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-pumpphoton regime of nonlinear quantum nanophotonics. Applying this unified analytic approach to 1D χ (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 χ (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.

Onset of non-Gaussian quantum physics in pulsed squeezing with mesoscopic fields

“…Interestingly, the multimode case exhibits a fractional asymptotic scaling of R(t) ∼ t 3/2 at t → 0, which is qualitatively different from the polynomial scaling R(t) ∼ t 2 of the single-mode model. Such scaling differences highlight the effects of multimode physics intrinsic to pulse propagation [64]. In fact, using the GIF approximation, we can analytically derive that R(t) ≈ 2t 3/2 /3 √ 2π regardless of the pulse shape, under appropriate conditions (see Appendix A for details), which shows excellent agreement with the MPS simulation.…”

“…Having formulated a tractable quantum model using GIF-principal supermodes, we now proceed to study how non-Gaussian quantum dynamics can affect the generation of pulsed squeezed light in the mesoscopic regime [67][68][69][70], where the number of photons involved is neither very large (which falls under an undepleted-pump approximation) nor very small (which results in highly quantum behavior qualitatively different from squeezing [29,64,71]). Experimentally, this would correspond to situations in which considerable (anti-)squeezing (e.g., ∼ 15 dB) can be generated with only dozens to hundreds of pump photons.…”

“…For a given material, scaling the waveguide geometries with respect to the operating wavelength results in η ∼ λ −4 SH and L χ (2) ∼ λ 10/3 SH , whose strong scaling with λ SH motivates operations in the regime of shorter wavelength to enhance nonlinearity [27,64]. Towards this end, a recent experiment at λ SH = 456.5 nm on PPLN nanophotonics has demonstrated conversion efficiency as high as η = 330 W −1 cm −2 (33 000 %W −1 cm −2 ) [79], which, assuming an advanced dispersion engineering |k FH | = 1 fs 2 mm −1 , leads to L eff = 1.4 cm.…”

Towards an Engineering Framework for Ultrafast Quantum Nonlinear Optics

“…[41][42][43] Our work in this domain of quantum optics has been strongly inspired by these continuum-limit fundamental models, whereas our central objective is to build up, from these fundamental models, an "abstraction stack" of numerical and modeling methodologies at varying levels of generality. As an initial foray, we discuss in this section our recent work on studying few-photon parametric downconversion in highly nonlinear waveguides, 44 where we find a striking analogy between these strongly-interacting few-photon dynamics and the physics of Fano-type discrete-continuum interactions. 45,46 By exploiting this analogy, we not only derive complete analytic expressions for system eigenstates under this subspace of the continuum Hamiltonian, but we also discover and can intuitively explain various exotic quantum features such as complete pump depletion and Rabi-like oscillations with subpolynomial decay.…”

“…These findings echo the well-known fact that phase-mismatch is a critical parameter in nonlinear optics, but with the somewhat surprising conclusion that unit-efficiency PDC occurs in the limit of large phase mismatch, contrary to conventional physical intuition that such interactions are most efficient at resonance. Furthermore, the Fano analogy is surprisingly general and can provide intuition about physics on a "system" level as well: 44 for a pair of coupled nonlinear waveguides, Fano interferences among multiple discrete-continuum interactions can lead to characteristic Fano lineshapes and the formation of a bound state in the continuum. 54 Finally, although the phenomenology of broadband few-photon PDC is not intrinsically a pulsed effect-that is to say, the Fanotype physics are not fundamentally different for pulsed vs. continuous-wave inputs 44 -such exotic dynamics only arise by virtue of the highly multimode/broadband nature of the signal field in this continuum limit.…”