Abstract The year 2015 was the International Year of Light. However, it also marked, the 20th anniversary of the first observation of Bose–Einstein condensation in atomic vapors by Eric Cornell, Carl Wieman and Wolfgang Ketterle. This discovery could be considered as one of the greatest achievements of quantum optics that has triggered an avalanche of further seminal discoveries and achievements. For this reason we devote this essay for the focus issue on ‘Quantum Optics in the International Year of Light’ to the recent revolutionary developments in quantum optics at the frontiers of all physics: atomic physics, molecular physics, condensed matter physics, high energy physics and quantum information science. We follow here the lines of the introduction to our book ‘Ultracold atoms in optical lattices: Simulating quantum many-body systems’ (Lewenstein et al 2012 Ultracold Atoms in Optical Lattices: Simulating Quantum Many-body Systems (Oxford: University Press)), and to a lesser extent the review article M Lewenstein et al (2007 Adv. Phys. 56 243 ). The book, however, was published in 2012, and many things has happened since then—the present essay is therefore upgraded to include the latest developments.
Abstract The year 2015 was the International Year of Light. However, it also marked, the 20th anniversary of the first observation of Bose–Einstein condensation in atomic vapors by Eric Cornell, Carl Wieman and Wolfgang Ketterle. This discovery could be considered as one of the greatest achievements of quantum optics that has triggered an avalanche of further seminal discoveries and achievements. For this reason we devote this essay for the focus issue on ‘Quantum Optics in the International Year of Light’ to the recent revolutionary developments in quantum optics at the frontiers of all physics: atomic physics, molecular physics, condensed matter physics, high energy physics and quantum information science. We follow here the lines of the introduction to our book ‘Ultracold atoms in optical lattices: Simulating quantum many-body systems’ (Lewenstein et al 2012 Ultracold Atoms in Optical Lattices: Simulating Quantum Many-body Systems (Oxford: University Press)), and to a lesser extent the review article M Lewenstein et al (2007 Adv. Phys. 56 243 ). The book, however, was published in 2012, and many things has happened since then—the present essay is therefore upgraded to include the latest developments.
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.
The year 2015 marks the 20th anniversary of the achievement of Bose–Einstein condensation (BEC) in atomic vapors. Atomic BEC, realized by Eric Cornell, Carl Wieman and Wolfgang Ketterle in 1995, commenced an exciting wave to explore quantum few- and many-body physics. Different from solid state matter and helium superfluids, atomic condensates in the gas phase come with drastically lower densities and temperatures, which place the systems in a unique regime where the atomic interactions are simple and precisely known. Furthermore, the condensates are typically weakly interacting: the interaction length scale of few nanometers is much shorter than the interatomic separation of hundreds of nanometers. Thus many early experimental observations can be well understood based on mean-field theory. One celebrated model is the Gross-Pitaevskii equation which provides a precise and quantitative description of weakly interacting Bose condensates [1]. Opportunities to extend cold atom research beyond the weak interaction regime emerged in the early 2000s. Several experimental schemes were developed to prepare atoms in the strong correlation and interaction regimes. One approach is loading atoms into an optical lattice, the interference pattern of laser beams. The lattice potential enhances the interactions of localized atoms and quenches their kinetic energy. A variety of lattice configurations are realized that promise novel quantum phases of ultracold atoms. Another route to strong interaction is based on Feshbach resonance, typically induced by magnetically shifting a molecular state near the scattering continuum of atoms. The resonant coupling between scattering atoms and the molecular state leads to a divergence of the atomic interaction length scale. Exactly on Feshbach resonance, the collision cross section reaches the quantum mechanical limit, and the system becomes strongly hydrodynamic with mean-free path as short as interparticle separation. Fascinating observations in the strong coupling regime soon followed: prominent examples include the superfluid-Mott insulator transition in optical lattices [2], resonantly interacting Fermi gases in the BEC–BCS (Bardeen–Cooper–Schieffer superfluid) crossover [3] and Efimov three-body states [4], and they lead to tremendous research interest into novel quantum states and quantum dynamics. One of the key motivations in these explorations is to uncover new, universal principles that underpin the physics of strongly correlated quantum systems. A well-studied universal behavior in many-body physics manifests in the critical phenomena near a continuous phase transition. Near the critical point, the system develops a diverging correlation length, which suppresses the dependence on other microscopic length scales. The systems are thus scale invariant and can be universally characterized by a few critical exponents. In cold atoms, divergence of correlation lengthes has been observed near the superfluid phase transition [5,6], as well as the superfluid-Mott insulator quantum phase transition in optical lattices. In the lattice experiments, scale invariance can be tested based on the equation of state measurements [7]. These works complement the transport measurements in condensed matter experiments. Has a new class of universal physics been discovered in atomic quantum gases? Yes, it turns out that a special class of strongly interacting quantum gas with ‘intrinsic’ scaling symmetry emerges near a Feshbach resonance [8]. Near the resonance, the scattering length scale diverges a → ∞ [9], unimaginable in classical systems, and the interaction length reaches the