1. Entanglement of Collective Quantum Variables for Quantum Memory and Teleportation N. P. Bigelow The Center for Quantum Information The University of Rochester CQI

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

3. 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 Accomplishments to Date

4. Simple, Long-lived On-Demand Entanglement is Required for Practical Quantum Information Networks: Quantum 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 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 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 There is a beneficial synergy with other CQI projects 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 CQI

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 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?

6. 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)

7. 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? Some Needs for the QI Toolbox

8. 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

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

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

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

12. 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” Measurement Variances as a Probe of Entanglement

13. A Quantum Spin has Uncertainties Relating its Knowable Components

14. How to Probe Entanglement of the Collective Atomic Spin 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 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

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-measured Process 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. 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

21. 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

22. 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 1 2

23. 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 L2 L1 R1 R2

24. 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

25. 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… Collaboration vehicle with Eberly, Marcus, Stroud, Walmsley

26. 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 CQI

27. Simple, On-Demand Entanglement of Trillions of Neutral Atoms : Quantum 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 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 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 CQI