Schrodinger cats and their power for quantum information processing

We outline a toolbox comprised of passive optical elements, single photon detection and superpositions of coherent states (Schrodinger cat states). Such a toolbox is a powerful collection of primitives for quantum information processing tasks. We illustrate its use by outlining a proposal for universal quantum computation. We utilize this toolbox for quantum metrology applications, for instance weak force measurements and precise phase estimation. We show in both these cases that a sensitivity at the Heisenberg limit is achievable.

Entanglement analysis of atomic processes and quantum registers

During recent years, quantum information processing and the study of N−qubit quantum systems have attracted a lot of interest, both in theory and experiment. Apart from the promise of performing efficient quantum information protocols, such as quantum key distribution, teleportation or quantum computation, however, these investigations also revealed a great deal of difficulties which still need to be resolved in practise. Quantum information protocols rely on the application of unitary and non–unitary quantum operations that act on a given set of quantum mechanical two-state systems (qubits) to form (entangled) states, in which the information is encoded. The overall system of qubits is often referred to as a quantum register. Today the entanglement in a quantum register is known as the key resource for many protocols of quantum computation and quantum information theory. However, despite the successful demonstration of several protocols, such as teleportation or quantum key distribution, there are still many open questions of how entanglement affects the efficiency of quantum algorithms or how it can be protected against noisy environments. To facilitate the simulation of such N−qubit quantum systems and the analysis of their entanglement properties, we have developed the Feynman program. The program package provides all necessary tools in order to define and to deal with quantum registers, quantum gates and quantum operations. Using an interactive and easily extendible design within the framework of the computer algebra system Maple, the Feynman program is a powerful toolbox not only for teaching the basic and more advanced concepts of quantum information but also for studying their physical realization in the future. To this end, the Feynman program implements a selection of algebraic separability criteria for bipartite and multipartite mixed states as well as the most frequently used entanglement measures from the literature. Additionally, the program supports the work with quantum operations and their associated (Jamiolkowski) dual states. Based on the implementation of several popular decoherence models, we provide tools especially for the quantitative analysis of quantum operations. As an application of the developed tools we further present two case studies in which the entanglement of two atomic processes is investigated. In particular, we have studied the change of the electron-ion spin entanglement in atomic photoionization and the photon-photon polarization entanglement in the two-photon decay of hydrogen. The results show that both processes are, in principle, suitable for the creation and control of entanglement. Apart from process-specific parameters like initial atom polarization, it is mainly the process geometry which offers a simple and effective instrument to adjust the final state entanglement. Finally, for the case of the two-photon decay of hydrogenlike systems, we study the difference between nonlocal quantum correlations, as given by the violation of the Bell inequality and the concurrence as a true entanglement measure.