maximum value allowed by quantum mechanics as 1/k, called the ‘unitarity limit’ and k is the momentum of the scattering state. A famous example is the strongly interacting Fermi gas in the BEC–BCS crossover regime, where the resonant interactions lead to strong pairing and and universal hydrodynamic behavior. An exciting development in the study of the BEC–BCS crossover focuses on the Fermi gas exactly on Feshbach resonance. Here the system, also called a ‘unitary Fermi gas’, is the most complex and strongly correlated. The resonant interaction, however, implies a special scaling symmetry of the system. To understand the symmetry, we consider a scale transformation: x → Λx that stretches the coordinates of all atoms by a factor of Λ, and thus reduces the atomic density n by a factor of Λ3 in a 3D gas and the kinetic energy Ek ∝ −∇2 by Λ2. One can see that both kinetic energy Ek and interaction energy in the unitarity limit na → n/k are reduced by the same factor Λ2. The system is thus hypothesized to be invariant under the scale transformation [8]. Remarkably, similar scaling symmetry also holds for 2D quantum gas with a constant coupling g = const. [10]. Here stretching the size of the 2D gas by a factor of Λ also reduces both the kinetic Ek and interaction energy gσ by Λ2, where σ is the 2D density. Since the scaling symmetry in these systems comes directly from the form of the interactions, intrinsic scale invariance is robust at all temperatures T and chemical potentials μ and does not rely on the proximity to a phase transition. The scaling symmetry suggests that the only independent variables are the ratios of the length scales or the equivalent energy scales. In a grand canonical ensemble, the independent ratio can be chosen as μ/kBT. This realization greatly simplifies theoretical description as well as the experimental characterization of the system. Theoretically, a new set of universal thermodynamic relations are expected to be insensitive to the microscopic details; experimentally, measurements are expected to collapse into universal functions that only depend on μ/kBT. Measurements on unitary Fermi gas and the 2D Bose gas are consistent with the scaling hypothesis, shown in Fig. 1(a) and (b). Remarkable quantitative agreement between measurements and calculations has greatly advanced our understanding of the ‘unitary Fermi gas’ and 2D atomic gas. Ultracold atomic gases which are intrinsically scale invariant: (a) unitary Fermi gas, (b) 2D Bose gas and (c) unitary Bose gas. The scaling symmetry suggests that thermodynamic observables only depend on the ratio of chemical potential and thermal energy |μ~=μ/kBT|. In (a), thermodynamic pressure of a unitary Fermi gas is compared with calculations and other measurements. Figure courtesy of M. Zwierlein [11]. In (b), the collapse of the density measurement at various temperatures (inset) confirms the scaling symmetry. Figure adopted from [12]. Panel (c) shows the three-body loss spectrum in a 6Li133Cs mixture. The geometric progression of the Efimov resonance positions at B = B1, B2 and B3 toward the Feshbach resonance at B0 results from the discrete scaling symmetry of Efimov physics. Figure adopted from [13]. We may expect the same scaling symmetry for a resonantly interacting Bose gas. Here, however, the scaling symmetry is more subtle because of the presence of three-body physics. Predicted by Vitaly Efimov in the context of nuclear physics [14], an infinite number of three-body bound states exist for resonantly interacting bosons and their energies follow a discrete scaling law, breaking the otherwise continuous scaling symmetry. Identical fermions do not form such three-body states due to Pauli's exclusion principle. Theoretically the three-body bound states are supported by the ‘Efimov potential’ V(R)∝ − 1/R2, where R is the characteristic length scale of the three interacting atoms. While the Efimov potential does not break the continuous scaling symmetry, the presence of discrete three-body states does break the symmetry. An alternative picture based on renormalization group limited cycles [15] also explains the discrete scaling symmetry of the system, a scenario that rarely happens in electronic systems. Experimentally, Efimov states have been observed in cold gases of alkali atoms, as well as in helium-4. The geometric scaling symmetry of Efimov states is reported in a recent experiment, shown in Fig. 1(c). The same discrete scaling symmetry is expected for unitary quantum gas of bosons, which, if confirmed, will establish a unique and fascinating class of strongly interacting quantum systems. While in this article, we focus on atoms in optical lattices and unitary atomic gases as primary examples of universal physics that have been actively investigated, efforts in many new research frontiers have shown promising prospects to uncover new universal physics in the strongly correlated and interacting systems. Non-equilibrium dynamics is one of the hottest directions. Ultracold atoms are particularly suited for the study of quantum dynamics due to their slow evolution time scales of miniseconds to seconds. Dynamics near a quantum phase transition and the thermalization of isolated quantum systems are two research topics with many unanswered questions. Cold atom experiments may provide new universal insights that go beyond current theoretical framework. Another exciting direction is quantum many-body systems with long range or very strong interactions. Examples include trapped ions, and condensates of exotic atoms with huge magnetic dipole moments, polar molecules, as well as those with Rydberg excitations. These systems possess various long range interactions. Novel universal dynamics, for example, propagation of information and entanglement, are predicted to depend solely on the asymptotic form of the interaction and the dimension of the systems. The author thanks Yijun Wang for discussion and careful reading of the article. This work was supported by National Science Foundation (PHY-0747907) and Army Research Office-Multiple University Research Initiative (W911NF-14-1-0003).
