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3.1 Rydberg Atoms Open Research Online The Open University’s repository of research publications and other research outputs Cold atoms for deterministic quantum computation with one qubit Thesis How to cite: Mansell, Christopher William (2014). Cold atoms for deterministic quantum computation with one qubit. PhD thesis The Open University. For guidance on citations see FAQs. c 2014 Christopher William Mansell https://creativecommons.org/licenses/by-nc-nd/4.0/ Version: Version of Record Link(s) to article on publisher’s website: http://dx.doi.org/doi:10.21954/ou.ro.0000f83b Copyright and Moral Rights for the articles on this site are retained by the individual authors and/or other copyright owners. For more information on Open Research Online’s data policy on reuse of materials please consult the policies page. oro.open.ac.uk UMR6STMCTGP Cold Atoms for Deterministic Quantum Computation with One Qubit Christopher William Mansell Department of Physical Sciences The Open University A thesis submitted for the degree of Doctor o f Philosophy August 2014 Date oj 5uJorwl5<5V/Oi'vv tp 2°1^ Dafe fXwardi 23 October 201*+ ProQuest Number: 13889386 All rights reserved INFORMATION TO ALL USERS The quality of this reproduction is dependent upon the quality of the copy submitted. In the unlikely event that the author did not send a com plete manuscript and there are missing pages, these will be noted. Also, if material had to be removed, a note will indicate the deletion. uest ProQuest 13889386 Published by ProQuest LLC(2019). Copyright of the Dissertation is held by the Author. All rights reserved. This work is protected against unauthorized copying under Title 17, United States C ode Microform Edition © ProQuest LLC. ProQuest LLC. 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, Ml 48106- 1346 ii Abstract In this thesis, I describe a proposal for experiments with dense ensembles of ultracold Rubidium atoms optically excited to high- lying electronic states known as Rydberg states. The proposed experiment is designed to implement a model of quantum com­ putation known as deterministic quantum computation with one qubit (DQC1). My proposal is novel among other proposals for Rydberg atoms because it employs mixed states and could provide insights into the source of the enhancements of quantum technology over classical technology. I demonstrate that ultracold atoms and Rydberg interactions offer new perspectives for exploring the DQCl model. This is mainly due to the large strength, long range and controllability of Rydberg interactions. My specific contributions include: a proposal that solves one of the main issues with implementing quantum logic gates between en­ sembles of atoms; numerical simulations of the proposed cold atom implementation of a DQCl protocol; and the design and laboratory implementation of a high-performance optical system for imag­ ing ultracold atoms. These contributions bring the experimental exploration of the DQCl model closer to realisation. List of Publications BETEROV, I.I., SAFFMAN, M., YAKSHINA, E.A., ZHUKOV, V.R, TRETYAKOV, D.B., ENTIN, V.M., RYABTSEV, I.I., MANSELL, C.W., MACCORMICK, C., BERGAMINI, S. k FEDORUK, M.R Quantum gates in mesoscopic atomic ensembles based on adiabatic passage and Rydberg blockade. Phys. Rev. A, 88, 010303 (2013). MANSELL, C.W. k BERGAMINI, S. A cold-atoms based processor for deterministic quantum computa­ tion with one qubit in intractably large Hilbert spaces. New Journal of Physics, 16, 053045 (2014). BETEROV, I.I., SAFFMAN, M., ZHUKOV, V.R, TRETYAKOV, D.B., ENTIN, V.M., YAKSHINA, E.A., RYABSTEV, I.I., MANSELL, C.W., MACCORMICK, C., BERGAMINI, S. k FEDORUK, M.R Coherent control of mesoscopic atomic ensembles for quantum in­ formation. Laser Physics , 24, 074013 (2014). Acknowledgements I would like to thank the members of the Cold Atoms research group at The Open University, especially Dr Silvia Bergamini, for their contributions to this work. I would also like to thank our collaborators, particularly our long-term collaborator, Dr. Ilya Beterov. IV Contents Contents v List of Abbreviations x List of Figures xi 1 Introduction 1 2 Background: Quantum Computation with Cold Atoms 5 2.1 Main Concepts of Quantum Computing ........................................ 6 2.1.1 Q u b its ................................................................................... 6 2.1.2 Gates ................................................................................... 8 2.2 Implementation of a Quantum Computer .........................................10 2.2.1 Requirements foran Implementation ................................ 11 2.2.2 Different Implementations ...................................................... 13 2.3 Cold A to m s .......................................................................................... 