Broadband Parametric Downconversion as a Discrete-Continuum Fano
Interaction
- URL: http://arxiv.org/abs/2009.01457v1
- Date: Thu, 3 Sep 2020 05:33:23 GMT
- Title: Broadband Parametric Downconversion as a Discrete-Continuum Fano
Interaction
- Authors: Ryotatsu Yanagimoto, Edwin Ng, Marc P. Jankowski, Tatsuhiro Onodera,
Martin M. Fejer, Hideo Mabuchi
- Abstract summary: We introduce a theoretical framework based on Fano's theory of discrete-continuum interactions.
We find a host of remarkable dynamical features due to the coupling of a discrete pump state to the signal continuum.
We show that the framework can be applied to higher-order parametric processes such as parametric three-photon generation.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- 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.
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