Quantum computing with naturally trapped sub-nanometre-spaced ions

Research output: ThesisDoctoral Thesis (compilation)

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Abstract

The main aim of this work, was to lay the foundations for the experimental realisation of a quantum mechanical controlled NOT gate in rare-earth-metal-ion-doped crystals.

Small amounts of rare-earth elements, added during the growth of some inorganic crystals, will become substituted into the crystal lattice as trivalent ions. The trivalent rare-earth-metal ions between cerium, with atomic number 58, and ytterbium, with atomic number 70, have a partly filled 4f shell, which does not extend spatially outside the full 5s and 5p shells. The 4f vacancies make electronic inner shell transitions possible between spectroscopic 4f terms. Some of these optical transitions have coherence times of the order of milliseconds, when the crystals are cooled down to ~ 4 K. There are several reasons for these extraordinary coherence times, which are approximately 8 orders of magnitude greater than those typical for electronic transitions in solids. The most important one is the cage-like shield which the outer 5s and 5p shells provide for the 4f electrons. Furthermore, since these ions are naturally trapped inside the crystal lattice there is no Doppler broadening of the line-width. The coherence properties of these optical transitions is one of the features that makes these materials attractive for use as a solid-state platform for quantum computing, using these ions as qubits. Another appealing characteristic is the fact that different ions have different optical resonance frequencies, which means that ions belonging to different qubits, which only have nm separation, can still be addressed separately by using different laser frequencies. Since the inter-ion spacing is so small, it is possible to make two ions interact strongly, although they are well shielded, through a permanent dipole-dipole interaction. This interaction can be turned on and off by switching between two different ways of encoding the qubit, a most useful feature. When the qubit is represented as a superposition between two ground state hyperfine levels, the interaction is turned off. The interaction is turned on selectively by transferring this superposition to the optical transition with a pi-pulse, for the specific ions that are to interact.

This thesis describes how peaks of ions, absorbing on a single transition, residing in spectral pits with no other ions, have been isolated. It is shown how these ions can be coherently transferred between hyperfine levels via the optically excited state, how the interaction between such peaks of ions representing qubits can be turned on and off, and how subgroups of ions with strong interaction can be distilled out. All the work described here has been performed using the ensemble approach.

The ensemble approach will, however, be difficult to scale up to large numbers of qubits. A method employing a single ion in each qubit, using a specialised ion for readout, has therefore also been proposed.

The rare-earth-metal-ion-based quantum computing experiments require a laser with coherence properties which at least match those of the material. To this end a frequency stabilisation system was developed for a dye laser. This system uses a transient spectral hole in a rare-earth-metal-ion-doped crystal, of the same kind that is used in the experiments, as frequency reference, and is to the authors knowledge the first demonstration of locking a dye laser to a spectral hole. This system provides a line-width of 1 kHz on a 10 microseconds timescale and a frequency drift below 1 kHz/s.
Original languageEnglish
QualificationDoctor
Awarding Institution
  • Atomic Physics
Supervisors/Advisors
  • Kröll, Stefan, Supervisor
Award date2006 Dec 15
Publisher
ISBN (Print)978-91-628-6907-6
Publication statusPublished - 2006

Bibliographical note

Defence details

Date: 2006-12-15
Time: 13:15
Place: Sal B, Fysiska Institutionen, Sölvegatan 14 Lund.

External reviewer(s)

Name: Schmidt-Kaler, Ferdinand
Title: Professor, dr
Affiliation: Quanteninformationsverarbeitung, Universität Ulm, Ulm, Tyskland

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<div class="article_info">M. Nilsson, L. Rippe, N. Ohlsson, T. Christiansson and S. Kröll. <span class="article_issue_date">2002</span>. <a href="javascript:downloadFile(547694)" class="article_link">Initial experiments concerning quantum information processing in rare-earth-ion doped crystals</a> <span class="journal_series_title">Physica Scripta</span>, <span class="journal_volume">vol T102</span> <span class="journal_pages">pp 178-185</span>. <span class="journal_distributor">Institute of Physics Publishing</span></div>
<div class="article_info">M. Nilsson, L. Rippe, R. Klieber, D. Suter and S. Kröll. <span class="article_issue_date">2004</span>. <a href="javascript:downloadFile(547695)" class="article_link">Holeburning techniques for isolation and study of individual hyperfine transitions in inhomogeneously broadened solids, demonstrated in Pr[3] +:Y[2]SiO[5]</a> <span class="journal_series_title">Phys. Rev.</span>, <span class="journal_volume">vol B 70</span> <span class="journal_pages">pp 214116</span>. <span class="journal_distributor">The American Physical Society</span></div>
<div class="article_info">L. Rippe, M. Nilsson, R. Klieber, D. Suter and S. Kröll. <span class="article_issue_date">2005</span>. <a href="javascript:downloadFile(547696)" class="article_link">Experimental demonstration of efficient and selective population transfer and qubit distillation in a rare-earth metal-ion-doped crystal</a> <span class="journal_series_title">Phys. Rev.</span>, <span class="journal_volume">vol A 71</span> <span class="journal_pages">pp 062328</span>. <span class="journal_distributor">The American Physical Society</span></div>
<div class="article_info">J.H. Wesenberg, K. Moelmer, L. Rippe and S. Kröll. <span class="article_issue_date">2006</span>. <span class="article_title">Scalable designs for quantum computing with rare-earth-ion-doped crystals</span> <span class="journal_series_title">Phys. Rev.</span>, <span class="journal_distributor">The American Physical Society</span> (submitted)</div>
<div class="article_info">L. Rippe, B. Julsgaard, A. Walther and S. Kröll. <span class="article_issue_date">2006</span>. <span class="article_title">Laser stabilization using spectral hole burning</span> <span class="journal_series_title">Phys. Rev.</span>, <span class="journal_distributor">The American Physical Society</span> (submitted)</div>
<div class="article_info">L. Levin (Levin is the authors former surname).. <span class="article_issue_date">2002</span>. <a href="javascript:downloadFile(547699)" class="article_link">Mode-hop-free electro-optically tuned diode laser</a> <span class="journal_series_title">Opt. Lett.</span>, <span class="journal_volume">vol 27</span> <span class="journal_pages">pp 237</span>. <span class="journal_distributor">Optical Society of America</span></div>

Subject classification (UKÄ)

  • Atom and Molecular Physics and Optics

Keywords

  • Laserteknik
  • Laser technology
  • Atom- och molekylärfysik
  • Atomic and molecular physics
  • akustik
  • optik
  • Elektromagnetism
  • optics
  • acoustics
  • Electromagnetism
  • Fysik
  • Physics
  • entanglement
  • spectroscopy
  • rare-earth-metal-ion-doped crystals spectral hole-burning
  • inversion
  • excitation
  • laser stabilization
  • quantum computation
  • quantum gate

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