A Broadband Nanowire Quantum Dot Cavity Design for the Efficient Extraction of Entangled Photons

Abstract

A bright source of on-demand entangled photons is needed for quantum networks. A single quantum dot in a site-selected nanowire waveguide is a promising candidate for realizing such sources. However, such sources are associated with poor single-photon indistinguishability, limiting their applicability in quantum networks. A common approach for enhancing the single-photon indistinguishability in quantum dot-based entangled photon sources is to implement a broadband optical cavity. Achieving a high-Purcell cavity while retaining the advantages of the nanowire, such as directional emission, a broad operational bandwidth, and high light extraction efficiency, has been a significant challenge. Here, we propose a nanowire cavity based on quasi-bound states in the continuum formed by the strong coupling of two resonant optical modes. We numerically predict this design to support a cavity mode with 4 nm bandwidth and a Purcell enhancement of $\sim$17. This cavity mode enables a directional far-field emission profile (88% overlap with a Gaussian) with a light extraction efficiency of $\sim$74%. Our solution opens up a route for generating entangled photon pairs with enhanced extraction efficiency and single-photon indistinguishability for the practical realization of quantum networks.

Figures (6)

• Figure 1: (a) Schematic of the quasi-BIC cavity, consisting of a QD in a NW on a gold mirror. (b) E-field profile of the vertical NW cross-section ($\hat{x}-\hat{z}$ plane) with height (H) of 1375 nm and diameter (D) of 420 nm. (c) Simulated Purcell enhancement as a function of wavelength. (d) Far-field radiation pattern of the NWQD quasi-BIC cavity.
• Figure 2: (a) Purcell enhancement as a function of wavelength for a nanowire with diameter 420 nm, equipped with a bottom gold mirror and a QD emitter placed on-axis at 30 nm below the top. As the height of the nanowire is increased from 1200 nm to 1500 nm, two resonances labeled A and B undergo strong coupling leading to the formation of an avoided crossing at point C. The maximum Purcell enhancement is obtained at this point C due to the formation of a quasi-BIC. (b), (c) and (d) show the electric field intensity of the resonances labeled A, B and C, respectively at the vertical cross-section of the nanowire.
• Figure 3: Purcell factor as a function of wavelength and scaling factor ($\mathrm{s}$). The quasi-BIC resonance occurs at the wavelength with the highest Purcell factor. To determine the cavity dimensions for a target wavelength, a corresponding scaling factor (s) can be found from this plot. The cavity dimensions can be calculated as $\mathrm{H'}=\mathrm{s.H}$ and $\mathrm{D'}=\mathrm{s.D}$ where D and H correspond to a design wavelength of 900 nm. The avoided crossings formed at 940 nm and 870 nm for scaling factors 1.035 and 0.965, respectively (indicated by dashed circles) are shown in the side panels.
• Figure 4: (a) Purcell enhancement as a function of wavelength for a nanowire with D = 420 nm placed on a gold mirror with the QD on the NW axis located 30 nm from the top. As the height of the nanowire is varied from 350 nm to 2.1 $\mu m$, 6 occurrences of the quasi-BIC condition can be observed (dashed white circles). (b) With the same nanowire diameter and QD location, in the absence of the bottom mirror, the number of quasi-BIC occurrences is reduced to 3. (c) Far field radiation profiles of all the quasi-BIC modes as a function of height with and without a bottom gold mirror. The radiation pattern without a bottom mirror corresponds to multipoles of increasing order, starting with a quadrupolar pattern at H=470 nm. However, in the presence of a bottom mirror, the radiation pattern was found to become more convergent with increasing nanowire height. Among all the radiation patterns, the one corresponding to H=1380 nm, is the most directional.
• Figure 5: (a) Bottom-up nanowire growth often results in a top crown (shown in inset) instead of a flat top. For the optimal dimensions (D=1375 nm and H= 420 nm), the crown height is varied and the Purcell enhancement is plotted as a function of wavelength and crown height. (b) In top-etched nanowires, there is a significant chance of off-axis QD placement (shown in inset). Purcell enhancement has been plotted against wavelength for QD displacements of up to 100 nm.