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Methods and apparatus of entangled photon generation using four-wave mixing

Ryan M. Camacho

Published Jan 23, 2023• 0 citations
OpenAlex

Abstract

A non-linear optical device is provided. The device comprises an optical disk or ring microresonator fabricated from a material that exhibits an optical nonlinearity able to produce degenerate four-wave mixing (FWM) in response to a pump beam having a pump frequency in a specified effective range. The microresonator is conformed to exhibit an angular group velocity minimum at a pump frequency within the specified effective range such that there is zero angular group velocity dispersion at the pump frequency. We refer to such a pump frequency as the "zero dispersion frequency". In embodiments, excitation of the resonator by a pump beam of sufficient intensity at the zero-dispersion frequency causes the resonator to emit a frequency comb of entangled photon pairs wherein the respective frequencies in each pair are symmetrically placed about the zero-dispersion frequency.

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A non-linear optical device is provided. The device comprises an optical disk or ring microresonator fabricated from a material that exhibits an optical nonlinearity able to produce degenerate four-wave mixing (FWM) in response to a pump beam having a pump frequency in a specified effective range. The microresonator is conformed to exhibit an angular group velocity minimum at a pump frequency within the specified effective range such that there is zero angular group velocity dispersion at the pump frequency. We refer to such a pump frequency as the "zero dispersion frequency". In embodiments, excitation of the resonator by a pump beam of sufficient intensity at the zero-dispersion frequency causes the resonator to emit a frequency comb of entangled photon pairs wherein the respective frequencies in each pair are symmetrically placed about the zero-dispersion frequency.
A novel quantum mechanical formulation of the bi-photon wavefunction and spectra resulting from four-wave mixing is developed for azimuthally symmetric systems. Numerical calculations are performed verifying the use of the angular group velocity and angular group velocity dispersion in such systems, as opposed their commonly used linear counterparts. The dispersion profile and bi-photon spectra of two illustrative examples are given, emphasizing the physical origin of the effects leading to the conditions for angular momentum and energy conservation. A scheme is proposed in which widely spaced narrowband entangled photons may be produced through a four-wave mixing process in a chip-scale ring resonator. The entangled photon pairs are found to conserve energy and momentum in the four-wave mixing interaction, even though both photon modes lie in spectral regions of steep angular group velocity dispersion.
A method for preparing an entangled quantum state of an atomic ensemble is provided. The method includes loading each atom of the atomic ensemble into a respective optical trap; placing each atom of the atomic ensemble into a same first atomic quantum state by impingement of pump radiation; approaching the atoms of the atomic ensemble to within a dipole-dipole interaction length of each other; Rydberg-dressing the atomic ensemble; during the Rydberg-dressing operation, exciting the atomic ensemble with a Raman pulse tuned to stimulate a ground-state hyperfine transition from the first atomic quantum state to a second atomic quantum state; and separating the atoms of the atomic ensemble by more than a dipole-dipole interaction length.
The work is devoted to the problem of developing integrated single-photon sources based on spontaneous four-wave mixing in ring microresonators. Considering the silicon nitride microresonator as an example, we calculate the group velocity dispersion in a wide wavelength range for the case when the ring resonator is composed of straight and curved sections, and show that for different pump wavelengths it is possible to find an optimal ratio of the height and width of the waveguide, thereby achieving zero group velocity dispersion at a minimum height. Such waveguides, which provide zero dispersion and have a minimum height, are optimal for creating ring microresonators that generate single-photon states via non-degenerate spontaneous four-wave mixing.
Systems and methods are described for an optical microscope using an interferometric source of multi-color, multi-beam entangled photons. A method includes: downconverting a beam of coherent energy to provide a beam of multi-color entangled photons; converging two spatially resolved portions of the beam of multi-color entangled photons into a converged multi-color entangled photon beam; transforming at least a portion of the converged multi-color entangled photon beam by interaction with a sample to generate an entangled photon specimen beam; and combining the entangled photon specimen beam with an entangled photon reference beam within a single beamsplitter. An apparatus includes: a multi-refringent device providing a beam of multi-color entangled photons; a condenser device optically coupled to the multi-refringent device, the condenser device converging two spatially resolved portions of the beam of multi-color entangled photons into a converged multi-color entangled photon beam; a beam probe director and specimen assembly optically coupled to the condenser device; and a beam splitter optically coupled to the beam probe director and specimen assembly, the beam splitter combining an entangled photon specimen beam from the beam probe director and specimen assembly with an entangled photon reference beam.
The work is devoted to the problem of developing integrated single-photon sources based on spontaneous four-wave mixing in ring microresonators. Considering the silicon nitride microresonator as an example, we calculate the group velocity dispersion in a wide wavelength range for the case when the ring resonator is composed of straight and curved sections, and show that for different pump wavelengths it is possible to find an optimal ratio of the height and width of the waveguide, thereby achieving zero group velocity dispersion at a minimum height. Such waveguides, which provide zero dispersion and have a minimum height, are optimal for creating ring microresonators that generate single-photon states via non-degenerate spontaneous four-wave mixing.