Mesoscopic physics and nanoelectronics concentrate on systems with dimensions somewhere between atomic and everyday macroscopic scale. Modern technology enables construction of submicron nanostructures where modeling based on classical physics has proven inadequate. It is possible to design electric circuits where dynamics of single electrons and photons are controlled using state-of-the-art experimental methods. For quantitative understanding of these systems it is necessary to resort to a quantum-mechanical description. Quantum phenomena, such as tunneling and a wave-like interference of particles, are essential ingredients of physics in mesoscopic systems. Field of mesoscopic physics contains a rich variety of topics ranging from fundamental condensed matter physics to quantum information processing and possible future technological applications. \n \nThis thesis presents theoretical studies of mesoscopic quantum phenomena in nanostructures and small electronic devices. We have focused on effects of environment fluctuations and investigated connections between fluctuations and transport phenomena. Decoherence in quantum bits (qubits) and quantum state engineering in superconducting circuits are also studied. The theoretical analysis in each case requires an open-system treatment. \n \nEffects of current fluctuations on quantum probe systems have been studied in detail. We have calculated transitions induced by current noise and discussed how these could be used for characterization of fluctuations. We have also shown that electric fluctuations play a key role in radiation and photon heat transport in nanostructures. Motivated by recent advances in mesoscopic electron-photon systems, we have studied a response of a coupled resonator-qubit system, squeezing of quantum fluctuations in small superconducting circuits and investigated decoherence in Josephson flux qubits.
Mesoscopic physics and nanoelectronics concentrate on systems with dimensions somewhere between atomic and everyday macroscopic scale. Modern technology enables construction of submicron nanostructures where modeling based on classical physics has proven inadequate. It is possible to design electric circuits where dynamics of single electrons and photons are controlled using state-of-the-art experimental methods. For quantitative understanding of these systems it is necessary to resort to a quantum-mechanical description. Quantum phenomena, such as tunneling and a wave-like interference of particles, are essential ingredients of physics in mesoscopic systems. Field of mesoscopic physics contains a rich variety of topics ranging from fundamental condensed matter physics to quantum information processing and possible future technological applications. \n \nThis thesis presents theoretical studies of mesoscopic quantum phenomena in nanostructures and small electronic devices. We have focused on effects of environment fluctuations and investigated connections between fluctuations and transport phenomena. Decoherence in quantum bits (qubits) and quantum state engineering in superconducting circuits are also studied. The theoretical analysis in each case requires an open-system treatment. \n \nEffects of current fluctuations on quantum probe systems have been studied in detail. We have calculated transitions induced by current noise and discussed how these could be used for characterization of fluctuations. We have also shown that electric fluctuations play a key role in radiation and photon heat transport in nanostructures. Motivated by recent advances in mesoscopic electron-photon systems, we have studied a response of a coupled resonator-qubit system, squeezing of quantum fluctuations in small superconducting circuits and investigated decoherence in Josephson flux qubits.
The work involves a study of physical phenomena that take place at very small length scales, below one micro-meter. At temperatures roughly below one degree Kelvin, quantum-mechanical effects may rule in electronic transport. Macroscopic quantum-coherent effects that occur in metallic superconducting microstructures, are particularly intriguing. Large-scale quantum information processing is widely believed to be attainable utilizing such physical systems. This work concentrates on answering the question of how the described quantum-mechanical systems may be used as sensitive measuring devices. Considerable attention is paid to energy-storing metallic microstructures whose electrical properties resemble those of the familiar inductor or capacitor. This research involves primarily experimental investigations conducted around temperatures of 0.1 Kelvin. Methods both at low and at radio frequencies have been used. The experimental findings have been modelled theoretically, and theoretical concepts for new physical phenomena have been introduced. An inductively measured radio-frequency Cooper-pair transistor, the L-SET, has been developed and experimentally verified in this work. Being highly sensitive, fast, and non-invasive, the L-SET appears to be the most promising method for measuring electric charge. Sensitivity in charge measurements of 20 millionths of the electron charge (micro-e) within one second, and an input bandwidth of 100 MHz, have been demonstrated. It has been shown theoretically that the ultimate measurement accuracy is about 0.1 micro-e within a second. A new phase detector based on the Cooper-pair transistor has been proposed. This system has also been shown to be potentially usable as a quantum bit. A new type of radio-frequency single-electron transistor built using a multi-walled carbon nanotube has been fabricated and operated. Technologies have been developed in order to make the physical nano- or microstructures. A method has been presented to fabricate non-superconducting tunnel junctions. Consequences of the inverse superconducting proximity effect on the studied superconducting structures were considered. Measurement procedures were investigated for a new low-noise nanoamplifier, the Bloch-oscillating transistor. Single superconducting tunnel junctions were tested as detectors of energy states of the environment, or of noise.
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.
