Transcript Long-Lived Entanglement of Trillions of Atoms in a Simple

Entanglement of Collective Quantum
Variables for Quantum Memory and
Teleportation
N. P. Bigelow
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The Center for Quantum
Information
The University of
Rochester
CQI
A Tall Pole Item in QI
How to Realize Robust,
Long- Lived
Entanglement of Many
Particles for
Quantum Information
Storage and Processing
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CQI
Accomplishments to Date
We performed the first experimental demonstration of
long-lived entanglement of the spins of 1012 neutral,
ground-state atoms in a simple atomic vapor cell
by using the interaction of the atomic sample
with polarized laser light
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Simple, Long-lived On-Demand Entanglement
is Required for Practical Quantum Information Networks:
Quantum Memory, Teleportation and Quantum Repeaters
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CQI
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 projects
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 distances
Relevance
Extensible 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
Important Quantum Information Protocols:
Entanglement 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.
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?
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Quantum Information Processing:
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
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)
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Some Needs for the QI Toolbox
How to entangle many, many atoms?
Can we do so in a simple way?
Can we introduce a “new” physics
approach to the QI toolbox?
How to have long coherence times?
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Entangling the Collective Quantum
Variables 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
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
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By Entangling Collective Variables Long
Lived Entanglement Can be Realized
What is
Collective Spin?
S   sˆi
i
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• 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.
•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]
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Possible Applications to “Other” Solid State Systems – e.g. an electron gas
Entanglement can be produced by the
interaction of atoms with polarized light
Atom
AAAs
Photons
Photons
Entangled
Atoms
Entanglement is
produced through a QND
interaction – a non-local
Bell measurement
Kuzmich, Bigelow, Mandel, EPL, 42, 481 (1998)
Duan, Cirac, Zoller, Polzik, PRL 85, 5643 (2000)
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Entanglement is produced
using only coherent light
Atom
AAAs
J
Photons
S
S
J 
Photons
J
S 
Entangled
Atoms
Optically Thick Sample + Forward Scattering of Optical Field
Analogue of 2-mode squeezed state
Forward scattered mode is key
ˆ xs 
ˆ xJ
Hˆ  S J 
I
Forward scattering, indistinguishability
& QND Hamiltonian
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
Measurement Variances
as a Probe of Entanglement
How Can We Probe the Collective Spin?
How Can We Sense Entanglement?
Collective quantum state not necessarily
detectable in single particle properties
(a “bug” and a “feature”)
Recall the quantum mechanics of a spin
and the connection to “noise”
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A Quantum Spin has Uncertainties
Relating its Knowable Components
Quantum Uncertainty Disc f or
Transverse Spin Component
Quantum Uncertainty
Transverse Spin
Component
z
2
y
z
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How to Probe Entanglement of the
Collective Atomic Spin
Quantum Uncertainty Disc f or
Transverse Spin Component
An Ideal EPR State
Of Entangled Spins (Gaussian
Quantum Variables) Obeys
S
2
y ,z
 S
2

Duan, Giedke, Cirac, Zoller PRL 84, 2722 (2000);
Simon & Peres-Horodecki PRL 84, 2726 (2000)
Non-factorable state
Non-classical quantum variance (noise) only visible in the collective spin
Example of how quantum properties are observable in collective properties but
not single particle
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Variance of Collective Spin –
A 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 Variance
Measurement of Entanglement
To characterize the quantum spin
variance or noise of the collective
spin, a “thermal” sample is first used
to calibrate the system (spin “light
bulb”.
l/ 4
Dx
polarizing
beamsplitter
coated Cs cell
Then, the system is (1) prepared in a
Coherent Spin State - a minimum
uncertainty state (e.g. completely
polarized), then (2) entangled and (3)
the spin fluctuation is re-measured
Process can be performed pulsed (ns
or slower), or CW
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Our Entanglement Figure of
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
in small glass cells
The apparatus is
compact
The 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
minimize wall relaxation - many ms lifetimes
Entanglement Can Be Realized in
Even Smaller Cells!
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Logical Extrapolation – Entanglement
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
D1
D1
D2
D2
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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)
Underway
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What Does the Future Include?
Raman Processes and Photon Counting:
Parallel Geometry and Conditional Measurement
• 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

i †

1
 †
  S e S 0a 0a
12 2  1
2  1 2
e
mi rrors
2

D1
beam
spl itter
1
f ilter
D2
g1
g2
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 L1L2 and R1-R2 to L2-R2 – entanglement transfer achieved
L2
mirror
mirror
entangled
entangled
L1
R2
D1
beam
splitter
D2
R1
What Does the Future Include?:
Raman Processes - Spontaneous and Stimulated
• Treatment does not emphasize coherent processes - use multilevel 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
e
(I. Cirac, QO5
Summer 2001)
g
e
g1
g2
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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
• 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…
– M<20 lbs
– P<100 watts
Collaboration vehicle with Eberly, Marcus, Stroud, Walmsley
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Published 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
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UR
CQI
Simple, On-Demand Entanglement
of Trillions of Neutral Atoms :
Quantum Memory, Teleportation and Quantum Repeaters

UR
QuickTime™ and a
Photo - JPEG decompressor
are needed to see this picture.
CQI
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 atoms
Relevance
Estensible 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 light
Milestones for Future Work
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
–Create entangled atomic samples that are
–To use measurements of quantum “noise” widely separated in space
–Teleport the state of massive matter
to probe entanglement
–Quantum repeaters