This thesis is devoted to the study of quantum mechanical effects that arise in systems of reduced dimensionality. Specifically, we investigate coherence and correlation effects in quantum transport models. In the first part, we present a theory of Markovian and non- Markovian current correlations in nanoscopic conductors. The theory is applied to obtain the spectrum of quantum noise and high-order current correlations at finite frequencies in quantum-dot systems. One of the main conclusions is that only the non-Markovian approach contains the physics of vacuum fluctuations. In the second part, we study the coupling of superconducting qubits to optical atomic systems and to cavity resonators. We propose a hybrid quantum system consisting of a flux qubit coupled to NV centers in diamond. We also demonstrate the existence of the so-called Bloch-Siegert shift in the ultra-strong coupling regime between a flux qubit and a LC resonator. Throughout the thesis, we make special emphasis on the study of decoherence effects produced by the distinct dissipative baths to which the various types of qubits presented in this thesis are inevitably coupled.
This thesis is devoted to the study of quantum mechanical effects that arise in systems of reduced dimensionality. Specifically, we investigate coherence and correlation effects in quantum transport models. In the first part, we present a theory of Markovian and non- Markovian current correlations in nanoscopic conductors. The theory is applied to obtain the spectrum of quantum noise and high-order current correlations at finite frequencies in quantum-dot systems. One of the main conclusions is that only the non-Markovian approach contains the physics of vacuum fluctuations. In the second part, we study the coupling of superconducting qubits to optical atomic systems and to cavity resonators. We propose a hybrid quantum system consisting of a flux qubit coupled to NV centers in diamond. We also demonstrate the existence of the so-called Bloch-Siegert shift in the ultra-strong coupling regime between a flux qubit and a LC resonator. Throughout the thesis, we make special emphasis on the study of decoherence effects produced by the distinct dissipative baths to which the various types of qubits presented in this thesis are inevitably coupled.
This thesis is devoted to the study of quantum mechanical effects that arise in systems of reduced dimensionality. Specifically, we investigate coherence and correlation effects in quantum transport models. In the first part, we present a theory of Markovian and non- Markovian current correlations in nanoscopic conductors. The theory is applied to obtain the spectrum of quantum noise and high-order current correlations at finite frequencies in quantum-dot systems. One of the main conclusions is that only the non-Markovian approach contains the physics of vacuum fluctuations. In the second part, we study the coupling of superconducting qubits to optical atomic systems and to cavity resonators. We propose a hybrid quantum system consisting of a flux qubit coupled to NV centers in diamond. We also demonstrate the existence of the so-called Bloch-Siegert shift in the ultra-strong coupling regime between a flux qubit and a LC resonator. Throughout the thesis, we make special emphasis on the study of decoherence effects produced by the distinct dissipative baths to which the various types of qubits presented in this thesis are inevitably coupled.
This thesis consists of theoretical studies of superconducting qubits, and trapped bosons and fermions at ultracold temperature. In superconducting qubits I analyze the resonant properties and decoherence behavior of dc SQUID phase qubits, in which one junction acts as a phase qubit and the rest of the device provides isolation from dissipation and noise in the bias lead. Typically qubit states in phase qubits are detected by tunneling it to the voltage state. I propose an alternate non-destructive readout mechanism which relies on the difference in the magnetic flux through the SQUID loop due to state of the qubit. I also study decoherence effects in a dc SQUID phase qubit caused by the isolation circuit. When the frequency of the qubit is at least two times larger than the resonance frequency of the isolation circuit, I find that the decoherence time of the qubit is two orders of magnitude larger than the typical ohmic regime, where the frequency of the qubit is much smaller than the resonance frequency of the isolation circuit. This theory is extended to other similar superconducting quantum devices and has been applied to experiments from the group at the University of Maryland. I also demonstrate, theoretically, vacuum Rabi oscillations, analogous to circuit-QED, in superconducting qubits coupled to an environment with resonance. The result obtained gives an exact analytical expression for coherent oscillation of state between the system (the qubit) and the environment with resonance. Next I investigate ultracold atoms in harmonically confined optical lattices. They exhibit a `wedding cake structure' of alternating Mott shells with different number of bosons per site. In regions between the Mott shells, a superfluid phase emerges at low temperatures which at higher temperatures becomes a normal Bose liquid. Using finite-temperature quantum field theoretic techniques, I find analytically the properties of the superfluid, Bose liquid, and Mott insulating