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arXiv:1811.01207 · Physica A Statistical Mechanics and its Applications

Hermite–Gaussian model for quantum states

Marcelo Losada, Ignacio S. Gomez, Federico Holik

Published Jun 19, 2019• 1 citation
arXivHTMLPDF
DOI
10.1016/j.physa.2019.121806

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We show that the transfer of the angular spectrum of the pump beam to the two-photon state in spontaneous parametric down-conversion enables the generation of entangled Hermite-Gaussian modes. We derive an analytical expression for the two-photon state in terms of these modes and show that there are restrictions on both the parity and order of the down-converted Hermite-Gaussian fields. Using these results, we show that the two-photon state is indeed entangled in Hermite-Gaussian modes. We propose experimental methods of creating maximally-entangled Bell states and nonmaximally entangled pure states of first order Hermite-Gaussian modes.
Based on quantum Stokes operators and non-Kolmogorov spectrum model of index-of-refraction fluctuation, the analytical formulas for the quantum degree of depolarization of quantization Hermite-Gaussian (QHG) beams propagating in a turbulent atmosphere slant channel are derived.The nonclassical polarization properties of QHG beams propagating in turbulent atmosphere are studied numerically.It is found that the polarization fluctuations of QHG beams are dependent of the turbulence factors such as spectrum powerlaw exponent, refractive index structure parameter at the ground and zenith angle.The degree of depolarization of QHG beams has a saltation and reaches the minimum value at spectrum power-law exponent α = 11/3, the refractive index structure parameter at the ground of the turbulent atmosphere slightly affects the polarization degree of QHG beams which have travelled a long distance, and the change of polarization degree decreases with the increasing zenith angle.Furthermore, the numerical simulations show that QHG beams with higher photonnumber level, lower beam order, shorter wavelength are less affected by the turbulence.These results indicate that One can choose low-order QHG beams with wavelength λ = 690 nm as optical carrier, increase photon number, set the size of transmitting aperture w 0 as about 0.1 m, and detect communication signals at the central region of beams to improve the performance of a polarization-encoded free-space quantum communication system.
Abstract A theoretical analysis is presented on the photoexcitation of a macroscopic atomic target by a Hermite–Gaussian (HG) beam within the framework of density matrix theory. Special emphasis is paid to the influence of the incoming HG mode on the population of an excited state and the emitted fluorescence radiation. In particular, a general expression for the alignment parameter of the excited state is derived, which depends on the beam parameters of the HG mode. Although the developed theory can be applied to any atomic system, here the electric dipole transition in neutral sodium atoms is investigated when driven by three , and modes. For this optical (valence‐shell) excitation, it is demonstrated that the population of the excited state is sensitive to the beam waist and the mode index of the HG beam. Furthermore, the influence of beam parameters on the angular distribution and linear polarization of the emitted fluorescence radiation is discussed.