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.
The study of Bose-Einstein condensation has undergone a remarkable expansion during the last twenty years. Observations of this phenomenon have been reported in a number of diverse atomic, optical, and condensed matter systems, facilitated by remarkable experimental advances. The synergy of experimental and theoretical work in this broad research area is unique, leading to the establishment of Bose-Einstein condensation as a universal interdisciplinary area of modern physics. This chapter reviews the broad expansion of Bose-Einstein condensation physics in the past two decades. Introduction The field of Bose-Einstein condensation (BEC) has undergone an explosive expansion during the past twenty years. Newcomers to this field are now often introduced to this as a universal phenomenon, which nonetheless exhibits diverse (and sometimes strikingly different) manifestations. Despite such differences, the common underlying theme creates a unique identity across many different energy and length scales. The study of BEC as a universal phenomenon was highlighted in a focused conference in 1993, leading to the publication of the well-known “green book” [1], which surveyed the breadth of the field of condensate physics at that time. The success of the conference led to a second meeting in 1995, at which Eric Cornell and Carl Wieman announced the achievement of Bose-Einstein condensation of ultracold 87 Rb atoms in a harmonic trap. That work began an explosion of new research in the field of cold atoms, which has continued to this day, and this very success inevitably led many of those studying cold atoms to pay less attention to other types of condensates. Wolfgang Ketterle gives a historical overview of this exciting period of time in Chapter 3. Recently, various scientific meetings have worked to re-establish the physical connections across different BEC systems, and in 2013 a workshop was held with the focused goal of improving communications across disciplines. This present book is an outgrowth of that meeting. The Situation Before the Revolution Because of the great success of the cold atom BEC and other BEC systems in the past twenty years, it may be hard for young scientists to understand the climate of BEC research in the early 1990s. At that time, there was only one known example of BEC, namely liquid helium-4, and there was a small but vocal minority of scientists who questioned whether BEC was established even in that system.
Seventy years after Einstein's prediction, the seminal achievement of Bose–Einstein condensation in dilute atomic gases in 1995 has provided us with a new form of quantum matter. Such quantum matter can be described as a single giant matter wave. By loading it into an artificial periodic potential formed by laser light—a so-called optical lattice—it has become possible to probe matter far beyond the wave-like description. In a review of a series of experiments with ultracold quantum gases in optical lattices, we show that the granularity of the matter wave field, caused by the discreteness of atoms, gives rise to effects going beyond the simple single matter wave description. Bose–Einstein condensates in optical lattices have thereby opened novel possibilities for investigating strongly correlated many-particle phenomena of condensed matter physics and have opened new opportunities for quantum information processing with neutral atoms
One of the most active areas in atomic, molecular and optical physics is the use of ultracold atomic gases in optical lattices to simulate the behaviour of electrons in condensed matter systems. The larger mass, longer length scale, and tuneable interactions in these systems allow the dynamics of atoms moving in these systems to be followed in real time, and resonant light scattering by the atoms allows this motion to be probed on a microscopic scale using site-resolved imaging. This book reviews the physics of Hubbard-type models for both bosons and fermions in an optical lattice, which give rise to a rich variety of insulating and conducting phases depending on the lattice properties and interparticle interactions. It also discusses the effect of disorder on the transport of atoms in these models, and the recently discovered phenomenon of many-body localization. It presents several examples of experiments using both density and momentum imaging and quantum gas microscopy to study the motion of atoms in optical lattices. These illustrate the power and flexibility of ultracold-lattice analogues for exploring exotic states of matter at an unprecedented level of precision.