Quantum Statistics of Linear and Nonlinear Optical Phenomena

Peřina, Jan

doi:10.1007/978-94-011-2400-3

Cited by 294 publications

(403 citation statements)

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“…1). A very simple and feasible choice is the coherent states r s ja͘ ͗aj defined by the eigenvalue equation aja͘ aja͘, where a is the annihilation or ladder operator a lq 1 ip͑͞2l͒, with l a suitable constant [2][3][4]. Since the complex parameter a is allowed to vary, the statistics of the measurement Q͑k, a͒ depend on the variables k and a, and is given by Q͑k, a͒ ͗ajD͑k͒ja͘ .…”

Section: (Received 22 December 1998)mentioning

confidence: 99%

Complete Characterization of Arbitrary Quantum Measurement Processes

1999

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We examine two simple and feasible practical schemes allowing the complete determination of any quantum measuring arrangement. This is illustrated with the example of parity measurement.PACS numbers: 03.65. Bz, 42.50.Ar, 42.50.Dv In the most standard picture of quantum mechanics the statistics of every measurement are governed by the projection of the system state on the orthogonal eigenstates of a set of commuting self-adjoint operators representing the measured observables. This implicitly assumes that the measurement is performed on a closed system.A more complete and realistic picture must encompass the possibility of controllable as well as unpredictable couplings of the observed system with external agents. This is to say that the measurement is performed, in general, on an open system. Among other consequences, this extends the idea of observables beyond self-adjoint operators, introducing generalized measurements described by positive operator measures (POMs).In particular, this occurs when a standard measurement is preceded by an interaction of the observed system with other degrees of freedom that are in a fixed and known initial state [1]. On the other hand, the process can also involve uncontrollable influences (usually undesired) of outer degrees of freedom. This is frequently the case with couplings with reservoirs and other mechanisms leading to losses and decoherence effects, for instance. In many practical situations it is not possible to predict which external variables are involved or the way they affect the performance of the measurement. In other words, to some extent, the real measurement differs from the intended one in an unpredictable way.In this paper we present two simple and feasible practical procedures that allow us to determine completely any quantum measurement process. The objective of such a characterization is to obtain in practice the actual POM governing the statistics. This would allow one to ascertain to what extent the planned performance is reached by revealing undesired deviations.The system, which is the object of the observation, and the external variables involved are described by the Hilbert spaces H s and H a , respectively. Since the total Hilbert space H H s ≠ H a represents by definition a closed system, the system-environment interaction can always be implemented by a unitary operator U acting on H . The system is initially in an arbitrary state with density matrix r s , while the external variables will be in some state r a that does not depend on r s . After the interaction, some set of compatible observables are measured on the output state Ur s r a U y . The statistics of the measurement are given by the projection on a set of orthonormal vectors jk͘ whose span need not coincide with H s :where P ͑k͒ is the probability of the outcome k. This is a standard ideal measurement because H s ≠ H a is a closed system. Since r a is fixed and does not depend on r s , the information provided by the measurement can be regarded as information about r s . This interpr...

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Section: (Received 22 December 1998)mentioning

confidence: 99%

Complete Characterization of Arbitrary Quantum Measurement Processes

1999

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“…They take energy from the pump field during the interaction. The nonlinear interaction mediated by the material with χ (2) nonlinearity is described by the following nonlinear interaction momentum operatorĜ int [26,30,31]: To reveal a spatio-spectral structure of the fields suitable for describing the nonlinear interaction we first consider the generation of individual photon pairs in the weak nonlinear interaction. In this case, the pump field is treated classically and an emitted photon pair is described by a quantum state |ψ si obtained by the first-order perturbation solution of the corresponding Schrödinger equation.…”

Section: The Model Of Ultra-intense Twin Beams Involving Pump Depmentioning

confidence: 99%

Spatial, spectral, and temporal coherence of ultraintense twin beams

Peřina

2016

Phys. Rev. A

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Using the model of parametric interaction based on the spatio-spectral Schmidt modes and generalized parametric approximation, we analyze coherence and mode structure of ultra-intense twin beams generated in the regime with pump depletion. We show that the increase of spatial and spectral coherence with the increasing pump power observed for moderate powers is replaced by the decrease for the pump powers at which pump depletion occurs. This behavior of coherence is opposed to that exhibited by the number of spatio-spectral modes effectively constituting the twin beam. The conditions for maximal coherence are analyzed considering pump-beam parameters (spectral width, transverse radius). The existence of additional coherence maxima occurring at even higher pump powers is predicted and explained by the oscillatory evolution of the modes' populations.

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“…Explicit examples of many other two-and multimode nonclassicality witnesses, corresponding to violations of classical inequalities, can be found in, e.g., Refs. [14,19,23,[27][28][29][30].…”

Section: A Examples Of Truncated Nonclassicality Witnessesmentioning

confidence: 99%

Sudden vanishing and reappearance of nonclassical effects: General occurrence of finite-time decays and periodic vanishings of nonclassicality and entanglement witnesses

et al. 2011

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Analyses of phenomena exhibiting finite-time decay of quantum entanglement have recently attracted considerable attention. Such decay is often referred to as sudden vanishing (or sudden death) of entanglement, which can be followed by its sudden reappearance (or sudden rebirth). We analyze various finite-time decays (for dissipative systems) and analogous periodic vanishings (for unitary systems) of nonclassical correlations as described by violations of classical inequalities and the corresponding nonclassicality witnesses (or quantumness witnesses), which are not necessarily entanglement witnesses. We show that these sudden vanishings are universal phenomena and can be observed: (i) not only for two-or multi-mode but also for single-mode nonclassical fields, (ii) not solely for dissipative systems, and (iii) at evolution times which are usually different from those of sudden vanishings and reappearances of quantum entanglement.

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Quantum Statistics of Linear and Nonlinear Optical Phenomena

Abstract: Pefina, Jan, 1936-Quantum statistics of linear and nonlinear optical phenomena by Jan Pefina. --2nd completely rev. ed. p. cm. Includes bibliographical references (p. ) and index.

Cited by 294 publications

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Complete Characterization of Arbitrary Quantum Measurement Processes

Complete Characterization of Arbitrary Quantum Measurement Processes

Spatial, spectral, and temporal coherence of ultraintense twin beams

Sudden vanishing and reappearance of nonclassical effects: General occurrence of finite-time decays and periodic vanishings of nonclassicality and entanglement witnesses

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