Center for Quantum Information: Advancing Quantum Research and Technology

1. The Center for Quantum Information ROCHESTER HARVARD CORNELL STANFORD RUTGERS LUCENT TECHNOLOGIES Year Three Review Harvard, February 2002

2. Center for Quantum Information ROCHESTER HARVARD CORNELL STANFORD RUTGERS LUCENT TECHNOLOGIES • Ian Walmsley • Carlos Stroud • Joseph Eberly • Nicholas Bigelow • Atomic • Molecular • Optical • Physics • Toby Berger • Tom Cover • Martin Morf • Decoherence • Entanglement • Fidelity • Resources • Quantum Information Theory • Mesoscopic • Electronics • Charles Marcus • Michael Gershenson • Yoshi Yamamoto • Communications • Physics • Richart Slusher • Lov Grover • Jason Stark

3. Center for Quantum Information ROCHESTER HARVARD CORNELL STANFORD RUTGERS LUCENT TECHNOLOGIES The team assembles in Rochester Development of common language, goals, and perspectives. • Workshops • Annual reviews • International Conference • Weekly joint group meetings • New graduate course • Public lectures

4. Center for Quantum Information ROCHESTER HARVARD CORNELL STANFORD RUTGERS LUCENT TECHNOLOGIES International Conference Series Initiated Tutorial speakers and their topics D. Bruss (Univ. Hannover): Characterizing Entanglement P.L. Knight (Imperial College): Quantum Information Science D. Mermin (Cornell Univ.): Quantum Computing J. Preskill (Caltech): Quantum Error Correction Invited Speakers D. DiVincenzo, IBM - Yorktown Heights, USA S. Popescu, Univ. Bristol, UK J. Rarity, Defence Evaluation & Research Agency, UK I. Cirac, Univ. of Innsbruck, Austria R. Clark, U. New South Wales, Australia B. Terhal, IBM - Yorktown Heights, USA E. Polzik, Aarhus Univ., Denmark J. Lukens, SUNY Stony Brook, USA M. Plenio, Imperial College, UK R. Blatt, Univ. of Innsbruck, Austria I. Chuang, IBM - San Jose, USA J.P. Poizat, Inst. d'Optique, France A. Ekert, Univ. of Oxford, UKR. Hughes, Los Alamos National Laboratory, USA J. Schmiedmayer, Univ. Heidelberg, Germany A. Karlsson, Royal Institute of Technology, Kista, Sweden W. Wootters, Williams College, USA D. Bouwmeester, Univ. of Oxford, UK P. Zoller, Univ. of Innsbruck, Austria S. Braunstein, Univ. Bangor, UKK. Banaszek, Univ. Oxford, UK and Univ. Warsaw, PolandW. Munro, Hewlett-Packard, UK • Approximately 300 attendees in joint meetings • Tutorial talks and invited speakers covering the whole range of disciplines • Follow up meeting Oxford, June 2003.

5. Center for Quantum Information ROCHESTER HARVARD CORNELL STANFORD RUTGERS LUCENT TECHNOLOGIES Cross-disciplinary Entanglement Ph.D. Dissertations “Quantum information and computing in multilevel systems,” Ashok Muthukrishnan, University of Rochester. “Coherence, charging, and spin effects in quantum dots and quantum point contacts,” Sara M. Cronenwett “Tradeoff problems in quantum information theory,” Igor Devetak, Cornell University Ph. D. Students William Oliver (electron entanglement) Jon Yard (information theory an quantum information) David Julian (information theory and duality of the theory of data compression David Aronstein (revivals and classical-motion bases of quantum wave packets) Benjamin Brown (coherent control of cold molecular formation) Kam Wai Chan (Schmidt-mode evolution leading to control of entanglement) Pablo Londero (molecular dimers for quantum information studies) Alberto Marino (entangement and teleportation of states of matter) Jeffrey S. Pratt (dynamical evolution of entanglement and entanglement transfer) Alfred U’Ren (engineering entanglement using quasi phase matched nonlinear waveguides) Sungjong Woo Vitaly Podzorov New Graduate Course Stanford University, Applied Physics 225 – Quantum Information Spring 2001, Professor Yamamoto. New course popular with students from several departments. Cross-disciplinary publications K.Banaszek, I.Devetak, "Fidelity trade-off for finite ensembles of identically prepared qubits", Phys. Rev. A 64, 052307 (2001).

6. Center for Quantum Information ROCHESTER HARVARD CORNELL STANFORD RUTGERS LUCENT TECHNOLOGIES Quantitative Data • More than 40 peer reviewed publications in print. • More than 40 conference presentations. • Three completed PhD theses. • New international conference series initiated. • 15 students and 4 postdocs working on Center projects.