Exact quantum Monte Carlo methods for correlated electron systems

Thema dieser Arbeit ist die Entwicklung und Kombination verschiedener numerischer Methoden, sowie deren Anwendung auf Probleme stark korrelierter Elektronensysteme. Solche Materialien zeigen viele interessante physikalische Eigenschaften, wie z.B. Supraleitung und magnetische Ordnung und spielen eine bedeutende Rolle in technischen Anwendungen. Es werden zwei verschiedene Modelle behandelt: das Hubbard-Modell und das Kondo-Gitter-Modell (KLM). In den letzten Jahrzehnten konnten bereits viele Erkenntnisse durch die numerische Lösung dieser Modelle gewonnen werden. Dennoch bleibt der physikalische Ursprung vieler Effekte verborgen. Grund dafür ist die Beschränkung aktueller Methoden auf bestimmte Parameterbereiche. Eine der stärksten Einschränkungen ist das Fehlen effizienter Algorithmen für tiefe Temperaturen.rnrnBasierend auf dem Blankenbecler-Scalapino-Sugar Quanten-Monte-Carlo (BSS-QMC) Algorithmus präsentieren wir eine numerisch exakte Methode, die das Hubbard-Modell und das KLM effizient bei sehr tiefen Temperaturen löst. Diese Methode wird auf den Mott-Übergang im zweidimensionalen Hubbard-Modell angewendet. Im Gegensatz zu früheren Studien können wir einen Mott-Übergang bei endlichen Temperaturen und endlichen Wechselwirkungen klar ausschließen.rnrnAuf der Basis dieses exakten BSS-QMC Algorithmus, haben wir einen Störstellenlöser für die dynamische Molekularfeld Theorie (DMFT) sowie ihre Cluster Erweiterungen (CDMFT) entwickelt. Die DMFT ist die vorherrschende Theorie stark korrelierter Systeme, bei denen übliche Bandstrukturrechnungen versagen. Eine Hauptlimitation ist dabei die Verfügbarkeit effizienter Störstellenlöser für das intrinsische Quantenproblem. Der in dieser Arbeit entwickelte Algorithmus hat das gleiche überlegene Skalierungsverhalten mit der inversen Temperatur wie BSS-QMC. Wir untersuchen den Mott-Übergang im Rahmen der DMFT und analysieren den Einfluss von systematischen Fehlern auf diesen Übergang.rnrnEin weiteres prominentes Thema ist die Vernachlässigung von nicht-lokalen Wechselwirkungen in der DMFT. Hierzu kombinieren wir direkte BSS-QMC Gitterrechnungen mit CDMFT für das halb gefüllte zweidimensionale anisotrope Hubbard Modell, das dotierte Hubbard Modell und das KLM. Die Ergebnisse für die verschiedenen Modelle unterscheiden sich stark: während nicht-lokale Korrelationen eine wichtige Rolle im zweidimensionalen (anisotropen) Modell spielen, ist in der paramagnetischen Phase die Impulsabhängigkeit der Selbstenergie für stark dotierte Systeme und für das KLM deutlich schwächer. Eine bemerkenswerte Erkenntnis ist, dass die Selbstenergie sich durch die nicht-wechselwirkende Dispersion parametrisieren lässt. Die spezielle Struktur der Selbstenergie im Impulsraum kann sehr nützlich für die Klassifizierung von elektronischen Korrelationseffekten sein und öffnet den Weg für die Entwicklung neuer Schemata über die Grenzen der DMFT hinaus.

Universal quantum computation with continuous-variable cluster states

We describe a generalization of the cluster-state model of quantum computation to continuous-variable systems, along with a proposal for an optical implementation using squeezed-light sources, linear optics, and homodyne detection. For universal quantum computation, a nonlinear element is required. This can be satisfied by adding to the toolbox any single-mode non-Gaussian measurement, while the initial cluster state itself remains Gaussian. Homodyne detection alone suffices to perform an arbitrary multimode Gaussian transformation via the cluster state. We also propose an experiment to demonstrate cluster-based error reduction when implementing Gaussian operations.

Long distance coupling of a quantum mechanical oscillator to the internal states of an atomic ensemble

We propose and investigate a hybrid optomechanical system consisting of a micro-mechanical oscillator coupled to the internal states of a distant ensemble of atoms. The interaction between the systems is mediated by a light field which allows the coupling of the two systems in a modular way over long distances. Coupling to internal degrees of freedom of atoms opens up the possibility to employ high-frequency mechanical resonators in the MHz to GHz regime, such as optomechanical crystal structures, and to benefit from the rich toolbox of quantum control over internal atomic states. Previous schemes involving atomic motional states are rather limited in both of these aspects. We derive a full quantum model for the effective coupling including the main sources of decoherence. As an application we show that sympathetic ground-state cooling and strong coupling between the two systems is possible.

