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EPJ Web of Conferences

Transformations properties of quantum optical signals in phase modulator

Alexander Trifanov, Ekaterina S. Trifanova

Published Jan 1, 2019• 0 citations
Publisher

Abstract

We investigate evolution of multimode quantum light in electro-optical modulator, using semiclassical model of phase modulation process. For the case of monochromatic incoming signal, we consider transformation of its spectrum and calculate statistical properties of each frequency mode. Particularly, we find that for the case of initial coherent state our result is covered by the well-known classical model. While for the case of initially squeezed state we observe single- and multi-mode squeezing in frequency spectrum of modulated light.

DOI
10.1051/epjconf/201922002017

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We investigate evolution of multimode quantum light in electro-optical modulator, using semiclassical model of phase modulation process. For the case of monochromatic incoming signal, we consider transformation of its spectrum and calculate statistical properties of each frequency mode. Particularly, we find that for the case of initial coherent state our result is covered by the well-known classical model. While for the case of initially squeezed state we observe single- and multi-mode squeezing in frequency spectrum of modulated light.
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We present a quantum mechanical model to evaluate the time evolution of quantum states of light in an electro-optic phase modulator (EOPM). The phase modulator is analogous to a multilevel atomic system with equally spaced energy levels, each of which corresponds to the sidebands of the phase modulated optical field. Using perturbation theory, we solve the equations governing the interaction of the optical field with a modulating field both with and without phase velocity mismatch. A unitary operator that evolves any given quantum state allows us to evaluate the response of EOPM for single photon, coherent and squeezed states. We apply these results to the analysis of frequency coded quantum key distribution scheme.
We present a detailed analysis of the quantum description of electro-optical phase modulation. The results define a black-box type model for this device, which may be especially useful in the engineering steps leading to the design of complex quantum information systems incorporating one or more of these devices. By constructing an explicit representation of the phase modulation scattering operator, it is shown that an approach based entirely on its classical description leads to unphysical modes associated to non-positive frequencies. After modifying this operator, phase modulation is described, for the first time to the best of our knowledge, in terms of a unitary scattering operator Ŝ defined over positive-frequency modes. The modifications introduced by Ŝ in the process of sideband generation by phase modulation are shown to be insignificant when the radiation belongs to optical bands, thus being consistent with the classical description. Finally, the model is employed to characterize the important case of multitone radio- frequency modulation of an optical signal.
We theoretically study electro-optic light modulation based on a quantum model where the linear electro-optic effect and the externally applied microwave field result in the interaction between optical cavity modes. The model assumes that the number of interacting modes is finite, and effects of the mode overlapping coefficient on the strength of the intermode interaction can be taken into account through dependence of the coupling coefficient on the mode characteristics. We show that, under certain conditions, the model is exactly solvable and can be analyzed using the technique of the Jordan mappings for the su(2) Lie algebra. Analytical results are applied to study effects of light modulation on the frequency dependence of the photon counting rate. In contrast to the limiting case of an infinitely large number of interacting modes, when the number of interacting modes is finite, the sideband intensities reveal strongly nonmonotonic behavior supplemented with asymmetry of the intensity distribution provided the pumped mode is not central. We also analyze different regimes of two-modulator transmission and establish the conditions of validity of the semiclassical approximation by applying the methods of polynomially deformed Lie algebras for analysis of the model with quantized microwave field.
Hamiltonian of a parametric process describing the interaction of a finite number of optical cavity modes, with the microwave field is proposed. Three-boson interaction is due to electro-optical effect. Analysis of the model is based on the algebraic properties of multimode field operators who, under certain assumptions, are su (2) algebra generators. The features of the transformation of the quantum states of signal photons in the electro-optical modulator are investigated. The limit on the number of interacting modes from the proposed (restricted) model to the traditionally used (unrestricted) model of electro-optical modulator is investigated.
We use the effective Hamiltonian approach to parametric frequency modes interaction to investigate the dynamics of quantum polarization states for each frequency mode under phase modulation process based on the full quantum model. We consider the case of a finite number of interacting frequency modes and show that the transformation of polarization states induced by the nonvanishing difference between the phase velocities of different polarization components is determined by the rotation of the Stokes vectors obtained from the mean values and the dispersions of the Stokes operators.