Mesoscopic physics considers systems of appropriate size and at time scales of the order of decoherence time, which allows us to analyse the transformation of information from a quantum state to a classical signal, occurring in a process of quantum measurement. We concentrate on the limiting cases of weak and strong coupling between a mesoscopic source of noise and a subsystem functioning as a detector. In the ``weak coupling'' part we elaborate on the idea of cross-correlation measurements for quantum noise detection and develop a set of original methods to tackle the perturbation theory up to fourth order. In the ``strong coupling'' part we provide an exact solution for one-dimensional system out of equilibrium, strongly interacting with a localized state and predict some remarkable experimentally verifiable features, such as Fermi-edge singularity in the noise induced transition rates and unusually pronounced manifestation of non-Gaussian noise effects.
Mesoscopic physics considers systems of appropriate size and at time scales of the order of decoherence time, which allows us to analyse the transformation of information from a quantum state to a classical signal, occurring in a process of quantum measurement. We concentrate on the limiting cases of weak and strong coupling between a mesoscopic source of noise and a subsystem functioning as a detector. In the weak coupling'' part we elaborate on the idea of cross-correlation measurements for quantum noise detection and develop a set of original methods to tackle the perturbation theory up to fourth order. In the strong coupling'' part we provide an exact solution for one-dimensional system out of equilibrium, strongly interacting with a localized state and predict some remarkable experimentally verifiable features, such as Fermi-edge singularity in the noise induced transition rates and unusually pronounced manifestation of non-Gaussian noise effects.
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
Generalized quantum measurement schemes are described by positive operator-valued measures going beyond the projection postulate, which predicts the instantaneous collapse of the systems wave function. This allows to take the noninvasive limit and investigate the correlations of such weak measurements which enables the observation of non-commuting observables within the same system. We propose a scheme in which the detector is coupled to the measured system for a finite time, as it is the case in many real setups. This leads to non-Markovian effects appearing by memory functions which are related to symmetric and antisymmetric correlators of the detector variables [12]. We investigate these functions addressing the role of equilibrium and non-equilibrium detectors and how they differ from and could realize the standard Markovian measurement respectively. The latter scheme leads to the symmetrized operator order (aka Keldysh ordering), which is widely used in quantum measurement discussions. We show that the non-Markovian measurement scheme yields information beyond the standard approach, allowing e.g. for the proof of the non classical nature of a system (quasiprobability statistics) by second-order correlation functions [13].We further propose setups in mesoscopic electronic circuits to realise those concepts. One possibility is to use two double quantum dots coupled to a common quantum system. The detectors cross correlations are read out and by tuning the dot parameters, it is possible to explore the non-Markovian nature of the measurement setup.
The efficiency of the future devices for quantum information processing will be limited mostly by the finite decoherence rates of the qubits. Recently, substantial progress was achieved in enhancing the time within which a solid-state qubit demonstrates coherent dynamics. This progress is based mostly on a successful isolation of the qubits from external decoherence sources. Under these conditions, the material-inherent sources of noise start to play a crucial role. In most cases, the noise that the quantum device demonstrates has a 1/ f spectrum. This suggests that the environment that destroys the phase coherence of the qubit can be thought of as a system of two-state fluctuators, which experience random hops between their states. In this short review, the current state of the theory of the decoherence due to the qubit interaction with the fluctuators is discussed. The effect of such an environment on two different protocols of the qubit manipulations, free induction and echo signal, is described. It turns out that in many important cases the noise produced by the fluctuators is non-Gaussian. Consequently, the results of the interaction of the qubit with the fluctuators are not determined by the pair correlation function alone. We describe the effect of the fluctuators using the so-called spin-fluctuator model. Being quite realistic, this model allows one to exactly evaluate the qubit dynamics in the presence of one fluctuator. This solution is found, and its features, including non-Gaussian effects, are analyzed in detail. We extend this consideration to systems of large numbers of fluctuators, which interact with the qubit and lead to the 1/ f noise. We discuss existing experiments on the Josephson qubit manipulation and try to identify non-Gaussian behavior.
Abstract Recent experimental results point to the existence of coherent quantum phenomena in systems made of a large number of particles, despite the fact that for many-body systems the presence of decoherence is hardly negligible and emerging classicality is expected. This behaviour hinges on collective observables, named quantum fluctuations , that retain a quantum character even in the thermodynamic limit: they provide useful tools for studying properties of many-body systems at the mesoscopic level, in-between the quantum microscopic scale and the classical macroscopic one. We herein present the general theory of quantum fluctuations in mesoscopic systems, and study their dynamics in a quantum open system setting, taking into account the unavoidable effects of dissipation and noise induced by the external environment. As in the case of microscopic systems, decoherence is not always the only dominating effect at the mesoscopic scale: certain types of environment can provide means for entangling collective fluctuations through a purely noisy mechanism.
Correlations in the open quantum systems manifest a rich phenomenology under the influence of various physical sources of noise. We theoretically study the dynamics of quantum correlations and their classical counterparts in a two-qubit system, measured by one-norm geometric quantifiers. We consider both qubits are initially prepared in the arbitrary X-type states and locally subjected to nonequilibrium dephasing environments with non-Markovian and nonstationary statistical features. We then explore the effects of nonequilibrium on the abrupt changes in the evolution of geometric correlations in the weak- and strong-coupling regimes. Particularly, in the weak-coupling regime, we show that the environmental nonequilibrium feature can efficiently control the appearance of double-sudden transitions and the decay rate in geometric quantum correlation dynamics. However, in the strong-coupling case, we show that the nonequilibrium nature can prolong the interval for the frozen quantum correlation and suppresses the number of multiple sudden changes in its decay rate. Moreover, the abrupt change from decay to a constant regime in classical correlation evolution reveals the emergence of the pointer-state basis. We show that the pointer-state basis appearance can be retarded in the weak-coupling case when the environment deviates from equilibrium. However, in a strong-coupling regime, we observe the metastable pointer-states basis characterized by multiple, successive sudden transitions in classical correlation dynamics. Remarkably, we unveil that the nonequilibrium feature may suppress the apparition of the metastable pointer-states basis.
This is a course on noise which covers some of the scattering theory for normal metals, Hanbury Brown and Twiss analogs for noise correlations with electrons, noise correlations in superconducting/normal metal junctions. Entanglement in such NS systems is described with a criterion for violating Bell inegalities. The last section is devoted to the perturbative derivation of noise in a particular one dimensional correlated electron system (Luttinger liquid): edge states in the fractional quantum Hall effect, where the comparison of the quasiparticle tunneling current and noise allow to identidy the fractional charge of quasiparticles.