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arXiv:cond-mat/9905360

Quantum stochastic processes in mesoscopic conductors

Gerard J Milburn

Published May 25, 1999• 1 citation
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Abstract

We show an equivalence between the approach of Buttiker and the Fermi quantum stochastic calculus for mesoscopic systems. To illustrate the method we derive the current fluctuations in a two terminal mesoscopic circuit with two tunnel barriers containing a single quasi bound state on the well. The method enables us to focus on either the incoming/outgoing Fermi fields in the leads, or on the irreversible dynamics of the well state itself. The quantum stochastic calculus we use is the Fermi analogue of the input/output methods of quantum optics.

DOI
10.48550/arxiv.cond-mat/9905360

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We show an equivalence between the approach of Buttiker and the Fermi quantum stochastic calculus for mesoscopic systems. To illustrate the method we derive the current fluctuations in a two terminal mesoscopic circuit with two tunnel barriers containing a single quasi bound state on the well. The method enables us to focus on either the incoming/outgoing Fermi fields in the leads, or on the irreversible dynamics of the well state itself. The quantum stochastic calculus we use is the Fermi analogue of the input/output methods of quantum optics.
In quantum measurement theory it is necessary to show how a quantum source conditions a classical stochastic record of measured results. We discuss mesoscopic conductance using quantum stochastic calculus to elucidate the quantum nature of the measurement taking place in these systems. To illustrate the method we derive the current fluctuations in a two terminal mesoscopic circuit with two tunnel barriers containing a single quasi bound state on the well. The method enables us to focus on either the incoming/ outgoing Fermi fields in the leads, or on the irreversible dynamics of the well state itself. We show an equivalence between the approach of BÜttiker and the Fermi quantum stochastic calculus for mesoscopic systems.
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.
Basic Concepts. Canonical Quantization. Quantum States of the Electromagnetic Fields. Coherence of the Electromagnetic Fields. Quantum States of Atoms. Interaction between Atoms and Fields. Mathematical Methods for System-Reservoir Interaction. Stochastic Wavefunction Methods. Quantum Nondemolition Measurements. Semiconductor Bloch Equations. Excitons and Polaritons. Coulomb Blockade and Squeezing. Current Noise in Mesoscopic and Macroscopic Conductors. Nonequilibrium Green's Function Formalism. Quantum Statistical Properties of a Laser. Index.
The traditional approach to quantum parameter estimation focuses on the quantum state, deriving fundamental bounds on precision through the quantum Fisher information. In most experimental settings, however, performing arbitrary quantum measurements is highly unfeasible. In open quantum systems, an alternative approach to metrology involves the measurement of stochastic currents flowing from the system to its environment. However, the present understanding of current-based metrology is mostly limited to Markovian master equations. Considering a parameter estimation problem in a two-terminal mesoscopic conductor, we identify the key elements that determine estimation precision within the Landauer-Büttiker formalism. Crucially, this approach allows us to address arbitrary coupling and temperature regimes. Furthermore, we obtain analytical results for the precision in linear-response and zero-temperature regimes. For the specific parameter estimation task that we consider, we demonstrate that the boxcar transmission function is optimal for current-based metrology in all parameter regimes.