Degenerate squeezing in waveguides: a unified theoretical approach

Abstract

We consider pulsed-pump spontaneous parametric downconversion (SPDC) as well as pulsed single-and dual-pump spontaneous four-wave mixing processes in waveguides within a unified Hamiltonian theoretical framework. Working with linear operator equations in k-space, our approach allows inclusion of linear losses, self-and cross-phase modulation, and dispersion to any order. We describe state evolution in terms of second-order moments, for which we develop explicit expressions. We use our approach to calculate the joint spectral amplitude of degenerate squeezing using SPDC analytically in the perturbative limit, benchmark our theory against well-known results in the limit of negligible group velocity dispersion, and study the suitability of recently proposed sources for quantum sampling experiments. arXiv:1910.06873v2 [quant-ph] 23 Oct 2019 [1] R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, and J. F. Valley. Observation of squeezed states generated by four-wave mixing in an optical cavity. Phys. Rev. Lett.,

Beyond photon pairs: Nonlinear quantum photonics in the high-gain regime

“…In fact, as we show in Appendix G, whether due to waveguide SPDC, single-pump SFWM, or dual-pump SFWM, coupled operator equations for generating NDSV states can be placed in this general form. Similarly, as shown by Helt et al [93], coupled operator equations for SPDC, single-pump SFWM, or dual-pump SFWM generating DSV states in waveguides can be written in the form…”

“…In this section, following [93] and [94], we present a general formalism for considering degenerate as well as non-degenerate squeezing in waveguides where either a second-or third-order nonlinearity is dominant. The six nonlinear optical processes that this includes are spontaneous parametric downconversion (SPDC), single-pump spontaneous four-wave mixing (SFWM), and dual-pump SFWM for the creation of degenerate squeezed vacuum (DSV) states such as those in Section III E as well as SPDC, single-pump SFWM, and dualpump SFWM for the creation of non-degenerate squeezed vacuum (NDSV) states such as those in Section III F. Beginning with Hamiltonians of the form presented in Section II, suited to integrated photonics structures, we find that the Heisenberg equations of motion, in the limit of strong classical pumps and the undepleted pump approximation, lead to the expected classical coupled mode equations for the pump fields, as well as coupled operator equations for the generated fields.…”

Fast Simulation of Bosonic Qubits via Gaussian Functions in Phase Space

“…While passive Gaussian transformations can be effected in optics using phase shifters and beam-splitters, and while squeezing applied to vacuum can be achieved with nonlinear cavity resonators [62] or waveguides [63], inline squeezing-squeezing applied directly to an arbitrary input state-poses a greater challenge. A feasible approach to inline squeezing is possible by consuming an ancillary squeezed vacuum state [20].…”

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

“…Intuitively, Φz and Ψz are continuum analogues of â and b, respectively, and their commutation relations [ Φz , Φ † z ] = [ Ψz , Ψ † z ] = δ(z − z ) reflect the continuous nature of the photon-polariton fields they annihilate. For a χ (2) nonlinear waveguide, the dynamics of these quantum fields (in a frame comoving with the signal) are generically gov-erned by a Hamiltonian [31,[57][58][59][60]…”