Independent electrical control of two quantum dots coupled through a photonic-crystal waveguide

TL;DR

This paper demonstrates independent electrical control of two quantum dots coupled via a photonic-crystal waveguide, enabling scalable multi-emitter quantum photonic systems with coherent interactions.

Contribution

It introduces a method to individually tune and probe two quantum dots in a waveguide, advancing solid-state quantum emitter integration.

Findings

Successful individual electrical tuning of two quantum dots.

Observation of coherent coupling signatures between emitters.

Ability to perform spectroscopy on one emitter using the other.

Abstract

Efficient light-matter interaction at the single-photon level is of fundamental importance in emerging photonic quantum technology. A fundamental challenge is addressing multiple quantum emitters at once, as intrinsic inhomogeneities of solid-state platforms require individual tuning of each emitter. We present the realization of two semiconductor quantum dot emitters that are efficiently coupled to a photonic-crystal waveguide and individually controllable by applying a local electric Stark field. We present resonant transmission and fluorescence spectra in order to probe the coupling of the two emitters to the waveguide. We exploit the single-photon stream from one quantum dot to perform spectroscopy on the second quantum dot positioned 16$\mu$m away in the waveguide. Furthermore, power-dependent resonant transmission measurements reveals signatures of coherent coupling between the emitters. Our work provides a scalable route to realizing multi-emitter collective coupling, which has inherently been missing for solid-state deterministic photon emitters.

Full text

††preprint: APS/123-QED

A challenge of modern quantum photonics is to scale up deterministic solid-state photon-emitter systems in order to couple multiple emitters. The challenge pertains to the inherent inhomogeneities of the systems, e.g., self-assembled quantum dots (QDs) suffer from significant morphological inhomogeneities during growth, resulting in spectral deviations of the individual emitters. Moreover spatial variations within photonic nanostructures imply different Purcell enhancement factors and therefore emitted photon wavepackets Lodahl:15 . Similar challenges are found for other solid-state quantum emitters compatible with photonic nanostructures including organic molecules Faez:14 or single-defect centers Sipahigil:16 . Previous work on these platforms include the realization of high-quality single-photon sources Chu:17 ; Uppu:20 , entangled photon pairs Liu:19 , spin-photon interfaces Gao:12 , and coherent nonlinear optics Hwang:09 ; Javadi:15 ; Liang:18 .

Recent progress has focused on scaling these systems up and coupling multiple emitters. Most previous work has considered quantum emitters in bulk samples, where high-quality photon-photon interference Zhai:22 and near-field dipole-dipole coupling Trebbia:22 have been realized. In photonic nanostructures, super- and subradiant coupling through a cavity/waveguide was recently observed Evans:18 ; Tiranov:23 , however independent tuning of each emitter as required for scalability was not yet achieved. Various tuning mechanisms have been implemented based on strain Grim:19 , magnetic field Tiranov:23 , and electric field Papon:22 . The latter work realized independent tuning of QDs that were electrically isolated by etching shallow trenches into the device enabling quantum interference between two different waveguide single-photon sources.

Here, we extend the multi-emitter work and realize independent tuning of QDs efficiently coupled to the same photonic crystal waveguide (PhCW), cf. schematic illustration in Fig. 1a. PhCWs are excellent quantum photonic platforms, enabling near-unity light-matter coupling Arcari:14 by suppressing emission into free-space Mango:07 over a broad wavelength range, and enabling near-transform-limited optical transitions when the emitters are embedded in a p-i-n diode Pedersen:20 . We realize a PhCW device that is divided into two halves by etching a 100 nm wide and   50 nm shallow trench into the p-doped layer, whereby two halves are electrically isolated and therefore individually Stark tunable Bennett:10 ; Kirsanske:16 , as controlled by gate voltages $V_{1}$ and $V_{2}$, respectively. The trench is designed to have a minimal effect on the optical waveguide mode, which is consistent with the fact that no optical scattering is observed when imaging the trench region of the waveguide. The demonstrated approach could readily be extended to control additional QDs and therefore provides a route of scaling up the platform. We present resonant fluorescence and resonant transmission data while individually tuning each QD resonance frequency and implementing selective optical excitation.

