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Entanglement of Collective Quantum Variables for Quantum Memory and Teleportation

CQI. Entanglement of Collective Quantum Variables for Quantum Memory and Teleportation. N. P. Bigelow The Center for Quantum Information The University of Rochester. CQI. A Tall Pole Item in QI.

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Entanglement of Collective Quantum Variables for Quantum Memory and Teleportation

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  1. CQI Entanglement of Collective Quantum Variables for Quantum Memory and Teleportation N. P. BigelowThe Center for Quantum InformationThe University of Rochester

  2. CQI A Tall Pole Item in QI How to Realize Robust, Long- Lived Entanglement of Many Particles for Quantum Information Storage and Processing

  3. 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

  4. Simple, Long-lived On-Demand Entanglement is Required for Practical Quantum Information Networks:Quantum Memory, Teleportation and Quantum Repeaters CQI 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 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 detectorThere is a beneficial synergy with other CQI projects 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 quantum state of massive matter–Quantum repeaters

  5. 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 repeatersstrategies 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 qubitsWhat platform to use? What tool in our toolbox?

  6. Quantum Information Processing: Light and/or Atoms? Light as the Quantum SystemTo 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 SystemEntanglement 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 processingRecord so far: four trapped ions (C. Sackett et al. At NIST Boulder – Nature 2000)

  7. 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?

  8. 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 variablesof the ensemble using an optical interaction Readily achieve the required strong coupling without using a cavity or a trap Entangling the Collective Quantum Variables of the Atomic Vapor 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

  9. 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. By Entangling Collective Variables Long Lived Entanglement Can be Realized What is Collective Spin? • 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

  10. Entanglement can be produced by the interaction of atoms with polarized light 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)

  11. Entanglement is produced using only coherent light Optically Thick Sample + Forward Scattering of Optical FieldAnalogue of 2-mode squeezed stateForward scattered mode is key Forward scattering, indistinguishability & QND Hamiltonian

  12. 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 spinand the connection to “noise”

  13. A Quantum Spin has Uncertainties Relating its Knowable Components

  14. An Ideal EPR State Of Entangled Spins (Gaussian Quantum Variables) Obeys Duan, Giedke, Cirac, Zoller PRL 84, 2722 (2000); Simon & Peres-Horodecki PRL 84, 2726 (2000) Non-factorable state How to Probe Entanglement of the Collective Atomic Spin Non-classical quantum variance (noise) only visible in the collective spinExample of how quantum properties are observable in collective properties but not single particle

  15. 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)

  16. 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”. 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-measuredProcess can be performed pulsed (ns or slower), or CW

  17. 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)

  18. 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 The cells are constructed with a custom dry-film coating to minimize wall relaxation - many ms lifetimes

  19. Entanglement Can Be Realized in Even Smaller Cells!

  20. 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 Logical Extrapolation – Entanglement of “Separated Ensembles”

  21. 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) What Does the Future Include?: Teleportation of massive particle states Underway

  22. 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 What Does the Future Include?Raman Processes and Photon Counting:Parallel Geometry and Conditional Measurement 2 1

  23. 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 What Does the Future Include?Raman Processes and Photon Counting:Entanglement Swapping L2 R2 R1 L1

  24. 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 What Does the Future Include?:Raman Processes - Spontaneous and Stimulated (I. Cirac, QO5 Summer 2001)

  25. 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… What Does the Future Include? Collaboration vehicle with Eberly, Marcus, Stroud, Walmsley

  26. CQI 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

  27. Simple, On-Demand Entanglement of Trillions of Neutral Atoms :Quantum Memory, Teleportation and Quantum Repeaters 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 atomsRelevanceEstensible entanglement is an enabling technology for QI information storage and transmittal 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 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

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