstrated. Continuous variables
are advantageous because they provide access to an infinite dimensional state
space.
It is hard to “store” light ΨUR
Matter (Atoms) as the Quantum System
Entanglement of massive particles with multiple internal degrees of
freedom is more difficult but recognized as mandatory for realizing the entanglement lifetimes needed for information storage and processing
Record so far: four trapped ions (C. Sackett et al. At NIST Boulder –
Nature 2000)
How to entangle many, many atoms? How to entangle many, many atoms?
Can we do so in a simple way?Can we do so in a simple way?
Can we introduce a “new” physics Can we introduce a “new” physics
approach to the QI toolbox?approach to the QI toolbox?
How to have How to have longlong coherence times? coherence times?ΨUR
Some Needs for the QI Toolbox
Entangling the Collective Quantum Entangling the Collective Quantum Variables of the Atomic VaporVariables of the Atomic Vapor
• For a sample of many atoms, the accepted approach to entanglement is to build it up on a atom-by-atom basis – difficult (loss of single atom destroys entanglement, very sensitive to environment, spontaneous emission..)
• Our approach is to couple strongly to the collective variables of the ensemble using an optical interaction
• Readily achieve the required strong coupling without using a cavity or a trap
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we use the collective spin of the sample – the
“super moment” reflecting the
quantum sum of the individual
magnetic moments of the atom in the gas
What is Collective Spin?
By Entangling Collective Variables Long By Entangling Collective Variables Long Lived Entanglement Can be Realized Lived Entanglement Can be Realized
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rS = ˆ s ii
∑
• Entanglement of the Collective Spin is robust because the loss of coherence of one spin of our billions or trillions has little effect on the overall collective spin state – a robustness factor due to the intrinsic symmetry of collective state
• In a glass vapor cell, spin lifetimes are set by wall collisions and inhomogeneous magnetic fields–many milliseconds to seconds.
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•Collective Variables (in atomic physics)Spin-waves in H(Cornell U) and He-3 (ENS) [c. 1980](Stimulated Raman Scattering (Mostowski, Raymer…) [c. 1980] Present work [c. 1998]Light Storage - Hau, Fleischhauer, Lukin, Polzik..….[c. 2000]QI Theory: Cirac, Zoller…..[c. 2001/02]
Possible Applications to “Other” Solid State Systems – e.g. an electron gas
Entanglement can be produced by the Entanglement can be produced by the interaction of atoms with polarized lightinteraction of atoms with polarized light
AtomAAAs
Photons
Photons
Entangled Atoms
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Kuzmich, Bigelow, Mandel, EPL, 42, 481 (1998)Duan, Cirac, Zoller, Polzik, PRL 85, 5643 (2000)
Entanglement is produced through a QND interaction – a non-local
Bell measurement
Entanglement is produced Entanglement is produced using only coherent lightusing only coherent light
AtomAAAs
Photons
Photons
Entangled Atoms
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ˆ H I
=r S •
r J → ˆ σ x
s ˆ σ xJ
r S
r S
r J
r J
Optically Thick Sample Optically Thick Sample ++ Forward Scattering of Optical Field Forward Scattering of Optical FieldAnalogue of 2-mode squeezed stateAnalogue of 2-mode squeezed state
Forward scattered mode is keyForward scattered mode is key
r ′ S
r ′ J
Forward scattering, indistinguishability Forward scattering, indistinguishability & QND Hamiltonian & QND Hamiltonian
How Can We Probe the Collective Spin?How Can We Probe the Collective Spin?
How Can We Sense Entanglement?How Can We Sense Entanglement?
Collective quantum state not necessarily Collective quantum state not necessarily detectable in single particle propertiesdetectable in single particle properties
(a “bug” and a “feature”)(a “bug” and a “feature”)
Recall the quantum mechanics of a spinRecall the quantum mechanics of a spinand the connection to “noise”and the connection to “noise” ΨUR
Measurement Variances as a Probe of Entanglement
A Quantum Spin has Uncertainties A Quantum Spin has Uncertainties Relating its Knowable ComponentsRelating its Knowable Components
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Quantum Uncertainty Disc for Transverse Spin Component
Quantum Uncertainty Transverse Spin
Component
y
z
δz2
How to Probe Entanglement of the How to Probe Entanglement of the Collective Atomic SpinCollective Atomic Spin
An Ideal EPR StateOf Entangled Spins (Gaussian
Quantum Variables) Obeys
Duan, Giedke, Cirac, Zoller PRL 84, 2722 (2000); Simon & Peres-Horodecki PRL 84, 2726 (2000)
Non-factorable state
δr S y,z
2 ≤δr S ⊥
2
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Quantum Uncertainty Disc for Transverse Spin Component
Non-classical quantum variance (noise) only visible in the Non-classical quantum variance (noise) only visible in the collective spincollective spinExample of how quantum properties are observable in collective properties but Example of how quantum properties are observable in collective properties but
not single particlenot single particle
Variance of Collective Spin – Variance of Collective Spin – A Probe of EntanglementA Probe of Entanglement
When the Spins of the Sample are appropriately Entangled
The Spin Measurement Variance (noise) of
One Transverse Quadrature Can be Reduced Below the
“Quantum Limit”So, We Use Quantum Spin
Variance as Our Probe
(recall noise measurements presented by Yamamoto, discussed by Marcus)
Bigelow, Nature 409, 27 (2001)
Spin VarianceSpin Variance Measurement of Entanglement Measurement of Entanglement
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To characterize the quantum spin To characterize the quantum spin variance or noise of the collective variance or noise of the collective spin, a “thermal” sample is first used spin, a “thermal” sample is first used to calibrate the system (spin “light to calibrate the system (spin “light bulb”. bulb”.
