Transcript Long-Lived Entanglement of Trillions of Atoms in a Simple
Entanglement of Collective Quantum Variables for Quantum Memory and Teleportation
N. P. Bigelow
The Center for Quantum Information The University of Rochester
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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 10 12 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 QuickTime™ and a Photo - JPEG decompressor are needed to see this picture.
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
Approach –
variables of a macroscopic sample
–
interaction of the atoms with laser light
–
To couple light to the collective quantum To create on-demand entanglement using To use measurements of quantum “noise” as an entanglement detector
There is a beneficial synergy with other CQI projects
Present Status –We have demonstrated the entanglement of more than 10 12 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 entanglement, very sensitive to
–
difficult (loss of single atom destroys 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
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i
ˆ
i
• •
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]
Possible Applications to “Other” Solid State Systems – e.g. an electron gas
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Entanglement can be produced by the interaction of atoms with polarized light
Photons Atom AAAs 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
S J
Photons
J
Photons
J S
S
Optically Thick Sample
+
Forward Scattering of Optical Field Analogue of 2-mode squeezed state
Entangled Atoms
Forward scattered mode is key
ˆ
I
S
J
s x
J x
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 for 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 for Transverse Spin Component
An Ideal EPR State Of Entangled Spins (Gaussian Quantum Variables) Obeys
S y
2 ,
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
not single particle collective spin Example of how quantum properties are observable in collective properties but
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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)
Dx
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”. polarizing beamsplitter l / 4 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. 85 , 1594 (2000) The apparatus is compact The entire entanglement apparatus already fits on a 3 x 2 ft optical bench, including lasers QuickTime™ and a Photo - JPEG decompressor are needed to see this picture. 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! QuickTime™ and a Photo - JPEG decompressor are needed to see this picture. UR 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 D2 D1 D2 D1 UR 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 UR 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 12 1 2 S 1 † e i S † 2 0 a 1 0 a 2 e mirrors 2 D1 1 beam splitter D2 filter 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 L1 L2 and R1-R2 to L2-R2 – entanglement transfer achieved L1 entangled L2 mirror D1 beam splitter mirror D2 R2 entangled R1 What Does the Future Include?: Raman Processes - Spontaneous and Stimulated • 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 e e (I. Cirac, QO5 Summer 2001) g g1 g2 UR • 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… Collaboration vehicle with Eberly, Marcus, Stroud, Walmsley UR • Kuzmich, Bigelow, Mandel, EPL, 42 , 481 • Kuzmich et al., PRA 60 , 2346 • Kuzmich, Mandel, Bigelow, PRL, 85 , 1594 • Bigelow, Nature, 409 , 27 UR CQI Simple, On-Demand Entanglement of Trillions of Neutral Atoms : Quantum Memory, Teleportation and Quantum Repeaters UR CQI QuickTime™ and a Photo - JPEG decompressor are needed to see this picture. 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 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 10 12 atoms using coherent laser light Milestones for Future Work –Create entangled atomic samples that are widely separated in space –Teleport the state of massive matter –Quantum repeatersThe atoms are contained in small glass cells
What Does the Future Include?
Published Record of Our Work