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Entanglement of Collective Quantum Variables for Quantum Memory and Teleportation N. P. Bigelow UR 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 UR 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 UR Simple, Long-lived On-Demand Entanglement is Required for Practical Quantum Information Networks: Quantum Memory, Teleportation and Quantum Repeaters UR QuickTime™ and a Photo - JPEG decompressor are needed to see this picture. 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? UR 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) UR 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? UR 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 UR By Entangling Collective Variables Long Lived Entanglement Can be Realized What is Collective Spin? S sˆi i UR • 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] UR 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) UR 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 UR 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” UR 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 UR 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 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 UR 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 UR 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 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 D1 D1 D2 D2 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 i † 1 † S e S 0 a 0 a 12 2 1 2 1 2 e mirrors 2 D1 beam splitter 1 filter 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 UR 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 UR 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 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