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Reports on Progress in Physics

Experimental quantum simulations of many-body physics with trapped ions

Ch Schneider, Diego Porras, Tobias Schaetz

Published Jan 17, 2012• 362 citations
Publisher

Abstract

Direct experimental access to some of the most intriguing quantum phenomena is not granted due to the lack of precise control of the relevant parameters in their naturally intricate environment. Their simulation on conventional computers is impossible, since quantum behaviour arising with superposition states or entanglement is not efficiently translatable into the classical language. However, one could gain deeper insight into complex quantum dynamics by experimentally simulating the quantum behaviour of interest in another quantum system, where the relevant parameters and interactions can be controlled and robust effects detected sufficiently well. Systems of trapped ions provide unique control of both the internal (electronic) and external (motional) degrees of freedom. The mutual Coulomb interaction between the ions allows for large interaction strengths at comparatively large mutual ion distances enabling individual control and readout. Systems of trapped ions therefore exhibit a prominent system in several physical disciplines, for example, quantum information processing or metrology. Here, we will give an overview of different trapping techniques of ions as well as implementations for coherent manipulation of their quantum states and discuss the related theoretical basics. We then report on the experimental and theoretical progress in simulating quantum many-body physics with trapped ions and present current approaches for scaling up to more ions and more-dimensional systems.

DOI
10.1088/0034-4885/75/2/024401

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Quantum simulation ‐ an exciting adventure

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Quantum many-body systems, as they appear in different branches of physics and chemistry, are very hard to simulate. The number of parameters defining their quantum states grows exponentially with the number of constituents. This prevents us from exploring and investigating relevant problems involving relatively small numbers of subsystems even with the help of the most powerful supercomputers. Richard Feynman already noticed this difficulty back in 1981 when he wrote his visionary paper “Simulating Physics with Computers” [Int. J. Theor. Phys. 21:6/7, 467 (1982)]. There, he proposed to use quantum systems (as opposed to classical computers) to perform the simulation and in this way to circumvent the need to store and compute a colossal number of parameters, necessary to describe the pertaining superpositions. What was a visionary idea at that time has become a very active field of research in the last few years. 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Haroche and D. Wineland, for such ground-breaking experiments. Such experiments, often in combination with laser cooling of atoms or ions and Bose-Einstein condensation, have formed one of the pillars on which the field of quantum simulations is being established. Quantum simulations with cold atoms, either in magnetic traps or in optical lattices, with trapped ions, with photons, with superconducting devices, with quantum dots, etc., have been theoretically proposed and experimentally considered by many researchers. Most of the proposals so far deal with problems in condensed matter physics that are either difficult to tackle with modern supercomputers or are difficult to observe in solid state systems. This has established a very close link between different disciplines, like atomic, molecular, and optical (AMO) physics, and condensed matter physics. Although some of the experiments are still in their infancy, and a lot of research is still needed, the extraordinary progress made in all these research areas during the last few years makes us feel confident that in the not too distant future quantum simulators will provide a key tool to investigate many-body quantum systems. Furthermore, we also expect that quantum simulators will help quantum physicists to establish new and fruitful links to other scientific communities, like high-energy physics or quantum chemistry. The present special issue contains various review papers as well as research papers on quantum simulations. It starts out with two papers written by last year's Nobel Prize winners describing their foundational work (Wineland, p. 739 and Haroche, p. 763). The issue continues with three thorough, invited review papers covering different topics on quantum simulations. The first one reviews recent theoretical proposals to use cold atoms in optical lattices to simulate lattice gauge theories of the sort that appear in high-energy physics (U.-J. Wiese, p. 783). The second covers both theoretical proposals and experimental demonstrations of cold-atom systems to simulate the physics of matter in the presence of gauge fields, displaying so-called topological phenomena, which so far have only been observed in solid-state systems (I. Spielman, p. 794). The third one contains an extensive overview and new proposals to perform a broad range of quantum simulations using quantum dot systems (P. Barthelmy et al., p. 813). The issue also includes six original papers with a variety of theoretical proposals as well as the introduction of novel theoretical techniques related to the field of quantum simulation. 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Vibrational degrees of freedom in trapped-ion systems have recently been gaining attention as a quantum resource, beyond the role as a mediator for entangling quantum operations on internal degrees of freedom, because of the large available Hilbert space. The vibrational modes can be represented as quantum harmonic oscillators and thus offer a Hilbert space with infinite dimensions. Here we review recent theoretical and experimental progress in the coherent manipulation of the vibrational modes, including bosonic encoding schemes in quantum information, reliable and efficient measurement techniques, and quantum operations that allow various quantum simulations and quantum computation algorithms. We describe experiments using the vibrational modes, including the preparation of non-classical states, molecular vibronic sampling, and applications in quantum thermodynamics. We finally discuss the potential prospects and challenges of trapped-ion vibrational-mode quantum information processing.

