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.
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.
Over the last decade, quantum simulation and computation has progressed from a purely scientific testbed of quantum mechanics to a mature field that is starting to offer new insights into materials, quantum effects, and algorithms that are intractable with even the most state-of-the-art classical computation. Simulating certain quantum Hamiltonians that are theorized to be at the heart of high-Tc superconductivity, topological quantum systems such as the fractional quantum Hall effect or fundamental questions of thermalization quickly exceed the available memory of even the most advanced supercomputers – and in fact all memory in the world – due to the exponential growth of the Hilbert space with system size. As postulated by Feynman himself, the computational system best suited for solving quantum problems is to use a quantum system itself, as it can intrinsically represent the entanglement that is the key resource making quantum computing challenging but also promising. Apart from simulating problems in physics and chemistry, there is also tremendous excitement for quantum computers to provide speedups for general algorithms in optimization at a rate that is exponentially faster than existing classical programming. So far only a small class of algorithms has been actually proven to provide such a speedup, most prominently Shor's algorithm which can factor large prime numbers, and several other search and oracle algorithms. In the last two decades, many experiments using ultracold atoms, ions, or superconducting circuits have focused on analog quantum simulation. Here, a model Hamiltonian that is believed to capture all the relevant physics of the system of study is experimentally realized using different building blocks and interactions but replicating condensed matter effects at an increased scale. This has led to a number of bespoke experiments such as BEC/Fermigass machines, quantum gas microscopes and more exotic setups that are purpose built to study a particular effect. More recently, there has been a shift to develop more universal simulation platforms and optical tweezer arrays have emerged as a leading solution due to their high degree of reconfigurability. Through tremendous improvements in the degree of control and measurement of single qubits, error correction has become a viable route to build a true universal digital quantum computer. Even as we transition into the digital age of quantum simulation, certain classes of problems with additional physics constraints such as Fermionic statistics, gauge fields and lattice gauge theories still incur too large of an overhead to be encoded on these digital simulators. In this thesis, we use a highly degenerate twisted cavity to simulate the effect of a magnetic field on a two-dimensional system of interacting photons to enable realization of states of the quantum Hall effect. We design, build, and commission a new lens based cavity apparatus realizing a lowest Landau level for a mesoscopic number of modes. We demonstrate the integration of highly excited Rydberg atoms to mediate strong interactions and demonstrate photon blockade as well as mean field interactions. As a second application of cavities to quantum information leveraging our newfound comfort with intra-cavity optics, and experience with aberration modeling in resonators, we demonstrate a new class of small waist optical resonators enabled by lens-based cavities and then apply our understanding of optical aberrations in cavities to the development of a new class of cavity array. This Cavity Array Microscope (CAM) realizes a large number of cavities (up to currently 600) using only a fixed number of free space optics and is both scalable with constant overhead as well as compatible with Rydberg atoms. This platform provides a route to highly parallel quantum repeater operation or entanglement generation between atom arrays in the future.
A year passed-by full of exciting physics and new discoveries. One of the major announcements in 2013 was the discovery of the Higgs boson at CERN 1. ATLAS and CMS experiments confirmed that a new particle has been found which is compatible with the Higgs boson. In the same year, the Nobel Prize in physics was awarded to François Englert and Peter W. Higgs “for the theoretical discovery of a mechanism that contributes to our understanding of the origin of mass of subatomic particles…” 2. Although the prize went to two theory pioneers it is clear that this success was a result of major efforts of thousands of people, including experimentalists, engineers as well as people working in administration, logistic and funding. A truly Big Science enterprise. Annalen der Physik congratulates all people involved for this feast of human curiosity, endurance and the untiring will to understand nature. In addition to this, understanding fundamental physical laws can also be brought forward on a low energy scale which marked a major theme in Annalen der Physik last year, see our (double) special issue on “Precision Experiments and Fundamental Physics at Low Energies” edited by Klaus Blaum, Holger Müller, and Nathal Severijns3, 4. Other topics were of interest, too. Recently, and most likely inspired by the seminal work from Nobel laureates Serge Haroche 5 and David Wineland 6, our guest editors and advisory board members Rainer Blatt, Immanuel Bloch, Ignacio Cirac, and Peter Zoller organized the special issue “Quantum Simulation” which also presents the Nobel lectures of the afore mentioned prize winners 7. In this context I would like to point to the work of S. Schmidt and J. Koch “Circuit QED lattices – Towards quantum simulation with superconducting circuits” earlier last year 8 and to M. Schlosshauer, J. Kofler and A. Zeilinger's discussion on “The interpretation of quantum mechanics: from disagreement to consensus?” 