regions. This includes the finite temperature order parameter equation for the superfluid phase, excitation spectrum, Berezinskii-Kosterlitz-Thouless transition temperature and vortex-antivortex pair formation (in the two dimensional case), finite temperature compressibility and density - density correlation function. I also study interacting mixtures of ultracold bosonic and fermionic atoms in harmonically confined optical lattices. For a suitable choice of parameters I find emergence of superfluid and Fermi liquid (non-insulating) regions out of Bose-Mott and Fermi-band insulators, due to finite boson and fermion hopping. I also propose a possible experiment for the detection of superfluid and Fermi liquid shells through the use of Gauss-Laguerre and Gaussian beams followed by Bragg spectroscopy. Another area I explore is ultracold heteronuclear molecules such as KRb, RbCs and NaCs. I obtain the finite and zero-temperature phase diagram of bosons interacting via short range repulsive interactions and long-ranged isotropic dipolar interactions in two-dimensions. I build an analytical model for such systems that describes a first order quantum phase transition at zero temperature from a triangular crystalline phase (analogous to Wigner crystal phase of electrons) to superfluid phase. At finite temperature the crystalline phase melts, due to topological defects, to a hexatic phase where translational order is destroyed but hexagonal orientational order is preserved. Further temperature increase leads to the melting of the hexatic phase into a normal dipolar Bose liquid.
In this Thesis I discuss the exact dynamics of simple non-Markovian systems. I focus on fundamental questions at the core of non-Markovian theory and investigate the dynamics of quantum correlations under non-Markovian decoherence. \n \nIn the first context I present the connection between two different non-Markovian approaches, and compare two distinct definitions of non-Markovianity. The general aim is to characterize in exemplary cases which part of the environment is responsible for the feedback of information typical of non- Markovian dynamics. I also show how such a feedback of information is not always described by certain types of master equations commonly used to tackle non-Markovian dynamics. \n \nIn the second context I characterize the dynamics of two qubits in a common non-Markovian reservoir, and introduce a new dynamical effect in a wellknown model, i.e., two qubits under depolarizing channels. In the first model the exact solution of the dynamics is found, and the entanglement behavior is extensively studied. The non-Markovianity of the reservoir and reservoirmediated-interaction between the qubits cause non-trivial dynamical features. \n \nThe dynamical interplay between different types of correlations is also investigated. In the second model the study of quantum and classical correlations demonstrates the existence of a new effect: the sudden transition between classical and quantum decoherence. This phenomenon involves the complete preservation of the initial quantum correlations for long intervals of time of the order of the relaxation time of the system.
The development of solid-state quantum technologies requires the understanding of quantum measurements in interacting, nonisolated quantum systems.In general, a permanent coupling of detectors to a quantum system leads to memory effects that have to be taken into account in interpreting the measurement results.In this thesis we develop a microscopic framework for correlations in non-Markovian weak measurements.A special point of interest are the different orders of quantum mechanical operators that appear naturally in such a scheme.First, we analyze a generic setup of two detectors coupled to a quantum system and derive a compact formula in the weak-measurement limit that interpolates between an instantaneous (text-book type) and almost continuous -detector dynamics-dependent -measurement.A quantum memory effect that we term system-mediated detector-detector interaction is crucial to observe noncommuting observables simultaneously.A response function of the observed system variables introduces an antisymmetric operator order to the total result.We propose a mesoscopic double-dot detector setup in which the memory effect is tunable and that can be used to explore the transition to non-Markovian quantum measurements experimentally.The response and noise functions which we find to describe the system-mediated detector-detector interaction are analyzed in detail.They are compared to the phenomenological "equilibrium order" approach for non-Markovian measurements which was introduced in Ref. [1].We give an overview of the broad spectrum of results beyond "equilibrium order" in the microscopic model in a compendium of different detectors and discuss general mathematical properties of the detector functions.As the quantum measurement problem is not banned from our theory by operation in the weak measurement limit, but deferred from the system of interest to the detectors, we comment on the influence of the detector readout procedure on the results.Finally, we combine the phenomenological proposal for nonsymmetrized correlations in quantum noninvasive measurements [1] and our microscopic derivation of the systemmediated detector-detector interaction of second order to investigate higher-order correlations of non-Markovian weak