The recent interest in developing highly controllable quantum bits (qubits) based on superconducting circuits makes it necessary to get a deeper understanding of the physics of small Josephson junctions. Such devices have to be wisely engineered and well isolated from the noisy environment to observe non-classical physics. In this thesis, a real-time noise analysis was implemented by an autocorrelation calculation to identify the type of environmental effects affecting a superconducting circuit. This was used during switching current measurements of small Josephson junctions to track the effects of unwanted signals and identify their frequency components. The temperature dependence of the switching current distribution was used to further characterise the small Josephson junctions. Furthermore the fabrication of smal1 Josephson junctions is further developed by analysing the reliability and reproducibility of them. A systematic approach is shown to solve typical fabrication problems for example identifying and reducing mechanical stress between resist layers. As Josephson junctions show quantum mechanical effects on a macroscopic scale they are used in a wide range of applications especially in superconducting circuits.
Superconducting circuits, photonic cavities, and tiny mechanical oscillators are versatile systems in which quantum dynamics can be observed and controlled. These various technologies can be combined, and the resulting “circuits” are often referred to as nano-electromechanical or optomechanical systems. In the context of quantum physics, such devices are referred to as “mesoscopic” because they contain a large number of atoms. This terminology distinguishes them from the “microscopic” systems of atom-optics, such as single ions [364] and atoms [545, 233, 26], and the spins of individual nuclei [412]. Nano-engineered systems provide an especially powerful arena for exploring quantum measurement and control because of their potential to realize complex circuits. In this chapter we explain how to treat these systems and describe in detail a common method used to measure them. Superconducting circuits The electrical circuits that we describe in this chapter are quite different from those that use normal conductors, such as copper wire at room temperature. Normal conductors are subject to strong dissipation and decoherence from the environment. As a result the dynamical degrees of freedom of the circuits, the currents and voltages, behave as classical variables. In superconducting circuits, the resistance, and thus the dissipation, is so small that the currents and voltages behave as quantum mechanical degrees of freedom. Of course, the current in a wire is actually composed of many elementary particles that each obey quantum mechanics. Why then should the current act like a single quantum degree of freedom? A mechanical analogy is useful here. Recall that even though a macroscopic pendulum is composed of many particles, when one talks about the motion of the pendulum one means the motion of the center-of-mass of its constituent particles. Since the center of mass is merely a linear combination of the coordinates of each particle, it is itself a valid quantum mechanical coordinate with a conjugate momentum. In a similar way the total current in a superconducting wire is a collective degree of freedom that obeys quantum mechanics.
A mesoscopic circuit, where field quantization (e.g., coherent states and squeezed states) can be exhibited, is one of the ideal quantum systems for manifesting diverse quantum field theoretical phenomena and thermally statistical characteristics. Because of inevitable electromagnetic coupling (e.g., mutual capacitor coupling and mutual inductor coupling) in two neighboring mesoscopic electric circuits, quantum effects relevant to mesoscopic circuit coupling may play a key role in some devices of quantum information processing. Such a circuit coupling can lead to circuit entangled states, where the Fock number states of energy quanta in different circuits are entangled with each other. Since the time dependence in parameters of coupled-circuit Hamiltonian would result from environmental perturbations (e.g., temperature fluctuations in devices) or from some controllable manipulation (e.g., an incident ultrasonic wave), the circuit entangled states would evolve due to these external conditions. Time evolution of entangled states in coupled mesoscopic circuits is considered within a framework of time-dependent quantum theoretical formalism. Note that an applied photon field can also be coupled to such quantum entangled circuits. Then it is possible that an effect of entanglement transfer (i.e., transportation of superposition coefficients in the entangled state) from the quantum mesoscopic coupled LC circuits to the applied external photon field would also occur under some proper parameter conditions. The present characteristics of both quantized coupled mesoscopic circuits and entanglement transfer can also be found in some alternative microscopic- and mesoscopic-scale devices such as the systems in cavity quantum electrodynamics (QED).
Circuit QED techniques have been instrumental in manipulating and probing with exquisite sensitivity the quantum state of superconducting quantum bits coupled to microwave cavities. Recently, it has become possible to fabricate new devices in which the superconducting quantum bits are replaced by hybrid mesoscopic circuits combining nanoconductors and metallic reservoirs. This mesoscopic QED provides a new experimental playground to study the light-matter interaction in electronic circuits. Here, we present the experimental state of the art of mesoscopic QED and its theoretical description. A first class of experiments focuses on the artificial atom limit, where some quasiparticles are trapped in nanocircuit bound states. In this limit, the circuit QED techniques can be used to manipulate and probe electronic degrees of freedom such as confined charges, spins, or Andreev pairs. A second class of experiments uses cavity photons to reveal the dynamics of electron tunneling between a nanoconductor and fermionic reservoirs. For instance, the Kondo effect, the charge relaxation caused by grounded metallic contacts, and the photo-emission caused by voltage-biased reservoirs have been studied. The tunnel coupling between nanoconductors and fermionic reservoirs also enable one to obtain split Cooper pairs, or Majorana bound states. Cavity photons represent a qualitatively new tool to study these exotic condensed matter states.