Then, the system is (1) prepared in a Then, the system is (1) prepared in a Coherent Spin State - a minimum Coherent Spin State - a minimum uncertainty state (e.g. completely uncertainty state (e.g. completely polarized), then (2) entangled and (3) polarized), then (2) entangled and (3) the spin fluctuation is re-measuredthe spin fluctuation is re-measured
Process can be performed pulsed (ns Process can be performed pulsed (ns or slower), or CWor slower), or CW
Dx polarizingbeamsplitter
coated Cs cell
l/ 4
-
Our Entanglement Figure of Our Entanglement Figure of Merit is 70% out of 100%Merit is 70% out of 100%
• The SQL is the variance level for a sample of spins in a coherent, but not entangled, state known as a Coherent Spin State (CSS) - analogous to a coherent state of light
• The data is spin variance for the entangled sample and the line for the non- entangled sample
• ms coherence time set by transit time of atoms through laser beams (vs. <ns lifetimes)
Kuzmich, Mandel, Bigelow, PRL, 85, 1594 (2000)
The atoms are contained The atoms are contained in small glass cellsin small glass cells
The apparatus is compactThe entire
entanglement apparatus already fits
on a 3 x 2 ft optical bench, including lasers
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The cells are constructed with a custom dry-film coating to The cells are constructed with a custom dry-film coating to minimize wall relaxation - many ms lifetimesminimize wall relaxation - many ms lifetimes
Entanglement Can Be Realized in Entanglement Can Be Realized in Even Smaller Cells!Even Smaller Cells!
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Logical Extrapolation – Entanglement Logical Extrapolation – Entanglement of “Separated Ensembles”of “Separated Ensembles”
• Following our work, Polzik’s group in Aarhus used this approach to entangle atoms in two distinct and separated atomic cells (Nature 2001) - Effectively same as our single cell experiment with an added wall
NY Times, Nature, Scientific American
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D2
D1
D2
D1
≈
What Does the Future Include?: Teleportation of massive particle states
• We intentionally work with states that are well suited to teleportation – analogue to two-mode squeezed state
• Teleportation protocol established: Duan, Cirac, Zoller, Polzik, PRL 85, 5643 (2000)
D2
D1
D3
D41
2
3
ΨURUnderway
What Does the Future Include?Raman Processes and Photon Counting:
Parallel Geometry and Conditional Measurement
g1 g2
e
filter
mirrors
beamsplitter
1D
2D
• Photon counting techniques have proven invaluable in quantum information entanglement experiments
• Conditional measurement and photon counting can be used to realize alternative approaches to collective variable quantum information generation and processing
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Ψ 12± = 1
2S1†±e
iϕS2† ⎛
⎝
⎜ ⎜ ⎜
⎞
⎠
⎟ ⎟ ⎟0a 1
0a 2
1
2
What Does the Future Include?Raman Processes and Photon Counting:
Entanglement Swapping
• Coherent Raman pulse to top two cells (at common location distant from bottom two cells - three locations total)
• Click at D1 or D2 and entanglement is transferred from L1-L2 and R1-R2 to L2-R2 – entanglement transfer achieved
mirror
beam
splitterD1 D2
mirror
entangled entangled
L2
L1 R1
R2
What Does the Future Include?:Raman Processes - Spontaneous and Stimulated
(I. Cirac, QO5 Summer 2001)
• Treatment does not emphasize coherent processes - use multi-level properties of the atomic media to enhance performance and increase noise immunity
• Simple – modify laser frequencies/add additional diode laser• Use Raman scattering in forward direction
– Inherent increase in noise immunity if ground states are non-degenerate– Stimulated processes give large signals– Coherent processes minimize spontaneous forward scattering
g1 g2
e
g
e
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What Does the Future Include?
• Teleportation of massive particle states
• Exploit coherent atomic interaction
• Entanglement purification and repeater implementation
• Demonstration of a compact apparatus – M<20 lbs– P<100 watts
• Application of quantum control
• Realization in solids
• Quantum imprinting on the collective spin state
• Transfer to QI technology - error management, etc.
• Measures of entanglement –Schmidt rank, entropy…
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Collaboration vehicle with Eberly, Marcus, Stroud, Walmsley
Published Record of Our WorkPublished Record of Our Work
• Kuzmich, Bigelow, Mandel, EPL, 42, 481
• Kuzmich et al., PRA 60, 2346
• Kuzmich, Mandel, Bigelow, PRL, 85, 1594
• Bigelow, Nature, 409, 27
ΨUR
CQI
Simple, On-Demand Entanglement Simple, On-Demand Entanglement of Trillions of Neutral Atoms :of Trillions of Neutral Atoms :
Quantum Memory, Teleportation and Quantum RepeatersQuantum Memory, Teleportation and Quantum Repeaters
Objective–to create entanglement of a macroscopic collection of atoms–to create entangled samples separated by large distances–to teleport the quantum state of massive particles – a sample of atomsRelevanceEstensible entanglement is an enabling technology for QI information storage and transmittal
Present Status–We have demonstrated the entanglement of more than 1012 atoms using coherent laser lightMilestones for Future Work–Create entangled atomic samples that are widely separated in space–Teleport the state of massive matter–Quantum repeaters
Approach–To couple to the collective quantum variables of a macroscopic sample –To create on-demand entanglement using interaction of the atoms with laser light–To use measurements of quantum “noise” to probe entanglement
QuickTime™ and aPhoto - JPEG decompressor
are needed to see this picture.
ΨUR
CQI
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