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
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
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. 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. Finally, 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.
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 facilitate 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. 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 prove of the non classical nature of a system (quasiprobability statistics) by second-order correlation functions.
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.
In many real quantum systems the measurement is much less invasive than described by the projection postulate. For example, it is performed by weakly coupling a detector for a finite time to the system. The finite coupling time might lead to different measurement outcomes depending on the details of the interaction. We first investigate a generalized measurements scheme by means of positive operator-valued measures in the weak coupling limit and discuss the consequences appearing due to the non-Markovian interaction. Second we discuss the resulting quasiprobabilities, which in the case of a Markovian measurement scheme obey the so-called weak positivity, i.e. second-order correlation functions are positive semi-definite. In particular, we show a possible violation of weak positivity by second-order correlation functions for a frequency dependent detector measuring a spin-1/2 system. When both are themselves in an equilibrium state but at different respective temperatures, we find that the detection of the quantum behavior vanishes if the system temperature is larger than that of the detector.
A long-standing problem in quantum mesoscopic physics is which operator order corresponds to noise expressions like <I(-ω)I(ω)>, where I(ω) is the measured current at frequency ω. Symmetrized order describes a classical measurement while nonsymmetrized order corresponds to a quantum detector, e.g., one sensitive to either emission or absorption of photons. We show that both order schemes can be embedded in quantum weak-measurement theory taking into account measurements with memory, characterized by a memory function which is independent of a particular experimental detection scheme. We discuss the resulting quasiprobabilities for different detector temperatures and how their negativity can be tested on the level of second-order correlation functions already. Experimentally, this negativity can be related to the squeezing of the many-body state of the transported electrons in an ac-driven tunnel junction.
In the present Thesis we study the behavior of multi-time correlation functions and of thermodynamical quantities such as heat in open quantum systems undergoing an evolution generally affected by the presence of memory effects, i.e. non-Markovian. In the last decade, a large part of the scientific community in this field has dedicated its efforts to the understanding, precise definition and quantification of non-Markovianity in the quantum realm and now we have at our disposal several benchmark results and a plethora of different estimators that allow to determine the degree of non-Markovianity of a given dynamics. It comes therefore natural to investigate how other different dynamical quantities relate to such estimators also in order to understand the physical implications of memory effects on the statistics of observable quantities. In the first part of this work, a quantitative test of the violation of the so-called quantum regression theorem in presence of a non-Markovian dynamical regime is investigated. The quantum regression theorem represents a procedure that, whenever valid, allows to reconstruct two-time correlation functions of system's operators from the sole knowledge of the dynamics of mean values. It is worth stressing that two-time correlation functions are necessary in order to fully characterize the statistical properties of a quantum system, since they are able to catch aspects of the dynamics, such as fluorescence spectrum, in general not accessible looking at mean values. Despite their relevance however, obtaining two-time correlation functions often represents a formidable task, since the knowledge of the full "system+environment" dynamics is required, a generally too demanding request in the context of open quantum systems theory. The quantum regression theorem represents in this regard the easiest route to determine two-time correlation functions, this highlighting its importance. In this work we show that, in a pure-dephasing spin-boson model, the quantum regression theorem represents a stronger condition than non-Markovianity, in the sense that any presence of memory effects in the reduced dynamics inevitably results in violations to the former. These results have been published in [G.Guarnieri, A. Smirne, B. Vacchini, Phys. Rev. A 90, 022110 (2014)]. The second part of the Thesis is devoted to the characterization of heat ow at the microscopic level in open quantum systems, both finite and infinite dimensional. In particular we begin by studying the time behavior of its mean value in a non-Markovian dynamical regime, showing that, at variance with what happens in the Born-Markov semigroup limiting case, heat can backflow from the environment to the system. After providing a condition for the occurrence of such phenomenon and a measure for its amount for a given dynamics, the relationship with suitable non-Markovianity estimators is sought in two paradigmatic models, namely the spin-boson and the quantum brownian motion. The results, collected in [ G. Guarnieri, C. Uchiyama, B. Vacchini, Phys. Rev. A 93, 012118 (2016); G. Guarnieri, J. Nokkala, R. Schmidt, S. Maniscalco, B. Vacchini, Phys. Rev. A 94, 062101 (2016)], on the one hand allow for the identification of parameter-regions where the heat backflow is absent or maximum. On the other hand they show that the occurrence of heat backflow represents a stricter condition than non-Markovianity, in the sense that non-Markovianity allows for the observation of heat flowing back from the environment to the system and, vice versa, a Markovian dynamics prevents its occurrence. This Thesis concludes with the formulation of a new family of lower bounds to the mean dissipated heat in an environmental-assisted erasure-protocol scenario where Landauer's principle applies. As originally conceived for classical systems, this principle states that every irreversible erasure of information stored in a system inevitably carries along an amount of heat dissipated into the environment which is expended to perform the action. Within the framework recently put forward in [D. Reeb, M. M. Wolf, New J. Phys. 16, 103011 (2014)], which guarantees the validity of Landauer's principle in an open quantum systems scenario, we provide an asymptotically tight family of lower bounds to the dissipated heat which are also valid in the non-equilibrium setting. This construction is applied to an open system consisting of a three-level V-system, in which one transition is externally pumped by a laser field while the other is coupled through an XX-interaction to an environment consisting of a spin chain. Beside calculating all these quantities, an exact solution for the dynamics of such system is also provided. These results are collected in [G. Guarnieri, S. Campbell, J. Goold, S. Pigeon, M. Paternostro, B. Vacchini, in preparation].