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020 _a9783642012983
_9978-3-642-01298-3
024 7 _a10.1007/978-3-642-01298-3
_2doi
050 4 _aQC350-467
050 4 _aQC630-648
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_223
100 1 _aBarchielli, Alberto.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aQuantum Trajectories and Measurements in Continuous Time
_h[electronic resource] :
_bThe Diffusive Case /
_cby Alberto Barchielli, Matteo Gregoratti.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c2009.
300 _aXIV, 325 p. 30 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Physics,
_x0075-8450 ;
_v782
505 0 _aI General theory -- The Stochastic Schr#x00F6;dinger Equation -- The Stochastic Master Equation: Part I -- Continuous Measurements and Instruments -- The Stochastic Master Equation: Part II -- Mutual Entropies and Information Gain in Quantum Continuous Measurements -- II Physical applications -- Quantum Optical Systems -- A Two-Level Atom: General Setup -- A Two-Level Atom: Heterodyne and Homodyne Spectra -- Feedback.
520 _aThis course-based monograph introduces the reader to the theory of continuous measurements in quantum mechanics and provides some benchmark applications. The approach chosen, quantum trajectory theory, is based on the stochastic Schrödinger and master equations, which determine the evolution of the a-posteriori state of a continuously observed quantum system and give the distribution of the measurement output. The present introduction is restricted to finite-dimensional quantum systems and diffusive outputs. Two appendices introduce the tools of probability theory and quantum measurement theory which are needed for the theoretical developments in the first part of the book. First, the basic equations of quantum trajectory theory are introduced, with all their mathematical properties, starting from the existence and uniqueness of their solutions. This makes the text also suitable for other applications of the same stochastic differential equations in different fields such as simulations of master equations or dynamical reduction theories. In the next step the equivalence between the stochastic approach and the theory of continuous measurements is demonstrated. To conclude the theoretical exposition, the properties of the output of the continuous measurement are analyzed in detail. This is a stochastic process with its own distribution, and the reader will learn how to compute physical quantities such as its moments and its spectrum. In particular this last concept is introduced with clear and explicit reference to the measurement process. The two-level atom is used as the basic prototype to illustrate the theory in a concrete application. Quantum phenomena appearing in the spectrum of the fluorescence light, such as Mollow’s triplet structure, squeezing of the fluorescence light, and the linewidth narrowing, are presented. Last but not least, the theory of quantum continuous measurements is the natural starting point to develop a feedback control theory in continuous time for quantum systems. The two-level atom is again used to introduce and study an example of feedback based on the observed output.
650 0 _aMathematics.
650 0 _aQuantum theory.
650 0 _aMathematical physics.
650 1 4 _aClassical Electrodynamics.
_0http://scigraph.springernature.com/things/product-market-codes/P21070
650 2 4 _aApplications of Mathematics.
_0http://scigraph.springernature.com/things/product-market-codes/M13003
650 2 4 _aQuantum Physics.
_0http://scigraph.springernature.com/things/product-market-codes/P19080
650 2 4 _aMathematical Methods in Physics.
_0http://scigraph.springernature.com/things/product-market-codes/P19013
650 2 4 _aQuantum Optics.
_0http://scigraph.springernature.com/things/product-market-codes/P24050
650 2 4 _aComplex Systems.
_0http://scigraph.springernature.com/things/product-market-codes/P33000
700 1 _aGregoratti, Matteo.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783642012990
776 0 8 _iPrinted edition:
_z9783642242489
776 0 8 _iPrinted edition:
_z9783642012976
830 0 _aLecture Notes in Physics,
_x0075-8450 ;
_v782
856 4 0 _uhttps://doi.org/10.1007/978-3-642-01298-3
912 _aZDB-2-PHA
912 _aZDB-2-LNP
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