Abstract : This report results from a contract tasking Ludwig-Maximilian University of Munich as follows: In this new grant proposal, we specifically try to address important questions that have emerged out of our previous work and that should provide major advances for the field of quantum state engineering and quantum simulations, as well as quantum information processing. Possible applications also include non-classical matter wave field states that are especially useful for improving the performance of matter wave based atom interferometers. The grant proposal will be focused on research to be carried out on an existing and a completely novel experimental apparatus, focusing on two fundamental topics: (1) Generation of robust multi-particle entanglement in optical lattices, with low decoherence rates as a resource for quantum information processing and improved atom interferometers; and (2) The construction of a novel experimental apparatus with the possibility to address, observe and manipulate single atoms on single sites of an optical lattice. Based on our experience with previous experiments, we find these two topics to be of fundamental importance for future advances in this field.
Abstract : This report results from a contract tasking Ludwig-Maximilian University of Munich as follows: In this new grant proposal, we specifically try to address important questions that have emerged out of our previous work and that should provide major advances for the field of quantum state engineering and quantum simulations, as well as quantum information processing. Possible applications also include non-classical matter wave field states that are especially useful for improving the performance of matter wave based atom interferometers. The grant proposal will be focused on research to be carried out on an existing and a completely novel experimental apparatus, focusing on two fundamental topics: (1) Generation of robust multi-particle entanglement in optical lattices, with low decoherence rates as a resource for quantum information processing and improved atom interferometers; and (2) The construction of a novel experimental apparatus with the possibility to address, observe and manipulate single atoms on single sites of an optical lattice. Based on our experience with previous experiments, we find these two topics to be of fundamental importance for future advances in this field.
Many outstanding problems in quantum physics, such as high-Tc superconductivity or quark confinement, are still - after decades of research - awaiting commonly accepted explanations. One reason is that such systems are often difficult to control, show an intermingling of several effects, or are not easily accessible to measurement. To arrive at a deeper understanding of the physics at work, researchers typically derive simplified models designed to capture the most striking phenomena of the system under consideration. However, due to the exponential complexity of Hilbert space, even some of the simplest of such models pose formidable challenges to analytical and numerical calculations. In 1982, Feynman proposed to solve such quantum models with experimental simulation on a physically distinct, specifically engineered quantum system [Int. J. Theor.Phys. 21, 467]. Designed to be governed by the same underlying equations as the original model, it is hoped that direct measurements on these so called quantum simulators (QSs) will allow to gather deep insights into outstanding problems of physics and beyond. In this thesis, we identify four requirements that a useful QS has to fulfill, relevance, control, reliability, and efficiency. Focusing on these, we review the state of the art of two popular approaches, digital QSs (i.e., special purpose quantum computers) and analog QSs (devices with always-on interactions). Further, focusing on possibilities to increase control over QSs, we discuss a scheme to engineer quantum correlations between mesoscopic numbers of spinful particles in optical lattices. This technique, based on quantum polarization spectroscopy, may be useful for state preparation and quantum information protocols. Additionally, employing several analytical and numerical methods for the calculation of many-body ground states, we demonstrate the variety of condensed-matter problems that can be attacked with QSs consisting of ultracold ions or neutral atoms in optical lattices. The chosen examples, some of which have already been realized in experiment, include such diverse settings as frustrated antiferromagnetism, quantum phase transitions in exotic lattice geometries, topological insulators, non-Abelian gauge-fields, orbital order of ultracold Fermions, and systems with long-range interactions. The experimental realization of all of these models requires techniques which go beyond standard optical lattices, e.g., time-periodic driving of lattices with exotic geometry, loading ultracold atoms into higher bands, or immersing trapped ions into an optical lattice. The chosen models, motivated by important open questions of quantum physics, pose difficult problems for classical computers, but they may be amenable in the near future to quantum simulation with ultracold atoms or ions. While the experimental control over relevant models has increased dramatically in the last years, the reliability and efficiency of QSs has received considerably less attention. As a second important part of this thesis, we emphasize the need to consider these aspects under realistic experimental conditions. We discuss specific situations where terms that have typically been neglected in the description of the QS introduce systematic errors and even lead to novel physics. Further, we characterize in a generic example the influence of quenched disorder on an analog QS. Its performance for simulating universal behavior near a quantum phase transition seems satisfactory for low disorder. Moreover, our results suggest a connection between the reliability and efficiency of a QS: it works less reliable exactly in those interesting regimes where classical calculations are less efficient. If QSs fulfill all of our four requirements, they may revolutionize our approach to quantum-mechanical problems, allowing to solve the behavior of complex Hamiltonians, and to design nano-scale materials and chemical compounds from the ground up.