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Direct experimental access to some of the most intriguing quantum phenomena is not granted due to the lack of precise control of the relevant parameters in their naturally intricate environment. Their simulation on conventional computers is impossible, since quantum behaviour arising with superposition states or entanglement is not efficiently translatable into the classical language. However, one could gain deeper insight into complex quantum dynamics by experimentally simulating the quantum behaviour of interest in another quantum system, where the relevant parameters and interactions can be controlled and robust effects detected sufficiently well. Systems of trapped ions provide unique control of both the internal (electronic) and external (motional) degrees of freedom. The mutual Coulomb interaction between the ions allows for large interaction strengths at comparatively large mutual ion distances enabling individual control and readout. Systems of trapped ions therefore exhibit a prominent system in several physical disciplines, for example, quantum information processing or metrology. Here, we will give an overview of different trapping techniques of ions as well as implementations for coherent manipulation of their quantum states and discuss the related theoretical basics. We then report on the experimental and theoretical progress in simulating quantum many-body physics with trapped ions and present current approaches for scaling up to more ions and more-dimensional systems.
Direct experimental access to some of the most intriguing quantum phenomena is not granted due to the lack of precise control of the relevant parameters in their naturally intricate environment. Their simulation on conventional computers is impossible, since quantum behaviour arising with superposition states or entanglement is not efficiently translatable into the classical language. However, one could gain deeper insight into complex quantum dynamics by experimentally simulating the quantum behaviour of interest in another quantum system, where the relevant parameters and interactions can be controlled and robust effects detected sufficiently well. We report on the progress in experimentally simulating quantum many-body physics with trapped ions.
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.
We cannot translate quantum behavior arising with superposition states or entanglement efficiently into the classical language of conventional computers (Feynman et al. in Int. J. Theor. Phys. 21:467, 1982 ). A universal quantum computer could describe and help to understand complex quantum systems. But it is envisioned to become functional only within the next decade(s). A shortcut was proposed via simulating the quantum behavior of interest in another quantum system, where all relevant parameters and interactions can be controlled and observables of interest detected sufficiently well. For example simulating quantum spin systems within an architecture of trapped ions (Porras and Cirac in Phys. Rev. Lett. 92:207901, 2004 ). Here we specify how we simulate the spin and all necessary interactions and how we calibrate their amplitudes. For example via a two-ion phase-gate operation on two axial motional modes simultaneously at a fidelity exceeding 95%. We explain the complete mode of operation of a quantum simulator on the basis of our simple model case—the proof of principle experiment of simulating the transition of a quantum magnet from paramagnetic into entangled ferromagnetic order (Friedenauer et al. in Nat. Phys. 4:757, 2008 ) and emphasize some of the similarities and differences with a quantum computer.
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.
Quantum many-body systems, as they appear in different branches of physics and chemistry, are very hard to simulate. The number of parameters defining their quantum states grows exponentially with the number of constituents. This prevents us from exploring and investigating relevant problems involving relatively small numbers of subsystems even with the help of the most powerful supercomputers. Richard Feynman already noticed this difficulty back in 1981 when he wrote his visionary paper “Simulating Physics with Computers” [Int. J. Theor. Phys. 21:6/7, 467 (1982)]. There, he proposed to use quantum systems (as opposed to classical computers) to perform the simulation and in this way to circumvent the need to store and compute a colossal number of parameters, necessary to describe the pertaining superpositions. What was a visionary idea at that time has become a very active field of research in the last few years. The extraordinary progress of both theoretical and experimental research in quantum physics allows us now to tame, control, and manipulate various quantum systems with unprecedented precision. Laser, magnetic, electronic and other technologies enable us to arrange quantum subsystems in different geometries, modify their interactions, and detect them. This allows us to engineer Hamiltonians and emulate systems displaying some of the most intriguing quantum phenomena. This tremendous progress is, to a large extent, due to the pioneering work of many researchers during the last twenty to thirty years. Here, the investigations of basic phenomena with one or few atoms or photons were of particular impact. The degree of control achieved in the experiments has enabled the observation of mind-boggling quantum effects, related to the superposition principle or to entangled states, and their disappearance due to decoherence. In fact, the 2012 Nobel Prize has been awarded to two scientists, S. Haroche and D. Wineland, for such ground-breaking experiments. Such experiments, often in combination with laser cooling