A Hybrid (Al)GaAs-LiNbO$_3$ Surface Acoustic Wave Resonator for Cavity Quantum Dot Optomechanics

A hybrid device comprising a (Al)GaAs quantum dot heterostructure and a LiNbO$_3$ surface acoustic wave resonator is fabricated by heterointegration. High acoustic quality factors $Q>4000$ are demonstrated for an operation frequency $f\approx 300$ MHz. Frequency and position dependent optomechanical coupling of single quantum dots and the resonator modes is observed. Finally, fingerprints of cavity-mediated non-linear optomechanical coupling are detected for high acoustic pump levels.

Our device is fabricated by heterointegration of a (Al)GaAs heterostructure containing a single layer of droplet etched QDs onto a conventional single port LiNbO3 SAW resonator device 24 . A schematic of our device is shown in Figure 1 (a). The SAW resonator is patterned onto an oxygen-reduced 128° rotated Y-cut LiNbO3-x substrate. The resonator is formed by two metallic floating electrode acoustic Bragg-reflectors (150 fingers, aperture = 350 µm, nominal mirror separation = 4522 µm) and is aligned along the X-direction. The phase velocity of the SAW is %&',) = 3990 m/s along this direction. The nominal acoustic design wavelength and frequency are ̅ * = 13.3 µm and ̅ * = 300 MHz, respectively. The resonator is excited by applying an electrical rf signal of frequency +, to a 41 fingers interdigital transducer (IDT). The acoustic Bragg mirrors and the IDT are patterned during the same electron beam lithography step and finalized using a Ti (5 nm) / Al (50 nm) metallization in a lift-off process. The IDT is positioned off-center, close to one Bragg mirror and the large open area is used for the heterointegration of the III-V compound semiconductor film. Figure 1 (b) shows the rf reflectivity of our resonator device measured with the IDT at T = 300 K. In this spectrum we can identify nine pronounced phononic modes, which are consecutively numbered. The measured complex reflection $$ ( ) can be fitted by 25

Equation 1
In this expression .,* anddenote the internal and external quality factor of mode and external circuit, respectively. * is the resonance frequency of the -th mode. We find a mean H . = 2900 ± 700 (Δ HHHH = 100 ± 20kHz) and ̅ * = 296 MHz at room temperature. The given values are the mean of the distribution and their standard deviation of the mean. The full analysis is included in the supplementary material. These modes are split by the free spectral length -/012 = 416 ± 25 kHz. This value corresponds to cavity roundtrip time of 3 = $ 4%5 = 2.41 ± 0.15 µ and an resonator length 3 = 3 !"#,% !4%5 = 4800 ± 50 µm. The penetration length of the acoustic field into the mirror is given by 0 = | 6 | V = 145 µm, where = 3.3 µm is the width of the fingers of the mirror and 6 = 0.023 is the reflectivity coefficient of one finger 25,26 .
Using the lithographically defined , we calculate a resonator length + 2 0 = 4810 µm, which agrees well with the value derived from the experimental data. The heterointegration is realized by epitaxial lift-off and transfer onto a 50 nm thick and 3000 µm long Pd adhesion layer [27][28][29][30][31] . The heterostructure was grown by molecular beam epitaxy and consists of a 150 nm thick Al0.33Ga0.67As membrane with a layer of strain-free GaAs QDs 32 in its center. The membrane was heterointegrated onto the LiNbO3 SAW-resonator by epitaxial lift-off and transfer as described in Ref. 29 A transmission electron microscope (TEM) image of the LiNbO3-Pd-(Al)GaAs stack is shown in Figure 1 (a). The semiconductor membrane is laterally placed in the center of the resonator. After transfer, the membrane is etched to obtain straight edges and, thus, reduce scattering losses. The final membrane is 215 µm wide and extends over the full width of the resonator. Further details on the heterostructure and a optical micropcopy image are included in the supplementary material. The resonator mode spectrum after transfer recoded at T = 300 K is shown in Figure 1 (c) and is analyzed using Equation 1. The full analysis is also part of the supplementary material. By comparing these data to those before transfer we find that the mode spectrum and remain approximately constant within the experimental error at ̅ * = 295.8 MHz and 728+.9 = 406 ± 22 kHz. The corresponding cavity roundtrip time is 3,728+.9 = 2.46 ± 0.13 µs. Most importantly, high internal quality factors of H . = 2500 ± 300 (Δ HHHH = 120 ± 15 kHz) are preserved after transfer, which is of highest relevance for strong phonon-exciton coupling. Furthermore, all experimental data is well reproduced by finite element modelling (FEM) detailed in the supplementary material. For example, the experimental change of 3 after heterointegration of Δ 3 = 50 ns is in excellent agreement with 60 ns predicted by FEM. Furthermore, the reduction of the effective phase velocity in the hybridized region to %&',-,, = 3889 m/s gives rise to a spectral shift of the mode spectrum of Δ * = 10.5 MHz to lower frequencies. Note, that according to these calculations the absolute mode index changes from :86,) = + 707 of the bare resonator to :86,-,, = + 726, for the hybrid device. Next, we investigate the optomechanical coupling of single QDs to the phononic modes of the resonator in Figure 2. We measure the optomechanical response at low temperatures ( = 10 K) by time and phase averaged micro-photoluminescence spectroscopy 15 detailed in the supplementary material. In essence, the detected lineshape is a time-average of the dynamic optomechanical modulation of the unperturbed, Lorentzian QD emission line 33 . In a first step, we apply a constant rf power of +, = 5 dBm to the IDT at ; = 300.25 MHz. The measured | $$ | is plotted as a function of +, in the inset of Figure 2 (a). The main panel shows emission spectra of two QDs, QD1 and QD2 with (red) and without (black) the SAW resonating in the cavity. The two QDs are separated by ≃ 21 µm ≃ 1.6 %&' along the cavity axis and exhibit completely dissimilar behavior. While QD1 shows a pronounced broadening when the SAW is generated, the lineshape of QD2, apart from a weak reduction of the overall intensity remains unaffected. These types of behaviors are expected for QDs positioned at an antinode (QD1) or node (QD2) of the acoustic cavity field, as illustrated by the schematic. In a second step, we keep the optical excitation fixed and scan the radio frequency +, applied at a constant power level over wide range of frequencies 285 − 315 MHz and record emission spectra of a single QD (QD3). These data are fitted with a time-integrated, sinusoidally modulated Lorentzian 29,33 of width and amplitude . .