We start by demonstrating independent electrical tuning of QDs within the same PhCW by measuring the emitter resonance frequency as a function of an externally applied gate voltage. The QDs are optically excited with a tunable continuous wave (cw) laser: i) either directly through the waveguide in a resonant transmission (RT) experiment, in which case both emitters are simultaneously excited via the guided mode or ii) each QD is selectively excited from free-space in a resonance fluorescence (RF) experiment. In both experimental configurations, shallow-etched gratings Zhou:18 are used to efficiently couple light out from the waveguide mode, as sketched in Fig. 1a.

We begin by acquiring an RT spectrum to first identify the QDs that efficiently couple to the waveguide Thyrrestrup:18 . We show an exemplary transmission map in Fig. 1b, where scattering from the emitters results in an extinction of the detected signal as these photons are predominantly reflected Turschmann:19 . For this measurement, the gate voltage on the left section of the PhCW $\mathrm{V}_{1}$ is held constant, while $\mathrm{V}_{2}$ on the right-hand side is varied. Indeed, we observe that by varying $V_{2}$, only the transition resonances associated with QD2 tune, while those of QD1 remain constant, i.e. they appear as horizontal lines in Fig. 1b. That is, the device enables individual electrical tuning of the QDs, allowing to bring individual emitters into mutual resonance, as highlighted by the green dashed curve. Note that these two QDs are separated by $15.7\pm 2\mu m$ (see the SM ), corresponding to 22 $\pm$ 2 times the wavelengths in the PhCW for the estimated group velocity in the waveguide of 2 ($\pm 0.6$)$\times 10^{7}$.

Two resonances, associated with the in-plane orthogonal transition dipoles of InAs QDs Lodahl:15 , appear as parallel extinction lines for each emitter. For each QD, we select one transition (dashed green region in Fig. 1b), detune the other QD and measure RT for different excitation strengths. Figures 1c and d present the power-dependent normalized transmission $I_{\mathrm{RT}\left(0\right)}$ (see inset) for the two QDs, where the subscript [math] indicates that the emitter detuning is zero, here plotted against the Rabi frequency $\Omega_{p}$ (see SM for details). In both cases, the extinction decreases as the excitation power increases, as expected from theory (solid curves; see SM for more details on the model) Novotny:06 . We extract that both QDs are efficiently coupled to the PhCWs, with coupling coefficients $\beta_{1}=0.85\pm 0.05$ and $\beta_{2}=0.78\pm 0.09$, while residual slow spectral diffusion limits their coupling, see SM for full QD parameters. These results therefore demonstrate that the addition of a shallow trench allows us to electronically address QDs independently within the same waveguide mode.

To address each QD individually, we excite the QDs from free-space as shown in the insets of Fig. 2a and c. The excited QD1 emits a stream of single photons into the waveguide, which travels through the waveguide and scatters coherently off the second QD2. The signal, $I_{\mathrm{RF}}$, is measured at the output port on the right after QD2. The system is operated at a relatively high excitation intensity (Rabi frequency $\Omega_{p}=0.16$ GHz, or 3.3 photons per lifetime) in order to combat the effect of residual spectral diffusion, i.e. power broadening is also observed. We start by considering QD1 as the photon source. The single photons are emitted by QD1 resonantly excited at the laser frequency $\nu_{\mathrm{p}}$ and travel in both directions in the waveguide. We record photons traveling towards the right after they interact with QD2 by measuring $I_{\mathrm{RF}}$. Figure 2a shows a map of the signal as a function of the laser-QD1 detuning ($\nu_{\mathrm{p}}-\nu_{1}$) and QD1-QD2 detuning ($\nu_{1}-\nu_{2}$), of which the latter is voltage-controlled. When the two QDs are detuned, we measure $I_{\mathrm{RF}}=1$ kcnts/s and observe a linewidth of $0.49\pm 0.03$ GHz in Fig. 2b (green curve). When QD2 is tuned into resonance with QD1, it coherently reflects photons, leading to an extinction of the transmission. This effect can be seen in the cross-section data along the dashed blue line in Fig. 2a, which is plotted in blue in Fig. 2b. In this configuration, the recorded signal is independent of the phase lag associated with propagation between the two QDs, since this constitutes a global phase shift not affecting the intensity measurements (See SM for more information).

