Generation,propagation,and Measurement Of Multimode Quantum Light Fields

The generation,propagation,and measurement of multimode light fields have always been the most important and fundamental research topics in quantum theory.With the gradual clarification of physical picture and the increasing demand from scientific and engineering applications,it is necessary to further improve and refine the research model to obtain more detailed physical picture and more accurate quantitative results.In this dissertation,three main aspects are studied in detail,i.e.,the generation and propagation theory of multimode quantum light fields,the measurement and estimation theory of multimode light fields of multiple point sources,and the implementation schemes of parallel and simultaneous multimode decomposition measurement.In order to improve the existing theories of generation and propagation,this dissertation takes advantage of the fact that the field operators are the simultaneous solutions to both the Heisenberg equations of motion and Maxwell’s equations,and,under the quasi-monochromatic approximation,directly obtains a set of vector differential equations describing the space-propagation and coupling of the slowly-varying annihilation operators of the three waves.In the whole procedure,the anisotropic factor of the nonlinear medium is retained rigorously,and the errors incurred by the approximations of paraxial propagation and undepleted pump are avoided,which make the procedure more rigorous in theory,more clear in physical picture,and more accurate in quantification.When the central wavevectors of the involved three waves are collinearly matched,the above set of vector differential equations simplifies,and the resulted formulation is consistent with the set of differential equations in the semiclassical theory,which governs the coupling among the slowly-varying complex-amplitudes of the three waves.The major difference here is that the slowly-varying amplitudes are operator-valued,rather than complex-valued.Then,the standard linearized-fluctuation analysis is utilized,where the slowly-varying annihilation operators are separated into classical mean components and quantum fluctuation components.The classical mean components satisfy exactly the same set of three-wave coupling equations as those in the semiclassical theory,then they can be solved for by using the Jacobi function.In the meanwhile,the quantum fluctuation components satisfy a six-order matrix differential equation with the varying coefficient matrix constructed by the classical mean components,then they can be solved for numerically by using the fundamental solution matrix.After the normalization by the total power flow,the quantum fluctuation components can also be solved for analytically.To this end,the Floquet-Magnus theory is utilized for an approximate and periodical solution under a periodical approximation,and the Wei-Norman formula is utilized for the exact solution.Through these solutions,this dissertation reveals that the multimode squeezing transformation corresponds to a complicated physical process,which is constituted of intramodal rotation,squeezing,and anti-squeezing in the phase space,and of intermodal coupling.For comparison,the existing theories also obtain the time-evolution differential equations of the field operators from the Heisenberg equations of motion.However,to obtain a new set of differential equations describing the space propagation and coupling,some of the theories make a substitution for the Fourier annihilation operators and make some approximations.It is this substitution and these approximations that obscure the physical picture.Furthermore,the existing theories use the approximations of paraxial propagation and undepleted pump,and they simplify even completely ignore the factor related to the dispersion and walk-off angle in an anisotropic medium.As a result,the rigor of the theories and the quantification are reduced.In order to study the measurement and estimation theory of multimode light fields of multiple point sources,this dissertation starts from the quantum coherence theory and diffraction theory,and derives the eigenvalue problems of the spatial mode basis functions and the temporal mode basis functions from the mutual coherence functions and the diffraction integrals.Then,using the boundary conditions of spatially circular symmetry and temporally rectangular spectral density function,the spatial and temporal mode basis functions of the aperture fields are expressed with the prolate spheroidal functions.Using these mode basis functions,the mode decomposition and the first two moments of the aperture fields of the multiple point sources are studied analytically,and the quantum Cramer-Rao bounds for multi-parameter estimation of multimode Gaussian states are obtained via the quantum Fisher information matrix.Furthermore,the spatial mode basis functions of the circularly symmetric object surface are found analytically.Based on the parallel multimode channel model,an estimation theory is proposed to estimate the first two moments of the object fields from those measured of the aperture fields.The effectiveness of the estimation theory is confirmed by quantitative calculation of the quantum fidelity.In comparison to the existing theories,which mainly deal with the resolution between two point sources and two-mode fields,this theory is more general.In order to realize parallel and simultaneous multimode decomposition and measurement,the theory of frequency-resolved optical mode decomposition(FROMD)and the method of its arraying are proposed.FROMD uses a multi-frequency LO,arranges the frequencies of the LO to be symmetrical with respect to the frequency of the signal light field,and loads one temporal mode basis function onto a pair of symmetricalfrequency components of the LO.A multi-frequency electric heterodyne signal is obtained with balanced heterodyne detection,in which each pair of symmetricalfrequency components of the LO is mixed with the signal light field to generate positive and negative difference frequencies that are degenerated into the same intermediate frequency(IF)channel.In this manner,the signal light field is mixed with different temporal mode basis functions in different IF channels,and the vacuum fluctuation noises of the image bands are suppressed.Subsequently,a multichannel receiver is used to separate the IF channels and integrate them independently.This yields parallelly and simultaneously the measurement outcomes of the modal annihilation operators of the signal light field.When applied to single-mode quantum light fields,FROMD is exactly the same as the traditional balanced homodyne detection or bichromatic-LO balanced heterodyne detection,but it can also be applied to any multimode quantum light fields.