Realization of a tunable fiber-based double cavity system

Tunable cavities have proven to be highly attractive systems in cavity quantum electrodynamics thanks to their performance and flexibility. The possibility to form a cavity around any emitter while simultaneously spectrally matching the chosen transitions makes these cavities an important tool in photonic quantum technology. In this paper, we report on the experimental realization and theoretical description of a fiber-based resonator with two spatially and spectrally distinct cavity modes. The careful design of the structures was performed via finite-element simulations. Thanks to the intrinsic tunability of the system, one mode can be brought in resonance with the second one, forming a supermode resulting in a hybridized two-mode pattern in the emission spectrum. For its realization, we combine a monolithic bottom cavity, formed by two distributed Bragg reflectors, with a top movable fiber mirror forming an externally tunable cavity mode. When tuning the top cavity in resonance with the monolithic bottom one, the cavity modes exhibit a pronounced anticrossing behavior typical for mode hybridization. Differently from a standard open cavity, when embedding single emitters—in this case, InGaAs quantum dots—in the structure, the Purcell factor is not uniform for each wavelength. Furthermore, we find a strong influence of the simulated Purcell factor, as well as of the measured light extraction, depending on the placement of the emitter in the top or in the bottom cavity. The discussed two-mode cavity could be employed for simultaneously Purcell-enhancing multiple transitions of an emitter while preserving the single-photon nature of the emitters inside the device.

Figure 1

Schematic picture of the investigated double cavity structures. The device is based on two coupled cavities: one monolithic part—the bottom cavity—formed by two distributed Bragg reflectors (bottom and middle DBRs) with a GaAs cap spacer, and an open cavity—the top cavity—utilizing the middle DBR of the monolithic sample as well as a high-reflection coated end facet of an optical fiber as the top mirror. In the proper configuration a supermode can manifest between both cavities leading to hybridization of the two cavity modes. Two cases are here investigated, namely, when the quantum dot emitters are placed in the bottom [emitter position (pos) 2] or in the top (emitter position 1) cavity, respectively. In both configurations, the emitters, in this case quantum dots, are optimally placed in the electric-field maximum of the respective cavity.

Figure 2

Calculated quality factors of the double cavity structure for various different cavity lengths of the upper cavity. In the anticrossing region the Q factor is highly sensitive to the wavelength. Maximum Q factors of 100 000 can be achieved. Each depicted data point corresponds to a mode-field simulation. Exemplary mode profiles: For (a) and (b), light is mainly confined in the upper cavity; in (c) and (d), light is confined in the upper and lower cavities forming a supermode; and (d) and (e) depict higher-order transverse modes. Quality factors corresponding to (a)–(e) can be found in Table 1.

Figure 3

Simulations [(a) and (c)] and experimental data [(b) and (d)] for a double cavity with 32 bottom, 9 middle, and 11 top DBR pairs. The cavity length of both the bottom and the GaAs part of the top cavity is set to the wavelength $\lambda$: For In(Ga)As quantum dots emitting around 900 nm, this results in a thickness of $\approx 260$ nm. (a) and (b) show simulations for the expected intensity (product of calculated Purcell factor multiplied by the incoupling efficiency to the fiber) and corresponding experimental photoluminescence data for emitters implemented in the top cavity. (c) and (d) display simulation and experimental data, respectively, for emitters placed in the bottom cavity. For the measurement data [(b) and (d)], several spectra were acquired while increasing the length of the upper cavity (Up. Cav.) with nanometric resolution. Each horizontal line of the contour plot corresponds to a spectrum for a given cavity length. The respective intensities are color coded in a logarithmic scale for better visibility. Longitudinal and transversal modes can be clearly distinguished by their brightness and resemble the simulation data. Furthermore, the anticrossing regime is well pronounced. The black dashed lines are a guide to the eye for different cavity modes, $q$ being the longitudinal mode number, in order to determine the effective cavity length. The black arrow in (b) indicates the separation of longitudinal modes for a single cavity ($\sim 50$ nm for the given cavity length). In contrast, the simulated (c) and experimentally achieved (d) mode separation is around 10 nm for the given geometry. The white dashed line in (d) indicates the position of the spectrum in subplot (e). Here, an exemplary spectrum is shown, indicating once again the mode separation as well as the Q factors of the longitudinal modes forming the supermode. Quality factors for the selected positions (a*, c*, f*, and g*) can be found in Table 1.

Figure 4

Measurement data of an open cavity with 30 pairs of bottom DBRs, 12 pairs of middle DBRs, and 11 pairs of top DBRs. The bottom cavity is fabricated with a GaAs layer corresponding to $2.4\lambda$, while the top GaAs layer is chosen to be $1\lambda$ for an emitter of $\lambda =900$ nm in vacuum. The cavity is formed around a preselected InGaAs quantum dot placed in the top cavity. (a) Vertical scan of the fiber similar to the ones in Fig. 3. The bright vertical lines correspond to transitions of the embedded emitter. (b) For comparison, an artificial spectrum constructed out of the sum of the individual spectra in (a) is shown as a red line, and a reference spectrum of the quantum dot before placing it inside the cavity is shown in black. While the spectral features of the emitter transitions are still observable, the intensity distribution is modified due to a different light enhancement in the cavity structure. The brightness variation is consistent with the simulations in Fig. 3, where the Purcell enhancement is expected to be low in the anticrossing region and high outside. A small offset in wavelength arising from the usage of two different gratings has been accounted for. (c) Hanbury Brown and Twiss measurement performed for the quantum dot transition at 905.5 nm, revealing a second-order correlation value of $g^{\left(2\right)}\left(0\right)=0.11\pm 0.02$.