Engineering a Quantum Many-body Hamiltonian with Trapped Ions

While fault-tolerant quantum computation might still be years away, analog quantum simulators offer a way to leverage current quantum technologies to study classically intractable quantum systems. Cutting edge quantum simulators such as those utilizing ultracold atoms are beginning to study physics which surpass what is classically tractable. As the system sizes of these quantum simulators increase, there are also concurrent gains in the complexity and types of Hamiltonians which can be simulated. In this work, I describe advances toward the realization of an adaptable, tunable quantum simulator capable of surpassing classical computation. We simulate long-ranged Ising and XY spin models which can have global arbitrary transverse and longitudinal fields in addition to individual transverse fields using a linear chain of up to 24 Yb+ 171 ions confined in a linear rf Paul trap. Each qubit is encoded in the ground state hyperfine levels of an ion. Spin-spin interactions are engineered by the application of spin-dependent forces from laser fields, coupling spin to motion. Each spin can be read independently using state-dependent fluorescence. The results here add yet more tools to an ever growing quantum simulation toolbox. One of many challenges has been the coherent manipulation of individual qubits. By using a surprisingly large fourth-order Stark shifts in a clock-state qubit, we demonstrate an ability to individually manipulate spins and apply independent Hamiltonian terms, greatly increasing the range of quantum simulations which can be implemented. As quantum systems grow beyond the capability of classical numerics, a constant question is how to verify a quantum simulation. Here, I present measurements which may provide useful metrics for large system sizes and demonstrate them in a system of up to 24 ions during a classically intractable simulation. The observed values are consistent with extremely large entangled states, as much as ~95% of the system entangled. Finally, we use many of these techniques in order to generate a spin Hamiltonian which fails to thermalize during experimental time scales due to a meta-stable state which is often called prethermal. The observed prethermal state is a new form of prethermalization which arises due to long-range interactions and open boundary conditions, even in the thermodynamic limit. This prethermalization is observed in a system of up to 22 spins. We expect that system sizes can be extended up to 30 spins with only minor upgrades to the current apparatus. These results emphasize that as the technology improves, the techniques and tools developed here can potentially be used to perform simulations which will surpass the capability of even the most sophisticated classical techniques, enabling the study of a whole new regime of quantum many-body physics.

Circuit Quantum Electrodynamics with Transmon Qubits in the Ultrastrong Coupling Regime

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Quantum Dots As Biophotonics Tools.

This chapter provides a short review of quantum dots (QDs) physics, applications, and perspectives. The main advantage of QDs over bulk semiconductors is the fact that the size became a control parameter to tailor the optical properties of new materials. Size changes the confinement energy which alters the optical properties of the material, such as absorption, refractive index, and emission bands. Therefore, by using QDs one can make several kinds of optical devices. One of these devices transforms electrons into photons to apply them as active optical components in illumination and displays. Other devices enable the transformation of photons into electrons to produce QDs solar cells or photodetectors. At the biomedical interface, the application of QDs, which is the most important aspect in this book, is based on fluorescence, which essentially transforms photons into photons of different wavelengths. This chapter introduces important parameters for QDs' biophotonic applications such as photostability, excitation and emission profiles, and quantum efficiency. We also present the perspectives for the use of QDs in fluorescence lifetime imaging (FLIM) and Förster resonance energy transfer (FRET), so useful in modern microscopy, and how to take advantage of the usually unwanted blinking effect to perform super-resolution microscopy.

Measuring The Hydrodynamic Radius Of Quantum Dots By Fluorescence Correlation Spectroscopy.

Fluorescence Correlation Spectroscopy (FCS) is an optical technique that allows the measurement of the diffusion coefficient of molecules in a diluted sample. From the diffusion coefficient it is possible to calculate the hydrodynamic radius of the molecules. For colloidal quantum dots (QDs) the hydrodynamic radius is valuable information to study interactions with other molecules or other QDs. In this chapter we describe the main aspects of the technique and how to use it to calculate the hydrodynamic radius of quantum dots (QDs).

Atomic Charge Transfer-counter Polarization Effects Determine Infrared Ch Intensities Of Hydrocarbons: A Quantum Theory Of Atoms In Molecules Model.

Atomic charge transfer-counter polarization effects determine most of the infrared fundamental CH intensities of simple hydrocarbons, methane, ethylene, ethane, propyne, cyclopropane and allene. The quantum theory of atoms in molecules/charge-charge flux-dipole flux model predicted the values of 30 CH intensities ranging from 0 to 123 km mol(-1) with a root mean square (rms) error of only 4.2 km mol(-1) without including a specific equilibrium atomic charge term. Sums of the contributions from terms involving charge flux and/or dipole flux averaged 20.3 km mol(-1), about ten times larger than the average charge contribution of 2.0 km mol(-1). The only notable exceptions are the CH stretching and bending intensities of acetylene and two of the propyne vibrations for hydrogens bound to sp hybridized carbon atoms. Calculations were carried out at four quantum levels, MP2/6-311++G(3d,3p), MP2/cc-pVTZ, QCISD/6-311++G(3d,3p) and QCISD/cc-pVTZ. The results calculated at the QCISD level are the most accurate among the four with root mean square errors of 4.7 and 5.0 km mol(-1) for the 6-311++G(3d,3p) and cc-pVTZ basis sets. These values are close to the estimated aggregate experimental error of the hydrocarbon intensities, 4.0 km mol(-1). The atomic charge transfer-counter polarization effect is much larger than the charge effect for the results of all four quantum levels. Charge transfer-counter polarization effects are expected to also be important in vibrations of more polar molecules for which equilibrium charge contributions can be large.

