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Cited by 208Cold Atom Physics and Bose-Einstein CondensatesQuantum many-body systemsQuantum Information and Cryptography

Quantum simulations with cold trapped ions

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Johanning, Michael, Varón, Andrés F, Wunderlich, Christof·2009·Journal of Physics B: Atomic, Molecular and Optical Physics
DOI 10.1088/0953-4075/42/15/154009
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Abstract

The control of internal and motional quantum degrees of freedom of laser-cooled trapped ions has been subject to intense theoretical and experimental research for about three decades. In the realm of quantum information science, the ability to deterministically prepare and measure quantum states of trapped ions is unprecedented. This expertise may be employed to investigate physical models conceived to describe systems that are not directly accessible for experimental investigations. Here, we give an overview of current theoretical proposals and experiments for such quantum simulations with trapped ions. This includes various spin models (e.g. the quantum transverse Ising model or a neural network), the Bose–Hubbard Hamiltonian, the Frenkel–Kontorova model, and quantum fields and relativistic effects.

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Crossref · 10.1088/0953-4075/42/15/154009

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  • Trapped ions allow for exceptional control of experimental parameters, and initialization and read-out can be achieved with high fidelity.

    “Trapped ions are particularly interesting for the purpose of quantum simulation [19, 20, 21], as they allow for exceptional control of experimental parameters, and initialization and read-out can be achieved with high fidelity.”

    From Quantum simulation of the Dirac equation (2010) · cites this paper as [20]

  • Merkl et al. described the Zitterbewegung of ultra-cold atoms moving in one dimension and interacting with laser beams in a tripod system.

    “Merkl et al. [81] described the ZB of ultra-cold atoms moving in one-dimension and interacting with laser beams in a tripod system.”

    From Zitterbewegung (trembling motion) of electrons in semiconductors: a review (2011) · cites this paper as [81]

    Section 6.4.2 discusses simulating Zitterbewegung with trapped ions, not Merkl et al.’s proposed ultra-cold-atom tripod system. Searches for “Merkl” and “tripod” found no passage addressing that specific claim; page numbers were unavailable in our copy. (LLM, conf=0.76)

    Experimental — accuracy not yet measured

  • In the Merkl et al. system, the decay time of Zitterbewegung is inversely proportional to the k spread of a wave packet and the oscillation amplitude decreases as t^-1/2.

    “It was shown explicitly that in this case the decay time of ZB is inversely proportional to the k spread of a wave packet and that the oscillation amplitude decreases as t -1 / 2 .”

    From Zitterbewegung (trembling motion) of electrons in semiconductors: a review (2011) · cites this paper as [81]

    Section 6.4.2 (page unavailable) discusses Zitterbewegung in trapped ions and gives formulas for its frequency and amplitude, but not a decay law. Searches for Merkl, wave-packet k spread, decay time, and t^-1/2 found no passage addressing the claimed relationships. (LLM, conf=0.75)

    Experimental — accuracy not yet measured

  • The decay time of Zitterbewegung is inversely proportional to the momentum spread Δk of the wave packet.

    “One can show that the decay time is inversely proportional to the momentum spread ∆ k of the wave packet, see (16) and References [17, 81].”

    From Zitterbewegung (trembling motion) of electrons in semiconductors: a review (2011) · cites this paper as [81]

    Section 6.4.2 discusses Zitterbewegung’s frequency and amplitude and how to measure an ion’s position and momentum over time, but gives no relationship between decay time and wave-packet momentum spread. Searches for that inverse proportionality and for momentum width Δk found no passage addressing it; page numbers are unavailable in our copy. (LLM, conf=0.72)

    Experimental — accuracy not yet measured

  • The decay time of Zitterbewegung is usually much longer in one-dimensional systems.

    “The decay time is usually much longer in one-dimensional systems, see Figure 4 and References [17, 81].”

    From Zitterbewegung (trembling motion) of electrons in semiconductors: a review (2011) · cites this paper as [81]

    Section 6.1 describes a one-dimensional Dirac simulation, and section 6.4.2 discusses the frequency and amplitude of Zitterbewegung. Neither passage addresses its decay time or compares decay times across dimensions (searched: decay time, damping, lifetime). (LLM, conf=0.75)

    Experimental — accuracy not yet measured

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Cited by

Sorted by citations

Authors
Johanning, M., Varón, A. F., & Wunderlich, C.
Affiliations
University of Siegen (DE)
Venue
Journal of Physics B: Atomic, Molecular and Optical Physics
Publisher
IOP Publishing
Published
2009-07-15
Volume
42
Issue
15
Pages
154009
ISSN
  • 0953-4075 (ISSN-L)
  • 1361-6455
DOI
10.1088/0953-4075/42/15/154009
OpenAlex
W2057595669
Cited by
208
References
18
Citations by year
2026: 2 · 2025: 5 · 2024: 2 · 2023: 8 · 2022: 9 · 2021: 5 · 2020: 2 · 2019: 10 · 2018: 10 · 2017: 6 · 2016: 10 · 2015: 18 · 2014: 18 · 2013: 33 · 2012: 25
FWCI
13.00
Type
journal article
Language
en
Open access
Locations
  • Journal of Physics B Atomic Molecular and Optical Physics (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • arXiv (Cornell University)
Funders
  • European Commission
  • Deutsche Forschungsgemeinschaft
Topics
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Cold Atom Physics and Bose-Einstein Condensates
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
  • Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
Keywords
quantum simulation, cold trapped ions, laser cooling, spin systems, neural quantum states, Bose-Hubbard model, Frenkel-Kontorova model, quantum field theory, relativistic effects, quantum information

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