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Journal of Physics Conference Series

Quantum simulation of relativistic quantum physics with trapped ions

Christian F. Roos, R. Gerritsma, Gerhard Kirchmair, F. Zähringer, E. Solano, R. Blatt

Published Jan 10, 2011• 4 citations
Publisher

Abstract

Coupling internal and vibrational states of a string of trapped ions has proven to be an effective way of entangling the ions' internal states. This mechanism can be used for high-fidelity quantum gates, QND measurements of spin correlations and creation of large entangled states. However, spin-motion interactions are also of interest for the purpose of quantum simulations where the motional state no longer acts as an auxiliary quantum system only. Here, we describe an experiment where a laser-cooled trapped ion is set to behave as a free relativistic quantum particle.

DOI
10.1088/1742-6596/264/1/012020

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Coupling internal and vibrational states of a string of trapped ions has proven to be an effective way of entangling the ions' internal states. This mechanism can be used for high-fidelity quantum gates, QND measurements of spin correlations and creation of large entangled states. However, spin-motion interactions are also of interest for the purpose of quantum simulations where the motional state no longer acts as an auxiliary quantum system only. Here, we describe an experiment where a laser-cooled trapped ion is set to behave as a free relativistic quantum particle.
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.
Laser-ion interactions that collectively couple the pseudo-spins of a string of trapped ions to one of the string's vibrational modes [1] have been used by us to entangle a pair of40Ca+ions with very high fidelity [2–4]. In addition, we experimentally confirmed that this gate mechanism allows for entangling ions without having recourse to ground state cooling [3]. This opens the way to performing an entangling gate after having applied an operation which does not preserve the ions' motional state like for example state detection.
Trapped atomic ions are among the most advanced platforms for quantum simulation, computation, and metrology, offering long coherence times and precise, individual control over both internal and motional degrees of freedom. In this review, we present a pedagogical introduction to trapped-ion systems, covering the physics of ion trapping, qubit encodings, and laser-ion interactions. We explain how spin-dependent forces generated by light fields enable both analog and digital quantum simulations of spin and spin-boson models, as well as high-fidelity quantum logic gates. We then highlight an emerging frontier in the simulation of chemical dynamics, summarizing recent experiments that demonstrate the capability of trapped ions to simulate vibronic models and excitation-transfer processes. Finally, we outline future directions in quantum simulation and discuss open challenges in scaling up trapped-ion architectures.
We show that trapped ions are ideally suited for the simulation of quantum spin systems and for the observation of a rich variety of quantum phase transitions. By changing the laser intensities and polarizations, the dynamics of the internal states of the ions can be controlled in such a way that an Ising or Heisenberg-like interaction is induced between effective spins. Our scheme allows us to build an analog quantum simulator of spin systems with trapped ions and to observe and analyze quantum phase transitions with unprecedented opportunities for the measurement and manipulation of spins. The requirements for our proposal are met by current technology: it does not rely on the use of quantum gates, and striking many-body effects can be observed even when the fidelity of the simulation is smaller than the one required for quantum computation. Our proposal with trapped ions would solve many of the problems that are faced in the implementation of quantum simulations with neutral atoms in optical lattices.
We report on quantum simulations of relativistic scattering dynamics using trapped ions. The simulated state of a scattering particle is encoded in both the electronic and vibrational state of an ion, representing the discrete and continuous components of relativistic wave functions. Multiple laser fields and an auxiliary ion simulate the dynamics generated by the Dirac equation in the presence of a scattering potential. Measurement and reconstruction of the particle wave packet enables a frame-by-frame visualization of the scattering processes. By precisely engineering a range of external potentials we are able to simulate text book relativistic scattering experiments and study Klein tunneling in an analogue quantum simulator. We describe extensions to solve problems that are beyond current classical computing capabilities.
Quantum Simulation of Spin Models with Trapped Ions C. Monroe, W. C. Campbell, E. E. Edwards, R. Islam, D. Kafri, S. Koren- blit, A. Lee, P. Richerme, C. Senko, and J. Smith Joint Quantum Institute University of Maryland Department of Physics College Park, MD 20742, USA Summary. — Laser-cooled and trapped atomic ions form an ideal standard for the simulation of interacting quantum spin models. Effective spins are represented by appropriate internal energy levels within each ion, and the spins can be measured with near-perfect efficiency using state-dependent fluorescence techniques. By ap- plying optical fields that exert optical dipole forces on the ions, their Coulomb inter- action can be modulated in ways that give rise to long-range and tunable spin-spin interactions that can be reconfigured by shaping the spectrum and pattern of the laser fields. Here we review the theory behind this system, recent experimental data on the adiabatic prepration of complex ground states and dynamical studies with small collections of ions, and speculate on the near future when the system becomes so complex that its behavior cannot be modeled with conventional computers. PACS 03.67 – a. PACS 37.10 – Ty. PACS 75.25 – j. Introduction The advent of individual atomic control with external electromagnetic fields, both involving internal states through optical pumping and external states through laser cool- c Societ` a Italiana di Fisica