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Fluctuation and dissipation in quantum nonlinear optics

Shiekh Zia Uddin, Nicholas Rivera, Devin Seyler, Yannick Salamin, Jamison Sloan, Shutao Xu, Michelle Y. Sander, Marin Soljacic A

Published Jan 1, 2024• 0 citations
Publisher

Abstract

We present a new fluctuation-dissipation relation that shows how quantum noise transforms under engineered nonlinear dissipation found in many important nonlinear optical devices and validate the theory with experiments on nonlinear interferometers.
DOI
10.1364/cleo_si.2024.sf3j.4

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We constructed an efficient source of photon pairs using a waveguide-type nonlinear device and performed a two-photon interference experiment with an unbalanced Michelson interferometer. As the interferometer has two arms of different lengths, photons from the short arm arrive at the detector earlier than those from the long arm. We find that the arrival time difference (Delta L/c) and the time window of the coincidence counter (Delta T) are important parameters which determine the boundary between the classical and quantum regimes. Fringes of high visibility ( 80% +/- 10%) were observed when Delta T < Delta L/c. This result is explained only by quantum theory and is clear evidence for quantum entanglement of the interferometer's optical paths.
Ultracompact nonlinear optical devices utilizing two-dimensional (2D) materials and nanostructures are emerging as important elements of photonic circuits. Integration of the nonlinear material into a subwavelength cavity or waveguide leads to a strong Purcell enhancement of the nonlinear processes and compensates for a small interaction volume. The generic feature of such devices which makes them especially challenging for analysis is strong dissipation of both the nonlinear polarization and highly confined modes of a subwavelength cavity. Here we solve a quantum-electrodynamic problem of the spontaneous and stimulated parametric down-conversion in a nonlinear quasi-2D waveguide or cavity. We develop a rigorous Heisenberg-Langevin approach which includes dissipation and fluctuations in the electron ensemble and in the electromagnetic field of a cavity on equal footing. Within a relatively simple model, we take into account the nonlinear coupling of the quantized cavity modes, their interaction with a dissipative reservoir and the outside world, amplification of thermal noise and zero-point fluctuations of the electromagnetic field, and other relevant effects. We derive closed-form analytic results for relevant quantities such as the spontaneous parametric signal power and the threshold for parametric instability. We find a strong reduction in the parametric instability threshold for 2D nonlinear materials in a subwavelength cavity and provide a comparison with conventional nonlinear photonic devices.