7. Center for Quantum Information ROCHESTER HARVARD CORNELL STANFORD RUTGERS LUCENT TECHNOLOGIES Quantum Information Toolbox • Definitive set of tools not yet agreed upon • Several possibilities are beginning to emerge • a) Classical wave interference offers many of the same • benefits as quantum interference. • b) Fidelity tradeoff between single realization and ensemble is quantified. • c) Schmidt basis allows quantitative treatment of information in a Hilbert space continuum. New “entanglement force” is predicted. • d) Multilevel logic efficiently represents entanglement of multilevel systems. • e) Macroscopic collective quantum variables exist even in atomic vapors. • The various possible tools need to be explored in the variety of laboratory approaches available in CQI.

8. Series of phase coherent pulses forms desired radial wave packet M. L. Noel and C. R. Stroud, Jr. Phys. Rev. Lett. 77, 1913 (1996). Quantum Control and Rydberg Wave Packets Precision control of radial wave packet.

9. 3D Spatial Control Electronic Pixel Jake Bromage and C. R. Stroud, Jr. Phys. Rev. Lett. 83, 4963 (1999). Three Dimensional Quantum Control

10. Atomic Quantum Resources Quantum Logic within One Atom Entangled Multilevel Atoms • Efficient Use of Quantum Resources: • Entanglement is difficult to achieve and fragile • to preserve. • Take advantage of full resources in each atom • to minimize need for entanglement. • 7 atoms with 32 states per atom • (25)7 = 235, 35 bits with 7 atoms. Large State Space n = 50  2500 states  211 n = 100  10,000 states  213 n = 1000  1,000,000 states  220 Easily scaled to 5 –10 bits. Coherence times ~ milliseconds. • Problems • Inefficient encoding and readout. • Not scalable to useful levels. • Relatively little is known about multilevel • logic and algorithms. • Challenges: • Develop multilevel logical algorithms. • Develop schemes for entangling multilevel • quantum systems.

11. Most quantum information is naturally in multilevel form. • Entangled states of multilevel systems are not efficiently encoded in binary logic. • Multilevel logical operations offer powerful tools. Universal gate with 2 qudits Efficient dxd unitary operations. Proposed implementation in linear trap. A. Muthukrishnan and C. R. Stroud, Jr. "Multivalued logic gates for quantum computation," Phys. Rev. A 62, 52309 (2000).  Most Quantum Systems are Multilevel

12. Atomic Spin Entanglement A Laguerre-Gaussian laser beam carries both orbital and spin angular momenta. It is shown that this beam can produce entanglement of internal and center-of- mass degrees of freedom of an atom in a circular trap. A. Muthukrishnan and C. R. Stroud, Jr. "Entanglement of internal and external angular momenta in a single atom," submitted to J. Opt. B: Quant. Semi. Opt.Special issue. Angular Momentum is a Good Quantum Number High Rydberg states get closer together in energy. Separation in angular momentum is always h/2p

13. The Fourier conjugate of the energy level basis | j >n Wave packet states | k >t evenly distributed in time around a classical orbit. States encoded in a wave packet basis can be read out in energy basis thus trivially carrying out Fourier transformation. A. Muthukrishnan and C. R. Stroud, Jr. "Atomic wave packet basis for quantum information," Preprint quant-ph/0106165 at xxx.lanl.gov.A. Muthukrishnan and C. R. Stroud, Jr. "Quantum fast Fourier transform using multilevel atoms,"to be published in J. Mod. Opt. Quantum Fourier Transform in a Single Atom

14. Quantum Lessons from Rydberg Atoms • Dynamical wave packet states in a path integral representation have non-integer Bohr orbit quantization. • Most quantum states are not directly accessible from lower states. • Ehrenfest’s theorem holds quite generally for Rydberg states. • Entanglement can exist even in “classical-limit” states. Can we apply these lessons to develop new quantum information tools?

15. Center for Quantum Information ROCHESTER HARVARD CORNELL STANFORD RUTGERS LUCENT TECHNOLOGIES Atomic wave packet control • OBJECTIVES • Explore the unique quantum features of multilevel systems. • Develop tools to exploit the resources of multilevel quantum systems for quantum information processing. • APPROACHES • Develop algorithms using multilevel logic. • Explore alternatives to energy representations. • Experimental studies of macroscopic quantum variables. • ACCOMPLISHMENTS • Wave packet pixel produced. • Multilevel two-atom universal quantum gate proposed. • Single-atom quantum Fourier transform. • Entanglement of internal and COM angular momentum in single atom.