We start by reviewing some interesting results in mesoscopic physics illustrating nontrivial insights on Quantum Mechanics. We then review the general principles of dephasing (sometimes called “decoherence”) of Quantum-Mechanical interference by coupling to the environment degrees of freedom. A particular recent example of dephasing by a current-carrying (nonequilibrium) system is then discussed in some detail. This system is itself a manifestly Quantum Mechanical one and this is another illustration of detection without the need for “classical observers” etc. We conclude by describing briefly a recent problem having to do with the orbital magnetic response of conduction electrons (another manifestly Quantum Mechanical property): The magnetic response of a normal layer (N) coating a superconducting cylinder (S). Some recent very intriguing experimental results on a giant paramagnetic component of this response are explained using special states in the normal layer. It is hoped that these discussions illustrate not only the vitality and interest of mesoscopic physics but also its extreme relevance to fundamental issues in Quantum Mechanics.
We start by reviewing some interesting results in mesoscopic physics illustrating nontrivial insights on Quantum Mechanics. We then review the general principles of dephasing (sometimes called “decoherence”) of Quantum-Mechanical interference by coupling to the environment degrees of freedom. A particular recent example of dephasing by a current-carrying (nonequilibrium) system is then discussed in some detail. This system is itself a manifestly Quantum Mechanical one and this is another illustration of detection without the need for “classical observers” etc. We conclude by describing briefly a recent problem having to do with the orbital magnetic response of conduction electrons (another manifestly Quantum Mechanical property): The magnetic response of a normal layer (N) coating a superconducting cylinder (S). Some recent very intriguing experimental results on a giant paramagnetic component of this response are explained using special states in the normal layer. It is hoped that these discussions illustrate not only the vitality and interest of mesoscopic physics but also its extreme relevance to fundamental issues in Quantum Mechanics.
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.
Quantum decoherence is widely regarded as the principal dynamical mechanism through which classical behaviour emerges from quantum dynamics. This review presents a technical account of decoherence as an open-system phenomenon, emphasizing its mathematical framework, microscopic models, experimental evidence, and foundational implications. Starting from system-environment interactions and reduced density operators, we introduce completely positive trace-preserving maps and Lindblad master equations. We then discuss pure dephasing, pointer-state selection, quantum Brownian motion, spin-boson dynamics, and collisional decoherence. Experimental evidence from atom and molecular interferometry, superconducting qubits, and mesoscopic platforms is examined. Finally, the review assesses the role of decoherence in the quantum measurement problem. Decoherence explains preferred-basis selection and practical suppression of interference, but it does not independently account for the occurrence of a unique measurement outcome.
Experimental progress in the miniaturization of electronic devices has made routinely available in the laboratory small electronic systems, on the micrometre or sub-micrometre scale, which at low temperature are sufficiently well isolated from their environment to be considered as fully coherent. Some of their most important properties are dominated by the interaction between electrons. Understanding their behaviour therefore requires a description of the interplay between interference effects and interactions. The goal of this review is to address this relatively broad issue and more specifically to address it from the perspective of the quantum chaos community. I will therefore present some of the concepts developed in the field of quantum chaos which may be applied to the study of many-body effects in mesoscopic and nanoscopic systems. Their implementation is illustrated in a few examples of experimental relevance such as persistent currents, mesoscopic fluctuations of Kondo properties or Coulomb blockade. I will furthermore try to bring out, from the various physical illustrations, some of the specific advantages on more general grounds of the quantum chaos based approach.
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.
Mesoscopic physics is a sub-discipline of condensed-matter physics that focuses on the properties of solids in a size range intermediate between bulk matter and individual atoms. In particular, it is characteristic of a domain where a certain number of interacting objects can easily be tuned between classical and quantum regimes, thus enabling studies at the border of the two. In magnetism, such a tuning was first realized with large-spin magnetic molecules called single-molecule magnets (SMMs) with archetype Mn(12)-ac. In general, the mesoscopic scale can be relatively large (e.g. micrometre-sized superconducting circuits), but, in magnetism, it is much smaller and can reach the atomic scale with rare earth (RE) ions. In all cases, it is shown how quantum relaxation can drastically reduce classical irreversibility. Taking the example of mesoscopic spin systems, the origin of irreversibility is discussed on the basis of the Landau-Zener model. A classical counterpart of this model is described enabling, in particular, intuitive understanding of most aspects of quantum spin dynamics. The spin dynamics of mesoscopic spin systems (SMM or RE systems) becomes coherent if they are well isolated. The study of the damping of their Rabi oscillations gives access to most relevant decoherence mechanisms by different environmental baths, including the electromagnetic bath of microwave excitation. This type of decoherence, clearly seen with spin systems, is easily recovered in quantum simulations. It is also observed with other types of qubits such as a single spin in a quantum dot or a superconducting loop, despite the presence of other competitive decoherence mechanisms. As in the molecular magnet V(15), the leading decoherence terms of superconducting qubits seem to be associated with a non-Markovian channel in which short-living entanglements with distributions of two-level systems (nuclear spins, impurity spins and/or charges) leading to 1/f noise induce τ(1)-like relaxation of S(z) with dissipation to the bath of two-level systems with which they interact most. Finally, let us mention that these experiments on quantum oscillations are, most of the time, performed in the classical regime of Rabi oscillations, suggesting that decoherence mechanisms might also be treated classically.
This report on progress explores recent advances in our theoretical and experimental understanding of the physics of open quantum systems (OQSs). The study of such systems represents a core problem in modern physics that has evolved to assume an unprecedented interdisciplinary character. OQSs consist of some localized, microscopic, region that is coupled to an external environment by means of an appropriate interaction. Examples of such systems may be found in numerous areas of physics, including atomic and nuclear physics, photonics, biophysics, and mesoscopic physics. It is the latter area that provides the main focus of this review, an emphasis that is driven by the capacity that exists to subject mesoscopic devices to unprecedented control. We thus provide a detailed discussion of the behavior of mesoscopic devices (and other OQSs) in terms of the projection-operator formalism, according to which the system under study is considered to be comprised of a localized region (Q), embedded into a well-defined environment (P) of scattering wavefunctions (with Q + P = 1). The Q subspace must be treated using the concepts of non-Hermitian physics, and of particular interest here is: the capacity of the environment to mediate a coupling between the different states of Q; the role played by the presence of exceptional points (EPs) in the spectra of OQSs; the influence of EPs on the rigidity of the wavefunction phases, and; the ability of EPs to initiate a dynamical phase transition (DPT). EPs are singular points in the continuum, at which two resonance states coalesce, that is where they exhibit a non-avoided crossing. DPTs occur when the quantum dynamics of the open system causes transitions between non-analytically connected states, as a function of some external control parameter. Much like conventional phase transitions, the behavior of the system on one side of the DPT does not serve as a reliable indicator of that on the other. In addition to discussing experiments on mesoscopic quantum point contacts that provide evidence of the environmentally-mediated coupling of quantum states, we also review manifestations of DPTs in mesoscopic devices and other systems. These experiments include observations of resonance-trapping behavior in microwave cavities and open quantum dots, phase lapses in tunneling through single-electron transistors, and spin swapping in atomic ensembles. Other possible manifestations of this phenomenon are presented, including various superradiant phenomena in low-dimensional semiconductors. From these discussions a generic picture of OQSs emerges in which the environmentally-mediated coupling between different quantum states plays a critical role in governing the system behavior. The ability to control or manipulate this interaction may even lead to new applications in photonics and electronics.