Interplay Of Weak Interactions In The Atom-by-atom Condensation Of Xenon Within Quantum Boxes.

Condensation processes are of key importance in nature and play a fundamental role in chemistry and physics. Owing to size effects at the nanoscale, it is conceptually desired to experimentally probe the dependence of condensate structure on the number of constituents one by one. Here we present an approach to study a condensation process atom-by-atom with the scanning tunnelling microscope, which provides a direct real-space access with atomic precision to the aggregates formed in atomically defined 'quantum boxes'. Our analysis reveals the subtle interplay of competing directional and nondirectional interactions in the emergence of structure and provides unprecedented input for the structural comparison with quantum mechanical models. This approach focuses on-but is not limited to-the model case of xenon condensation and goes significantly beyond the well-established statistical size analysis of clusters in atomic or molecular beams by mass spectrometry.

Measurement Of The Hydrodynamic Radius Of Quantum Dots By Fluorescence Correlation Spectroscopy Excluding Blinking.

One of the most important properties of quantum dots (QDs) is their size. Their size will determine optical properties and in a colloidal medium their range of interaction. The most common techniques used to measure QD size are transmission electron microscopy (TEM) and X-ray diffraction. However, these techniques demand the sample to be dried and under a vacuum. This way any hydrodynamic information is excluded and the preparation process may alter even the size of the QDs. Fluorescence correlation spectroscopy (FCS) is an optical technique with single molecule sensitivity capable of extracting the hydrodynamic radius (HR) of the QDs. The main drawback of FCS is the blinking phenomenon that alters the correlation function implicating in a QD apparent size smaller than it really is. In this work, we developed a method to exclude blinking of the FCS and measured the HR of colloidal QDs. We compared our results with TEM images, and the HR obtained by FCS is higher than the radius measured by TEM. We attribute this difference to the cap layer of the QD that cannot be seen in the TEM images.

Photophysical properties and quantum chemical studies of poly(2,7-9,9'-dihexylfluorene-dyil)

This work reports the photophysical properties (excitation and fluorescence spectra, fluorescence quantum yield, fluorescence lifetimes) of the poly(2,7-9,9'-dihexylfluorene-dyil) in dilute solutions of four solvents (toluene, tetrahydrofuran, chloroform and ethyl acetate) as well as the properties in solid state. Photoluminescence showed spectra characteristic of disordered α-backbone chain conformation. Simulation of the electronic absorption spectra of oligomers containing 1 to 11 mers showed that the critical conjugation length is between 6 and 7 mers. We also estimated the theoretical dipole moments which indicated that a coil conformation is formed with 8 repeating units per turn. We also showed that some energy transfer process appears in solid state which decreases the emission lifetime. Furthermore, based on luminescent response of the systems herein studied and electroluminescent behavior reported on literature, both photo and electroluminescence emissions arise from the same emissive units.

Multiple classical limits in relativistic and nonrelativistic quantum mechanics

The existence of a classical limit describing the interacting particles in a second-quantized theory of identical particles with bosonic symmetry is proved. This limit exists in addition to the previously established classical limit with a classical field behavior, showing that the limit h -> 0 of the theory is not unique. An analogous result is valid for a free massive scalar field: two distinct classical limits are proved to exist, describing a system of particles or a classical field. The introduction of local operators in order to represent kinematical properties of interest is shown to break the permutation symmetry under some localizability conditions, allowing the study of individual particle properties.

Quantum statistical correlations in thermal field theories: Boundary effective theory

We show that the one-loop effective action at finite temperature for a scalar field with quartic interaction has the same renormalized expression as at zero temperature if written in terms of a certain classical field phi(c), and if we trade free propagators at zero temperature for their finite-temperature counterparts. The result follows if we write the partition function as an integral over field eigenstates (boundary fields) of the density matrix element in the functional Schrodinger field representation, and perform a semiclassical expansion in two steps: first, we integrate around the saddle point for fixed boundary fields, which is the classical field phi(c), a functional of the boundary fields; then, we perform a saddle-point integration over the boundary fields, whose correlations characterize the thermal properties of the system. This procedure provides a dimensionally reduced effective theory for the thermal system. We calculate the two-point correlation as an example.