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.
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.
This thesis is devoted to the theoretical characterization and generation of strongly correlated many-body states from the perspective of quantum information theory.We first study the entanglement properties of general many-body states and define a new measure for multipartite entanglement, the "Localizable Entanglement (LE)".It quantifies the maximal entanglement that can be localized, on average, between two parties by performing local measurements on the other parties.This measure provides knowledge of the "entanglement length", which is of particular importance in the context of quantum repeaters for long-distance quantum communication.We prove upper and lower bounds on LE in terms of two-body correlation functions and develop a method for the numerical computation of LE in one-dimensional spin systems.We analyze the localizable entanglement in various spin systems and observe characteristic features for a quantum phase transition such as a diverging entanglement length.In the second part of the thesis we focus on a specific many-body system: ultra-cold atoms in an optical lattice.This system is a promising candidate for the first physical realization of a "quantum simulator", but the temperature in current experiments is still too high.We propose, analyze and compare several schemes to cool the atoms close to the ground state of the strong interaction regime.In particular, we devise an algorithmic cooling protocol that combines occupation number filtering with spin-dependent lattice shifts.In addition, we propose two different physical realizations of filtering and also design protocols that generate an ensemble of quantum registers for quantum computation.In the third part we propose how to create entanglement in small atomic clouds by deforming and rotating the harmonic trapping potential.The resulting states are entangled in their motional degrees of freedom and can be identified with strongly correlated fractional quantum Hall states.For the case of two, three and four atoms we show how to adiabatically transform the unentangled ground state into the desired entangled state.We further discuss characteristic features of these states and propose how to create and detect them experimentally using an optical lattice setup. A Proof of the lower bound on LEA.1 Theorem on connected correlation functions and local measurements . . . . . . . . .
Ultracold atoms in optical lattices provide an extremely clean and controllable setting to explore quantum many-body phases of matter. Here we give a brief review of the strong-correlation physics that has been realized using such ultracold atoms in optical lattices ranging from the realization of Hubbard models to studies of quantum magnetism and the detection of single atoms with lattice site resolution. All this has opened up fundamentally new opportunities for the investigation of quantum many-body systems. Introduction Over the past years, ultracold atoms in optical lattices have emerged as versatile new systems to explore the physics of quantum many-body systems. On the one hand, they can be helpful in gaining a better understanding of known phases of matter and their dynamical behavior; on the other hand, they allow one to realize completely novel quantum systems that have not been studied before in nature [1, 2, 3]. Commonly, the approach of exploring quantum many-body systems in such a way is referred to as “quantum simulations.” Examples of some of the first strongly interacting many-body phases that have been realized both in lattices and in the continuum include the quantum phase transition from a superfluid to a Mott insulator [4, 5, 6], fermionic Mott insulators [7, 8], the achievement of a Tonks- Girardeau gas [9, 10], and the realization of the Bose-Einsten condensate (BEC)– Bardeen-Cooper-Schrieffer (BCS) crossover (see also Chapter 12) in Fermi gas mixture [11] using Feshbach resonances [12]. In almost all of these experiments, detection was limited to time-of-flight imaging or more refined derived techniques that mainly characterized the momentum distribution of the quantum gas [2]. For several years, researchers in the field have therefore aspired to employ in situ single-particle detection methods for the analysis of ultracold quantum gases. Only recently has it become possible to implement such imaging techniques, marking a milestone for the characterization and manipulation of ultracold quantum gases [13, 14, 15, 16, 17]. In our discussion, we will focus on one of the most successful of these techniques based on high-resolution fluorescence imaging. Despite being a rather new technique, such quantum gas microscopy has already proven to be an enabling technology for probing and manipulating quantum many-body systems. For the first time, controllable and strongly interacting many-body systems, as realized with ultracold atoms, could be observed on a local scale [17, 16].
