Isoenergetic model for optical downconversion and error-specific limits of the parametric approximation

Abstract

Optical downconversion is widely used for generating photon pairs, squeezed and entangled states of light, making it an indispensable tool in quantum optics and quantum information. In the regime where the pump is much stronger than the generated field, the standard parametric approximation treats the pump amplitude as a fixed parameter of the model. This approximation has a limited domain of validity since it assumes a non-depleted and non-entangled pump. By finding an approximate solution to the Schrödinger equation of the downconversion process, we obtain an improved analytical model beyond the parametric one, which accounts for pump depletion and pump-signal entanglement. The new model is advantageous, first, because it allows one to compute averages of field operators far beyond the domain of validity of the parametric approximation, and second, because it allows one to establish error-specific limits of the latter domain. For a given pump amplitude, we find a maximum squeezing parameter, up to which the approximation remains valid within a specified acceptable error. Our results confirm that recent experiments on Gaussian boson sampling, with a squeezing parameter of $r\approx 1.8$ and a coherent pump amplitude of $\alpha \approx 2\cdot 10^6$, can still be accurately described by the standard parametric approximation. However, we observe a sharp decline in validity as the squeezing parameter increases. For pump amplitudes of $\alpha \approx 2\cdot 10^6$, the parametric approximation breaks down when the squeezing parameter exceeds $r\approx 4.5$, whereas the new approximation remains valid up to $r\approx 6$ with an acceptable error of 1%.

17 pages, 3 figures, 1 table. Final accepted version

References in corpus (24)

• Gaussian Quantum Information
• Photonic quantum technologies
• Quantum computational advantage using photons
• Squeezed states of light and their applications in laser interferometers
• Gaussian Boson Sampling
• Time-Domain Multiplexed 2-Dimensional Cluster State: Universal Quantum Computing Platform
• Phase-Programmable Gaussian Boson Sampling Using Stimulated Squeezed Light
• Deterministic generation of a two-dimensional cluster state
• Modes and states in Quantum Optics
• Boson Sampling from Gaussian States
• Gaussian Boson Sampling with Pseudo-Photon-Number Resolving Detectors and Quantum Computational Advantage
• Theory of quantum frequency conversion and type-II parametric down-conversion in the high-gain regime
• Effects of time ordering in quantum nonlinear optics
• Regimes of classical simulability for noisy Gaussian boson sampling
• Pump depletion in parametric down-conversion with low pump energies
• Bloch-Messiah decomposition and Magnus expansion for parametric down-conversion with monochromatic pump
• Onset of non-Gaussian quantum physics in pulsed squeezing with mesoscopic fields
• Fourier-transform infrared spectroscopy with undetected photons from high-gain spontaneous parametric down-conversion
• Distinguishing noisy boson sampling from classical simulations
• Generator of spatial evolution of the electromagnetic field
• Pump Depletion in Parametric Amplification
• Theory of Multimode Squeezed Light Generation in Lossy Media
• Distinguishability in quantum interference with the squeezed states
• Exact solution for a class of quantum models of interacting bosons

Cited by in corpus (1)

• Exact State Evolution and Energy Spectrum in Solvable Bosonic Models