We review novel methods for the investigation, control and manipulation of neutral atoms in optical lattices. These setups allow unprecedented quantum control over large numbers of atoms and thus are very promising for applications in quantum information processing. After introducing optical lattices we discuss the superfluid (SF) and Mott insulating (MI) states of neutral atoms trapped in such lattices and investigate the SF-MI transition as observed experimentally recently. In the second part of the paper we give an overview of proposals for quantum information processing and show different ways to entangle the trapped atoms, in particular the usage of cold collisions and Rydberg atoms. Finally, we discuss briefly the implementation of quantum simulators, entanglement enhanced atom interferometers, and ideas for robust quantum memory in optical lattices.
Entanglement is a fundamental resource for quantum information processing [1-3], its applications including scalable quantum communication, secure quantum key distribution protocols for cryptography, and exponential speedup of quantum algorithms. It occurs naturally in manybody systems at low temperatures: This makes cold atoms good candidates to provide entangled states involving a large number of particles. For realizing and manipulating such states, an essential task is quantifying the actual amount of entanglement contained in the created state before using it for quantum information protocols. However, this task represents a major challenge, as it requires either full state tomography, scaling exponentially in the system size, or the assumption of unverified system characteristics such as its Hamiltonian or temperature. In this experiment [4], we obtain a quantification of multipartite entanglement from readily accessible measurements - that is, time-of-flight atomic density distribution - based on a recent proposal [5]. We directly observe and quantify the multipartite spatial entanglement between the sites of a periodic optical potential (optical lattice) that hosts massive bosonic particles. We characterize its behaviour when crossing the superfluid-Mott insulator transition and when varying temperature, demonstrating the robustness of our method. References [1] M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information, Cambridge University Press (Cambridge, 2000). [2]R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, Quantum entanglement, Rev. Mod. Phys. 81, 865-942 (2009). [3]O. Göhne and G. Tóth, Entanglement detection, Physics Reports 474, 1-75 (2009). [4]M. Cramer, A. Bernard, N. Fabbri, L. Fallani, C. Fort, S. Rosi, F. Caruso, M. Inguscio, and M. B. Plenio, Entanglement of bosons in optical lattices, E-print arXiv:1302.4897 [5]M. Cramer, M. B. Plenio, and H. Wunderlich, Measuring entanglement in condensed matter systems, Phys. Rev. Lett. 106, 020401 (2011).
This thesis is devoted to quantum information processing using strongly correlated many-body systems, and we have focused our interest on systems realized with ultracold atoms in optical lattices. We have proposed different protocols based either on the free dynamics followed by a particular initial state -out of the ground-state manifold-, or on the non-trivial quantum dynamics generated by the optimal modulation of optical lattices. Our protocols demonstrate the potential of strongly correlated systems to perform short-distance quantum communication. Protocols based on dynamical manipulations of the optical lattices have also been extended to two-dimensional lattices to prepare decoherence-free cluster states. We have also proposed a novel scheme combining free dynamics and continuous measurements, which lead to the Quantum Zeno effect, for quantum information processing in spin chains. Despite of the recent progress in using atoms trapped in optical lattices to prepare and manipulate strongly correlated systems, the precise detection and experimental characterization of such states is a major challenge in modem physics. We have exploited some of the proposed protocols to analyze strongly correlated systems from the quality of their performance when implementing a quantum information task. Our approach provides a new insight into the study of these complex and fascinating systems. Regarding the detection, we have also addressed the fundamental problem of inferring the state of a given quantum system. First, we have studied the optimal state estimation of the most fundamental quantum system, a two-level system or qubit. Second, we have also considered and proposed new methods to tackle the experimental challenge of detecting the many-body systems prepared with ultracold atoms in optical lattices. We have extended the applicability of the noise-correlation method to detect a mesoscopic Schrodinger cat many-body state. Despite the success of this method, it has the drawback that it demolishes the physical system. To overcome such limitation, we have proposed an . extension of the well-known Faraday effect at the quantum level, which yields a quantum non-demolition method to detect strongly correlated systems.
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