This thesis reports on new experimental techniques for the study of strongly correlated states of ultracold atoms in optical lattices. We used a high numerical aperture imaging system to probe 87Rb atoms in a two-dimensional lattice with single-site resolution. Fluorescence imaging allows to detect single atoms with a large signal to noise ratio and to reconstruct the atom distribution on the lattice. We applied this new technique to a two-dimensional Mott insulator and directly observed number squeezing and the emerging shell structure. A comparison of the radial density and variance distributions to theory provides a precise in situ temperature and entropy measurement from single images. We find entropies around the critical value for quantum magnetism. In a second series of experiments, we demonstrated two-dimensional single-site spin control in the optical lattice. The differential light shift of a tightly focused laser beam shifts selected atoms into resonance with a microwave field driving a spin flip. In this way, we reach sub-diffraction limited spatial resolution well below the lattice spacing. Starting from a Mott insulator with unity filling we were able to create arbitrary spin patterns. We used this ability to prepare atom distributions to study one-dimensional single-particle tunneling dynamics in a lattice. By discriminating the dynamics of the ground state and of the first excited band, we find that our addressing scheme leaves most atoms in the vibrational ground state. Moreover, we studied coherent light scattering from the atoms in the optical lattice and found diffraction maxima in the far-field. We showed that an antiferromagnetic order leads to additional diffraction peaks which can be used to detect this order also when single-site resolution is not available. The new techniques described in this thesis open the path to a wide range of novel applications from quantum dynamics of spin impurities, entropy transport, implementation of novel cooling schemes, and engineering of quantum many-body phases to quantum information processing.
In the past decades, rapid advances in the experimental control of quantum systems have opened up unparalleled capabilities of engineering exotic quantum states. Nowadays, we may consider ourselves witnesses of a second quantum revolution as strongly correlated quantum matter is regularly created, on a daily basis, within the most diverse platforms, e.g. arrays of Rydberg atoms, ultra-cold atoms in optical lattices, superconducting qubits, trapped ions, and quantum dots. In this era, dubbed Noisy-Intermediate Scale Quantum (NISQ) era, the effort in pursuing research for realizing quantum technologies with practical purposes, such as quantum computing, simulations, communication and metrology, has greatly accelerated, and we are just starting to experience the immense progress that could be achieved. The remarkable breakthrough we are facing builds upon seminal theoretical and experimental advances in quantum physics. The key achievements in atomic, molecular, and optical (AMO) physics have opened up the possibility of controlling, trapping, and measuring single atoms, one by one, with high accuracy and reliability. In parallel, from a theoretical point of view, the study of quantum entanglement and correlations has bridged AMO physics and quantum information with crucial proposals for the realization of universal quantum computers. In this context, entanglement has emerged as one of the key tools to characterize and to exploit quantum many-body systems for quantum information purposes. We will study quantum entanglement in several scenarios to investigate and probe complex quantum many-body systems. We will consider examples ranging from generic mixed states in equilibrium to out-of-equilibrium dynamics, with and without dissipation, and topologically non-trivial systems. The leitmotif of this work will be how entanglement and correlations can be exploited to characterize the many-body quantum state describing a physical system and how entanglement can be detected in an experimentally efficient manner.
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.
This thesis is devoted to exploit strong correlations among ultracold atoms in order to create novel, exotic quantum states. In the first two chapters, we devise dynamical out-of-equilibrium preparation schemes which lead to intriguing final states. First of all, we propose to create the elusive supersolid state via a quantum quench protocol. Supersolids – quantum hybrids exhibiting both superflow and solidity – have been envisioned long ago, but have not been demonstrated in experiment so far. Our proposal to create a supersolid state is perfectly accessible with current technology and may clear the way to the experimental observation of supersolidity. Another out-of-equilibrium preparation scheme is discussed in the second chapter, giving rise to novel Cooper pairs of bosons. Ordinarily, Cooper pairs are composed of fermions – not so in our setup! We show that a Mott state of local bosonic Bell pairs can evolve into a Cooper-paired state of bosons, where the size of the pairs becomes macroscopic. This state can be prepared via a quick, diabatic ramp from the Mott into the superfluid regime. Furthermore, we propose to use bosons featuring conditional-hopping amplitudes in order to create Abelian anyons in one-dimensional optical lattices. We derive an exact mapping between anyons and bosons via a “fractional” Jordan-Wigner transformation. We suggest to employ a laser-assisted tunneling scheme to establish the many-particle state of “conditional-hopping bosons”, thus realizing a gas of Abelian anyons. The fractional statistics phase can be directly tuned by the lasers. The realization of non-Abelian anyons would be especially delightful, due to their significance in topological quantum computation schemes. We propose to employ strongly correlated bosons in one-dimensional optical lattices to create the Pfaffian state – which is known to host non-Abelian anyons as elementary excitations. In this setup, three-body correlations are required to dominate the system, which we model by on-site interactions of atoms with diatomic molecules. Finally, we use strong correlations in one-dimensional systems to create the effect of spin-charge separation, as formulated theoretically first in 1968. For a model of two-component bosons we compute the effective mass of a spin-flip excitation via Bethe Ansatz. In the strongly correlated regime, we show that the effective mass reaches the total mass of all particles in the system. The spin wave thus travels much more slowly than the density wave, giving rise to a strong spin-charge separation.