Broadband Parametric Downconversion as a Discrete-Continuum Fano Interaction

Abstract

We introduce a theoretical framework based on Fano's theory of discrete-continuum interactions to analyze the quantum dynamics of broadband parametric downconversion (PDC) in the few-pump-photon regime of nonlinear quantum nanophotonics. Applying this unified analytic approach to 1D ${\chi }^{(2)}$-nonlinear waveguides, we find a host of remarkable dynamical features due to the coupling of a discrete pump state to the signal continuum, from unit-efficiency (i.e., complete) downconversion when the coupling is dissipative, to Rabi-like oscillations with sub-exponential decay when it is dispersive. The theory provides a straightforward way to analytically compute a full characterization of the PDC dynamics, including the complete eigensystem of the continuum Hamiltonian and expressions for the signal biphoton correlation function. We also apply the theory to study a pair of linearly coupled ${\chi }^{(2)}$ waveguides, where two discrete pump states simultaneously downconvert into a common-mode signal continuum, resulting in Fano interference that critically affects the PDC rate. Under appropriate conditions, the theory predicts characteristic Fano lineshapes and even complete destructive interference resulting in the full suppression of PDC, due to the formation of a bound pump state in the continuum. Generalizing further, we show that the framework can also be applied to higher-order parametric processes such as parametric three-photon generation, and we also find numerical signatures that Fano-type interactions occur even for multi-photon PDC under stronger pumping. Our results establish broadband PDC as yet another physical system natively exhibiting Fano-type interactions and advance a theoretical framework in which to understand the complicated quantum dynamics of strongly nonlinear broadband quantum optics.

The first two authors contributed equally to this work; 22 pages, 10 figures

References in corpus (13)

• Experimental quantum teleportation
• Photonic quantum technologies
• Metasurfaces with maximum chirality empowered by bound states in the continuum
• Climbing the Jaynes-Cummings Ladder and Observing its Sqrt(n) Nonlinearity in a Cavity QED System
• A bright, pulsed two-mode squeezer
• Perspective: Toward large-scale fault-tolerant universal photonic quantum computing
• Crystallization of strongly interacting photons in a nonlinear optical fiber
• Simple and efficient quantum key distribution with parametric down-conversion
• Bound states in the continuum in a single-level Fano-Anderson model
• Fermionic statistics suppresses Fano resonances
• Shortcuts to adiabaticity in the presence of a continuum: applications to itinerant quantum state transfer
• Quantum Theory of Light in a Dispersive Structured Linear Dielectric: a Macroscopic Hamiltonian Tutorial Treatment
• Spectral Effects of Strong Chi-2 Non-Linearity for Quantum Processing