Integrable cascaded frequency conversion using the time rescaling shortcut to adiabaticity

Abstract

In this letter we explore how full frequency conversion can be performed in shorter, integrable devices by using a STIRAP-like protocol modified by the time rescaling shortcut to adiabaticity. We show how the coupled equations for two simultaneous three-wave mixing processes can be written in terms of a STIRAP-like system, which creates robust conversion, albeit requiring long propagation distances inside a bulk crystal or waveguide. We then discuss how the time rescaling (TR) method can be modified to be applied in optical systems, then apply it in the conversion process to create a TR-STIRAP protocol, showing that full conversion is also obtained, but at a fraction of the propagation distance. We also show how the original shaping of the coupling coefficients required by the TR-STIRAP can be approximated by gaussian functions with high conversion fidelity, thus simplifying the experimental implementation. This protocol has the potential to be used in several areas, including the integration of photon sources and efficient detectors for quantum key distribution.

Figures (4)

• Figure 1: Conceptual representation of the cascaded conversion process: a pump and reference fields impinge upon a nonlinear crystal with two different spatial gratings. The cumulative result is to convert $\omega_{p} \rightarrow \omega_{+}$, while amplifying the reference field $\omega_{-}$.
• Figure 2: (a). Gaussian coupling coefficients created with engineered periodic pollings of the nonlinear crystal. We considered a crystal size of 80 mm and used d = L/10 and $\sigma = L/6$, $L$ being the length of the nonlinear crystal. (b). Nonlinear STIRAP-like conversion process: full conversion is achieve at long propagation distances (about 60 mm).
• Figure 3: Coupling coefficients and the frequency conversion process under the time-rescaling shortcut. 1(a). Contraction parameter $a=2.0$, 1(b) $a=5.0$ and $a = 10.0$. Notice that a larger $a$ require shorter variations of the coupling coefficients, with higher peak intensities. Full conversion process happens at $z/a$ of the original propagation distance.
• Figure 4: Fidelity of the frequency conversion process under simplified coupling coefficients. The gaussian approximation is equally effective for a wide range of contraction parameters. The blue curve represents the phase-match situation and the orange one, the situation with mismatch $\Delta = \kappa_{0}$.