9. Yet, there were more aspects in physics that seemed worth to be brought forward. Peter Hommelhoff, Matthias Kling, and Mark Stockman organized a special issue with invited contributions in the field of “Ultrafast Phenomena on the Nanoscale” 10, including intensely discussed problems in the field like high-harmonic generation 11-14. What else is out there? For 2014, Annalen der Physik has announced to publish focus issues on three major topics to catch up with recent research efforts in some of the most challenging and promising branches in our field. One of the most puzzling and controversially discussed questions concerns the destiny of our universe. Richard Battye, Ariel Goobar, and Jochen Weller organize the special issue “The Accelerating Universe” (submission deadline March 17, 2014). Invitations to participate are still open and can be viewed at www.ann-phys.org. This special issue complements the issue on “Dark Matter” by Matthias Bartelmann and Volker Springel 15 from 2012 with highlight articles from Lars Bergstrom 16, Carlos S. Frenk and Simon D.M. White 17 and many more. Another topic will be covered by Jack Harris, Peter Rabl and Albert Schliesser, focusing on “Quantum and Hybrid Mechanical Systems – From Fundamentals to Applications” (submission deadline May 2, 2014). This issue, too, adds nicely to our previous efforts to publish more articles in this field, see for example Pierre Meystre's overview article “A short walk through quantum optomechanics” 18. Further submissions are welcome! Finally, Francisco Guinea, Misha I. Katsnelson, and Tim Wehling will organize the issue “Two-dimensional Materials: Electronic Structure and Many-Body Effects” (submission deadline May 1, 2014). As the guest editors said these new materials “hold the promise for novel devices with designed electronic properties” thus being today's subject of basic research and tomorrow's everyday technology. For further details, please visit our homepage. In this current issue we present some interesting overview works in the fields of quantum optics (G. Feve et al. page 1) and two-dimensional spectroscopy (G. Scholes et al. page 31), as well as novel research work by P. Kinsler and M. McCall on spacetime transformation theory (page 51) and J. E. Hirsch's work on superconductivity and diamagnetism (page 63). R. L. Hall et al. report on Nodal theorems for the Dirac equation (page 79), C. Henkel and V. E. Mkrtchian describe the Casimir effect (page 87), A. Kolovsky discusses bosonic and fermionic carriers in one- and two-dimensional lattices (page 102), and Y. Fu et al. report on light absorbing by meta-nanorings (page 112). Enjoy reading Annalen der Physik!
Simulating quantum many-body systems on a classical computer generally requires a computational cost that grows exponential with the number of particles. This computational complexity has been the main obstacle to understanding various fundamental emergent phenomena in condensed matters such as high-Tc superconductivity and the fractional quantum-Hall effect. The difficulty arises because even the simplest models that are proposed to capture those phenomena cannot be simulated on a classical computer. Recognizing this problem in 1981, Richard Feynman envisioned a quantum simulator, an entirely new type of machine that exploits quantum superposition and operates by individually manipulating its constituting quantum particles and their interactions. Recent advances in various experimental platforms from cold atoms in optical lattices, trapped ions, to solid-state systems have brought the idea of Feynman to the realm of reality. Among those, interacting photons in superconducting circuits has been one of the promising platforms thanks to their local controllability and long coherence times. Early theoretical proposals have shown possibilities to realize quantum many-body phenomena of light using coupled cavity arrays such as Mott to superfluid transitions and fractional quantum Hall states. Start-of-the-art experiments include realization of interacting chiral edge states and stroboscopic signatures of localization of interacting photons in a three-site and a nine-site superconducting circuit, respectively. Interacting photons also serve as a natural platform to simulate driven-dissipative quantum many-body phenomena. A 72-site superconducting circuit has also recently been fabricated to study a dissipative phase transition of light.
Simulating quantum many-body systems on a classical computer generally requires a computational cost that grows exponential with the number of particles. This computational complexity has been the main obstacle to understanding various fundamental emergent phenomena in condensed matters such as high-Tc superconductivity and the fractional quantum-Hall effect. The difficulty arises because even the simplest models that are proposed to capture those phenomena cannot be simulated on a classical computer. Recognizing this problem in 1981, Richard Feynman envisioned a quantum simulator, an entirely new type of machine that exploits quantum superposition and operates by individually manipulating its constituting quantum particles and their interactions. Recent advances in various experimental platforms from cold atoms in optical lattices, trapped ions, to solid-state systems have brought the idea of Feynman to the realm of reality. Among those, interacting photons in superconducting circuits has been one of the promising platforms thanks to their local controllability and long coherence times. Early theoretical proposals have shown possibilities to realize quantum many-body phenomena of light using coupled cavity arrays such as Mott to superfluid transitions and fractional quantum Hall states. Start-of-the-art experiments include realization of interacting chiral edge states and stroboscopic signatures of localization of interacting photons in a three-site and a nine-site superconducting circuit, respectively. Interacting photons also serve as a natural platform to simulate driven-dissipative quantum many-body phenomena. A 72-site superconducting circuit has also recently been fabricated to study a dissipative phase transition of light.