quantum measurements.The general third-order correlator is introduced and the underlying physical processes are identified and discussed.We find a more complex behavior than in second-order correlations with four types of system operator orders which we denote third cumulant, noise susceptibility I and II and second-order susceptibility.We introduce a convenient diagrammatic description which we illustrate by an example of measuring the third-order correlations of the tunnel current through a barrier.v I would like to express my deep gratitude to all the people who contributed to this thesis.Special thanks to my supervisor Wolfgang Belzig for offering me the opportunity to work in his research group, for the numerous helpful discussions in which I learned a lot and which gave impetus to this work again and again, for being always patient and an excellent guidance during my studies.I also wish to express great thanks to my other collaborators, Adam Bednorz, whose ideas are an important part of the foundation of this work and who was always ready to comment new results and bring things forward, and Christoph Bruder, who was a great help in thinking through results and formulating them in an understandable manner while preparing parts of this work for publication.Many thanks to Maxim Trushin, who was willing to discuss our weak measurement formalism with the example of a graphene coherence measurement, and who contributed the initial idea of a optical detection of pseudospin superposition states as well as the description of the carrier statistics using the Liouville-von Neumann equation and very important parts of the discussion of the results.In this context I also want to acknowledge valuable discussions with Daniele Brida about the optical detection scheme and with Bertrand Reulet about third-order current correlations.Finally, I wish to thank the current and former members of the Quantum Transport Group
Superconducting qubits are fabricated "loss-free" electrical circuits on a chip with size features of tens of nanometers. If cooled to cryogenic temperatures below -273 °C they behave as quantum elements, similar to atoms and molecules. Such a qubit can be manipulated by fast-oscillating magnetic fields and its resulting quantum state can be measured using a proper magnetic detector. These qubits could be the basic elements for a quantum processor. To that order, multiple qubits have to controllably interact, and to that purpose very high quality resonators are fabricated on the same chip. Effectively the interaction results from the phase-coherent exchange of a single photon between qubit and resonator. In this way it is highly analogous to the so-called cavity QED in atomic physics where single atoms couple to a single trapped photon, all inside a cavity resonator. In this thesis, a superconducting flux qubit has been coupled to an LC resonator and coherent exchange of a single photon between qubit and resonator has been achieved. A striking option in these superconducting circuits, not attainable in "common" atomic cavity-QED, is that the interaction between qubit and photon can be made very large, up to the limit that one no longer can talk about the qubit and resonator as such. This limit requires a fully different description and it leads to novel effects, e.g. in the energy spectrum of the qubit-resonator composite. The Bloch-Siegert spectral shift is experimentally demonstrated in this thesis. As a small but critical technical aside a new type of control line filter has been developed, which allows strong suppression of excess electrical noise that forms a threat for qubit coherence. Having two modes of operation, it shorts all low-frequency noise if control is idle while being transparent if control is active, where short or open is determined by the control line signal level itself.
This thesis addresses two different topics related to the physics of nanoscale systems. The first topic concerns quantum correlations and entanglement between electrons in solid-state systems, with a focus on how to generate electronic orbital entanglement on a sub-decoherence time scale and how to achieve experimentally more feasible entanglement detection schemes. The second topic concerns heat transport and temperature fluctuations in nanoscale systems, with a focus on how to utilize temperature fluctuations for calorimetric detection of single particles. The thesis comprises five papers.In Paper I, we propose a quantum dot system to generate and detect, using cotunneling processes, orbitally entangled pairs of electrons on a sub-decoherence time scale.In Paper II, we investigate, by applying an entanglement witness, the minimal number of zero-frequency current cross-correlation measurements needed to detect bipartite entanglement between two flying qubits.In Paper III, we consider energy and temperature fluctuations, and the influence of charging effects, in a metallic island tunnel coupled to a normal metallic lead, the so-called single electron box.In Paper IV, we investigate nanoscale quantum calorimetry and propose a setup consisting of a metallic island and a superconducting lead to realize a nanoscale calorimeter that may probe the energies of tunneling electrons.In Paper V, we investigate photon transport statistics of a microwave cavity, including the short-time statistics of single photon emissions and the long-time statistics of heat transport through the cavity.