of atoms or ions and Bose-Einstein condensation, have formed one of the pillars on which the field of quantum simulations is being established. Quantum simulations with cold atoms, either in magnetic traps or in optical lattices, with trapped ions, with photons, with superconducting devices, with quantum dots, etc., have been theoretically proposed and experimentally considered by many researchers. Most of the proposals so far deal with problems in condensed matter physics that are either difficult to tackle with modern supercomputers or are difficult to observe in solid state systems. This has established a very close link between different disciplines, like atomic, molecular, and optical (AMO) physics, and condensed matter physics. Although some of the experiments are still in their infancy, and a lot of research is still needed, the extraordinary progress made in all these research areas during the last few years makes us feel confident that in the not too distant future quantum simulators will provide a key tool to investigate many-body quantum systems. Furthermore, we also expect that quantum simulators will help quantum physicists to establish new and fruitful links to other scientific communities, like high-energy physics or quantum chemistry. The present special issue contains various review papers as well as research papers on quantum simulations. It starts out with two papers written by last year's Nobel Prize winners describing their foundational work (Wineland, p. 739 and Haroche, p. 763). The issue continues with three thorough, invited review papers covering different topics on quantum simulations. The first one reviews recent theoretical proposals to use cold atoms in optical lattices to simulate lattice gauge theories of the sort that appear in high-energy physics (U.-J. Wiese, p. 783). The second covers both theoretical proposals and experimental demonstrations of cold-atom systems to simulate the physics of matter in the presence of gauge fields, displaying so-called topological phenomena, which so far have only been observed in solid-state systems (I. Spielman, p. 794). The third one contains an extensive overview and new proposals to perform a broad range of quantum simulations using quantum dot systems (P. Barthelmy et al., p. 813). The issue also includes six original papers with a variety of theoretical proposals as well as the introduction of novel theoretical techniques related to the field of quantum simulation. The field of quantum simulations is just starting, but we are confident that it will soon generate an even larger plethora of new ideas and discoveries, trigger interdisciplinary research, and lead us to the adventure of describing and understanding the quantum world. We hope that this special issue will help future researchers in such an exciting adventure. Rainer Blatt received his PhD degree in physics from the University of Mainz in 1981. As a postdoctoral fellow he worked on atomic beam cooling in Boulder, CO and later as a research assistant in Hamburg with single trapped ions. In 1995 he accepted a chair in experimental physics at the University of Innsbruck working on quantum information processing with trapped ions. Since 2003 he is also scientific director at the Institute for Quantum Optics and Quantum Information (IQOQI) of the Austrian Academy of Sciences. Immanuel Bloch received his PhD degree in physics from the Ludwig Maximilians University of Munich in 2000. As a junior group leader, he continued in Munich starting his work on ultracold quantum gases in optical lattices. In 2008 he was appointed scientific director of the newly founded division on Quantum Many-Body Systems at the Max Planck Institute of Quantum Optics. Since 2009 he also holds a chair in quantum optics at the Ludwig-Maximilians University of Munich. Ignacio Cirac received his PhD degree in physics from the Universidad Complutense de Madrid in 1991. He was professor at the Universities of Castilla-La Mancha and Innsbruck from 1991–1996 and 1996–2001, respectively. In 2001 he joined the Max-Planck Institute of Quantum Optics, where he leads the Theory Division. His current research interests include quantum information theory and quantum optics. Peter Zoller obtained his doctorate from the University of Innsbruck in 1977. He was Max Kade Fellow at the University of Southern California from 1978/79, and was JILA visiting Fellow 1981/82 and 1988. In 1990 he became JILA Fellow and professor of physics at the University of Colorado. At the end of 1994, he accepted a chair at the University of Innsbruck, where he has worked ever since. Since 2003, he has also held the position of Scientific Director at the Institute for Quantum Optics and Quantum Information (IQOQI) of the Austrian Academy of Sciences.
Vibrational degrees of freedom in trapped-ion systems have recently been gaining attention as a quantum resource, beyond the role as a mediator for entangling quantum operations on internal degrees of freedom, because of the large available Hilbert space. The vibrational modes can be represented as quantum harmonic oscillators and thus offer a Hilbert space with infinite dimensions. Here we review recent theoretical and experimental progress in the coherent manipulation of the vibrational modes, including bosonic encoding schemes in quantum information, reliable and efficient measurement techniques, and quantum operations that allow various quantum simulations and quantum computation algorithms. We describe experiments using the vibrational modes, including the preparation of non-classical states, molecular vibronic sampling, and applications in quantum thermodynamics. We finally discuss the potential prospects and challenges of trapped-ion vibrational-mode quantum information processing.