Envisioned by Richard Feynman in the early 1980s, quantum simulation has received dramatic impetus thanks to the development of a variety of plateforms able to emulate a wide class of quantum Hamiltonians.During the past decade, most of the quantum simulators have implemented rather well-known models, hence permitting a direct comparison with theoretical calculations and a precise benchmarking of their reliability.The field has now reached a maturity such that one can address difficult problems, which cannot be solved efficiently using classical algorithms.These advances provide unprecedented opportunities to explore previously unreachable fields, test theoretical predictions, and inspire novel approaches.This contribution is an elementary introduction to quantum simulation.We discuss the challenges, define both digital and analog quantum simulators, and list the demanding conditions they require.We also provide a brief account of the contributions gathered in the dossier on Quantum simulation in the Compte rendus Physique of the French Academy of Sciences [1][2][3][4][5][6].The latter completes excellent reviews that appeared previously, see for instance . Universal models and the role of simulations in many-body physicsUnderstanding the behavior of macroscopic quantum systems is a major challenge of modern physics.The basic laws of low-energy physics are by now quite well known at the microscopic, say atomic, scale.Conversely, many fundamental questions remain open, and even debated, about the collective dynamics at the macroscopic scale.By "macroscopic scale", here we mean systems made up of a huge number of constituents, or degrees of freedom, say 10 6 , 10 23 , or even more, as relevant in condensed matter physics or in astrophysics, for instance.Such huge systems cannot be treated exactly, be it a the classical level and, even worse, at the quantum level.Yet, it is the main outcome of the thermodynamic approach that the collective behavior of a macroscopic system can drastically differ from that of its elementary constituents.For instance, the elementary interactions between the H 2 O molecules are fundamentally unchanged when a water bucket turns from the liquid phase to the solid phase at zero degree Celsius.Similarly, the interactions between the microscopic magnetic moments do not show any brutal change when a magnetic material gets magnetized underneath the Curie temperature.Hence, the dramatic effects observed in macroscopic systems are governed by large-scale instabilities, without obvious counterparts at the microscopic level.This observation takes a universal character, summarized in the celebrated motto "More is Different" [15].Such so-called emerging phenomena also appear in quantum systems, where new effects that are impossible in the classical world show up below some critical temperature or at zero temperature when some interaction parameter passes through a critical value.Celebrated examples include the superfluid transition in helium or super-conducting transitions and other metal-insulator transitions in electronic systems.Strikingly enough at first sight, while emerging phenomena only appear in very large scale macroscopic systems, their germs are contained in the mutual interactions of their elementary constituents.Hence, local two-body interactions are sufficient to explain a huge class of phase transitions, such as the liquid-solid and magnetic transitions mentioned above.The Boltzmann statistical approach proved particularly successful in describing this connection between the microscopic and macroscopic scales.To understand emerging phenomena on grounds as fundamental as possible, the programme is now well established: One tries to identify the basic microscopic terms that seem to be relevant and disregards all the other microscopic details.One then elaborates a model, as generic as possible, likely to reproduce the main experimental observations.The most usual examples are the Ising and Heisenberg models for magnetic transitions, or the Hubbard model for metal-insulator transitions [16][17][18].Then all is left to do is to check that the phenomenon of interest indeed emerges from the dynamics of the simplified model.The realization of this programme is nothing but a simulation.It consists in building up a simplified system that mimics the main properties of a real system.
Quantum computers, although not yet available on the market, will revolutionise the future of information processing. Already now, quantum computers of special purpose, i.e., quantum simulators, are within reach. The physics of ultracold atoms, ions, and molecules offers unprecedented possibilities of control of quantum many systems, and novel possibilities of applications for quantum information and quantum metrology. Particularly fascinating is the possibility of using ultracold atoms in lattices to simulate condensed matter or even high energy physics. This book provides a comprehensive overview of ultracold lattice gases as quantum simulators, an interdisciplinary field involving atomic, molecular, and optical physics; quantum optics; quantum information; and condensed matter and high energy physics. It includes some introductory chapters on basic concepts and methods, and focuses on the physics of spinor, dipolar, disordered, and frustrated lattice gases, before reviewing in detail artificial lattice gauge fields with ultracold gases. The last part of the book moves onto a discussion of possible implementations universal quantum computers with ultracold atoms. After a crash course in quantum information theory, several models of quantum computation with ultracold gases are presented, as well as the current understanding of condensed matter from a quantum information perspective. The book ends with the general discussion of various detection methods that are unique for ultracold atoms.