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Reports on Mathematical Physics

Multiquantum systems and point processes I. Generating functionals and nonlinear semigroups

V. P. Belavkin

Published Aug 1, 1989• 10 citations
Publisher
DOI
10.1016/0034-4877(89)90026-8

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Multiquantum electron paramagnetic resonance transitions excited in a two-level system by tetrachromatic microwave irradiation

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A method to excite multiquantum transitions in a two-level system by application of continuous irradiation with a four-frequency microwave field is presented. The generated signal is composed of many intermodulation sidebands at different frequencies, which arise from the multiquantum transitions. These processes involve an odd number of photons, that are absorbed from, or emitted to two, three, or four fields. The correspondence between the frequency spectrum of the signal and possible pathways of multiquantum processes is found with recourse to the many mode Floquet theory. The reported experiments demonstrate the multiquantum origin of the detected intermodulation sidebands and their properties.

The Journal of Chemical Physics•Dec 1, 1998•8 citations
The algebraic approach to the description and representation of multiquantum (multicomponent) systems discussed in the present paper continues the approach developed in [5,9–12]. That is based on the generating multicomponent -state functional and the nonlinear completely positive map [3] functional method which extends in a natural way the variety of the processes regarded as quantum stochastic processes [2], including nonlinear ones with interaction in the system. The dynamics of such systems is considered in the Markovian approximation; the theory and classification of the corresponding “master equations” was constructed in [13]. In the nonlinear case we obtain in a natural way a nonlinear extension of the basic constructions and results of the representation theory and an extension to nonlinear structures (state and mapping) [3,81 which are good tools to describe systems with interaction.
Probability Measures in Terms of Creation, Annihilation and Neutral Operators (L Accardi et al.) Generating Function Methods for Orthogonal Polynomials and Jacobi-Szego Parameters (N Asai et al.) Multiquantum Markov Semigroups, Interacting Branching Processes and Nonlinear Kinetic Equations. Finite Dimensional Case (V Belavkin & C Williams) A Note on Vacuum-Adapted Semimartingales and Monotone Independence (A Belton) Regular Quantum Stochastic Cocycles have Exponential Product Systems (B V R Bhat & M Lindsay) Quantum Mechanics on the Circle Through Hopf q-Deformations of the Kinematical Algebra with Possible Applications to Levy Processes (V K Dobrev et al.) On Algebraic and Quantum Random Walks (D Ellinas) Dual Representations for the Schrodinger Algebra (P H Feinsilver & R Schott) A Limit Theorem for Conditionally Independent Beam Splittings (K H Fichtner et al.) On Quantum Logical Gates on a General Fock Space (W Feudenberg et al.) On an Argument of David Deutsch (R Gill) The Method of Double Product Integrals in Quantization of Lie Bialgebras (R Hudson) Asymptotics of Large Truncated Haar Unitary Matrices (J Reffy) Three Ways to Representations of Ba(E) (M Skeide) On Topological Entropy of Quotients and Extensions (J Zacharias) and other papers.
A method to excite multiquantum transitions in a two-level system by application of continuous irradiation with a four-frequency microwave field is presented. The generated signal is composed of many intermodulation sidebands at different frequencies, which arise from the multiquantum transitions. These processes involve an odd number of photons, that are absorbed from, or emitted to two, three, or four fields. The correspondence between the frequency spectrum of the signal and possible pathways of multiquantum processes is found with recourse to the many mode Floquet theory. The reported experiments demonstrate the multiquantum origin of the detected intermodulation sidebands and their properties.