15 2.3.1 Traps ...................................................................................... 16 2.3.1.1 Magnetic T rap s........................................................ 16 2.3.1.2 Optical Lattices.................................................... 17 2.3.1.3 Optical Dipole T rap s............................................... 18 2.3.2 Gates ...................................................................................... 19 2.4 Cold Atoms as a Platform for Quantum Computation ................... 20 2.4.1 Criterion 1: Scalability ............................................................ 20 v CONTENTS 2.4.2 Criterion 2: Initialisation............................................................21 2.4.3 Criterion 3: Long decoherence times compared to the time it take to perform a quantum logic gate....................... 21 2.4.4 Criterion 4: Universal G a tes .............................................. 22 2.4.5 Criterion 5: Read-out ...........................................................22 2.4.6 Criterion 6: Inter-converting between stationary and flying qubits..............................................................................23 2.4.7 Criterion 7: Transmitting the flying q u b its ......................... 23 2.5 Cold Atoms Compared to the Other Platform s ............................... 24 2.6 Summary .............................................................................................24 3 Quantum Gates With Rydberg Atoms 27 3.1 Rydberg Atoms ................................................................................... 28 3.1.1 Strong Interactions and Blockade ........................................ 29 3.1.2 Sensitivity To External F ie ld s .............................................. 30 3.1.3 Notable Rydberg Phenomena ...............................................31 3.2 Original Proposals for Rydberg Quantum Logic G ates...................33 3.2.1 Proposal with Single A tom s................................................. 33 3.2.1.1 Recent Developments ............................................... 35 3.2.2 Proposal with Ensembles of A to m s .....................................36 3.2.2.1 Recent Developments ............................................... 40 3.3 A Logic Gate based on Rydberg Interactions and Electromag- netically Induced Transparency ........................................................ 41 3.3.1 E I T ..................................................................................... 41 3.3.2 Logic Gate Between a Single Atom and an Ensemble . 43 3.4 Rydberg Interactions with Adiabatic Passage Techniques .... 47 3.4.1 Adiabatic Passage Techniques..............................................48 3.4.1.1 A R P ............................................................................49 3.4.1.2 STIRAP......................................................................50 CONTENTS 3.4.2 Logic Gate Between Two Ensembles .............................. 51 3.4.2.1 Deterministic Rydberg Excitation ..........................52 3.4.2.2 Deterministic De-excitation and Identity Gate . 53 3.4.2.3 Single-Qubit G a t e .................................................. 58 3.4.2.4 Two-Qubit g ate.........................................................60 3.5 Comparing the Different Gates ......................................................62 3.6 Summary .............................................................................................64 4 Background: The DQCl Model, Its Motivations and Proto­ cols 67 4.1 The DQCl Model .......................................... 68 4.1.1 The DQCl Protocol for Normalised Trace Estimation . 68 4.2 Motivation .............................................................................................72 4.2.1 Nonclassical Correlations as a Resource ............................... 73 4.3 Resources in the DQCl M odel ........................................................... 74 4.3.1 Entanglement .......................................................................... 74 4.3.2 Quantum Discord .......................................... 76 4.3.3 Geometric D isc o rd .................................................................78 4.3.4 Entangling Pow er ....................................................................79 4.4 Protocols . ................................................................................ 80 4.4.1 C h a o s .......................................................................................81 4.4.2 O v erlap ......................................................................... 81 4.4.3 M etrology................................................................................ 81 4.4.4 Thermodynamics ....................................................................82
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