A second and more complex scenario arises when QD2 acts as the single-photon source; here the measured signal is comprised of both the photons that are initially emitted to the right by QD2 and those reflected by QD1, as illustrated in the inset to Fig. 2c. Given the coherence of the photons scattered by QD1, the relative phase gain on the round trip between the emitters, $2\Delta\varphi$, as determined by the separation of the QDs, directly influences the $\mathrm{I}_{\mathrm{RF}}$ signal, as seen in Fig. 2c and d. A complex Fano-like lineshape in $\mathrm{I}_{\mathrm{RF}}$ is observed when both QDs are tuned into resonance (see blue curve in Fig. 2d), and the data are consistent with an overall phase separation of $\Delta\varphi\simeq 200\pi/180$, which sensitively determines the spectral shape of the signal, see SM for the analysis. This phase separation determines the dispersive/dissipative character of collective interaction between coherently coupled emitters Chu:22 . The present experiment demonstrates coherent scattering on a single quantum emitter of single photons emitted by another emitter.

Finally, we return to the original RT configuration as shown in Fig. 1a, tune both QDs into resonance and study the saturation behavior of the device. The joint resonance is probed at different excitation powers and the resultant photon flux-dependent transmission is plotted in Fig. 3a. As is the case for a single emitter Hwang:09 ; Javadi:15 ; jeannic:21 , the extinction decreases non-linearly with increasing excitation flux, as the emitter saturates. For the two-QD system, a peak extinction of about 0.5 is observed, which is stronger than the single-emitter response (dashed curves in Fig. 3a).

We overlay the modelled transmission of the two-QD system in the case where the emitters are uncoupled (purple curve) and coherently coupled (cyan curve) in Fig. 3a. Here, the system parameters extracted from earlier experiments (c.f. Table I in SM ) and $\Delta\varphi\simeq 200\pi/180$ are used without any additional adjustable parameters and remarkably good agreement between theory and experiment is observed (see SM for further details). We observe that the data best agree with the predictions for a coupled system, suggesting that the QDs couple via the PhCW mode. This is reinforced by the individual RT spectra, an example of which is shown in Fig. 3b for the case of $\Omega_{p}=0.05$ GHz. Here, the measured spectrum (circular markers) is overlayed with predictions for both the coupled and uncoupled system (showing the response of the individual QDs as dashed curves), observing that the uncoupled emitter theory overestimates the total extinction.

We have presented a quantum photonic system consisting of a PhCW that has been trenched to create two separate diode regions, each of which contains an efficiently coupled, high-quality QD. We are consequently able to address each QD separately, both with a local electric Stark field and with multiple optical excitation pathways. The system constitutes a versatile platform for multi-emitter experiments and technologies. Using this platform, we observe coherent scattering from both QDs, both when one is excited from free-space, and when both simultaneously interact with photons travelling through the guided mode. Our system therefore opens a window to the rich physics of cooperative quantum light-matter interactions in multiple-emitter systems.

This integrated platform can be readily scaled, for example by trenching the PhCW into additional sections, hence facilitating independent electric control of multiple emitters within the same waveguide. The approach paves a scalable route towards realizing many-emitter coherent and deterministic radiative coupling enabling creating scalable sub- or super-radiant collective quantum states Asenjogarcia:17b ; Albrecht:19 , accessing decoherence free sub-spaces for quantum computation Paulisch:16 or to realize complex photonic cluster states for quantum communications Economou:10 .