LEADER 05889nam 22008895 450 001 996466688503316 005 20200706030800.0 010 $a1-280-38489-1 010 $a9786613562814 010 $a3-642-01298-1 024 7 $a10.1007/978-3-642-01298-3 035 $a(CKB)1000000000773200 035 $a(SSID)ssj0000319714 035 $a(PQKBManifestationID)11252072 035 $a(PQKBTitleCode)TC0000319714 035 $a(PQKBWorkID)10342137 035 $a(PQKB)11485216 035 $a(DE-He213)978-3-642-01298-3 035 $a(MiAaPQ)EBC3064408 035 $a(PPN)136310036 035 $a(EXLCZ)991000000000773200 100 $a20100301d2009 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aQuantum Trajectories and Measurements in Continuous Time$b[electronic resource] $eThe Diffusive Case /$fby Alberto Barchielli, Matteo Gregoratti 205 $a1st ed. 2009. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2009. 215 $a1 online resource (XIV, 325 p. 30 illus.) 225 1 $aLecture Notes in Physics,$x0075-8450 ;$v782 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-642-01297-3 320 $aIncludes bibliographical references and index. 327 $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. 330 $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. 410 0$aLecture Notes in Physics,$x0075-8450 ;$v782 606 $aOptics 606 $aElectrodynamics 606 $aApplied mathematics 606 $aEngineering mathematics 606 $aQuantum physics 606 $aPhysics 606 $aQuantum optics 606 $aStatistical physics 606 $aDynamical systems 606 $aClassical Electrodynamics$3https://scigraph.springernature.com/ontologies/product-market-codes/P21070 606 $aApplications of Mathematics$3https://scigraph.springernature.com/ontologies/product-market-codes/M13003 606 $aQuantum Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P19080 606 $aMathematical Methods in Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P19013 606 $aQuantum Optics$3https://scigraph.springernature.com/ontologies/product-market-codes/P24050 606 $aComplex Systems$3https://scigraph.springernature.com/ontologies/product-market-codes/P33000 615 0$aOptics. 615 0$aElectrodynamics. 615 0$aApplied mathematics. 615 0$aEngineering mathematics. 615 0$aQuantum physics. 615 0$aPhysics. 615 0$aQuantum optics. 615 0$aStatistical physics. 615 0$aDynamical systems. 615 14$aClassical Electrodynamics. 615 24$aApplications of Mathematics. 615 24$aQuantum Physics. 615 24$aMathematical Methods in Physics. 615 24$aQuantum Optics. 615 24$aComplex Systems. 676 $a535.15 686 $a530$2sdnb 686 $aUD 8220$2rvk 700 $aBarchielli$b Alberto$4aut$4http://id.loc.gov/vocabulary/relators/aut$079237 702 $aGregoratti$b Matteo$4aut$4http://id.loc.gov/vocabulary/relators/aut 906 $aBOOK 912 $a996466688503316 996 $aQuantum Trajectories and Measurements in Continuous Time$92542483 997 $aUNISA