Equation 2
In Equation 2, ) and Δ denote the center energy of the emission peak and the optomechanical modulation amplitude due to the time-dependent deformation potential coupling. From our established FEM modelling 29 we obtain an optomechanical coupling parameter 14,15 =/ = 2500 µeV/nm. Figure 2 (b) and (c) show the simultaneously recorded reflected rf power ( +-,>-31-9 ) and Δ as a function of +, . Clearly, QD3 exhibits a series of strong optomechanical modulation peaks at frequencies at which pronounced cavity modes are observed (grey shaded area). This observation of a pronounced coupling to resonator modes is a first direct evidence of cavity enhanced coupling between SAW phonons and the exciton transition of a single QD. However, the detected optomechanical response, Δ ( +, ), of QD3 exhibits noticeably less peaks that +-,>-31-9 . We Fast Fourier transform (FFT) +-,>-31-9 ( +, ) and Δ ( +, ) to obtain time domain information. The result of these Fourier transform is plotted in Figure 2   We continue studying this mode index selective coupling in more detail. In Figure 3 we investigate the +, -dependence of the optomechanical response of QD3 and another different dot, QD4, in (a) and (b), respectively. The main panels show the optomechanical modulation amplitude Δ derived from best fits of Equation 2 and the upper panels the simultaneously measured +-,>-31-9 . All data are plotted as a function of the frequency shift with respect to the center mode = 5. From these electrical data we obtain the low temperature value of the mean quality factor H = 4430 ± 1560, an increase by a factor of ≈ 1.75 compared to the room tempaerature value. QD3 shows a strong optomechanical response when modes with odd mode index = 5, 7 are excited. In contrast, QD4 couples to modes with even index = 4, 6, 8. The width of these resonances corresponds to an optomechanically detected quality factor ?@ HHHHH = 1730 ± 420 Δ ?@ HHHHHH = 890 ± 30kHz. This decrease compared to the electrically measured value may arise from the fact that the linewidth of the QD transition Δ ≫ 1 GHz exceeds the resonator modes' frequency. Moreover, the splitting between modes which optomechanically couple to the QD is doubled compared to the measured electrically, and consequently, the corresponding time is half of the cavity roundtrip time. The alternating coupling behavior can be understood well considering the position of nodes and antinodes of the acoustic fields of different modes in the center of resonator. The qualitative profiles of the = 4, 5 and 6 are shown in Figure 3 (c). Clearly, modes with even (odd) index exhibit nodes (antinodes). Thus, a single QD positioned at nodes or antinodes can be selectively coupled to modes with either even or odd mode index, and QD3 and QD4 are two representative examples for each case. This simple picture applies well to modes ≥ 4, while for ≤ 3 a more complex behavior is observed. For QD4, we observe a strong optomechanical response at ( ! − $ )/2 and for QD3 similarly at ( A − ! )/2. We argue that this spectral feature could arise from nonlinear frequency conversion. Since the optomechanical response is observed exactly in the center between the two electrically detected modes, we argue that its origin could be a conversion of two off-resonant phonons of the same frequency to two cavity phonons with frequencies of the two adjacent modes. This type of process may be expected since the optical linewidth of the QD is at least three orders of magnitude larger than the . Specifically, in the case of QD3 one possible process is the conversion of two SAW phonons with frequency ( A − ! )/2 to a pair of cavity phonons, the first of frequency ! and a second of frequency A .
Since this process is a two-phonon process, we expect -analogous to two-photon processes nonlinear optics -a quadratic dependence on the applied acoustic power. Figure 4 (a) compares the measured optomechanical response of QD3 for three different +, . The full analysis is included in the supplementary information. The reflected rf power is given as a reference in the upper panel. As +, increases the optomechanical modulation amplitude Δ of QD3 increases and, moreover, new features develop, which are not observed for low +, in Figure 3 (b). Most notably, at the highest power level applied to the IDT, i.e. maximum number of phonons injected into the resonator, +, = 16 dBm, we observe clearly resolved new features at ( B − A )/2 and ( C − ; )/2. Such +, -scans were recorded for nine different +, and we extracted the maximum of the optomechanical modulation amplitude Δ /:D at ( A − ! )/2 (1, black), ; (2, red) and E (3, blue). The data is plotted as symbols in semilogarithmic representation as a function of +, in Figure 4 (b) to identify power law dependencies. We assume that the acoustic power injected into the cavity scales linear with +, . Thus, in the case of deformation potential coupling, Δ /:D ∝ +, $/! for one-phonon processes 34 . Consequently, Δ /:D ∝ +, for two-phonon processes. The lines in Figure 4 (b) are linear fits to the data from which we are able to determine the power law for the three selected frequencies. Clearly, ( A − ! )/2 (1, black) shows a markedly larger slope $ = 0.84 ± 0.04 than ; (2, red), ! = 0.69 ± 0.03 and E (3, blue), A = 0.72 ± 0.015. Based on above arguments, the optomechanical coupling to modes = 5 (2) and = 7 (3) is indeed due to one-phonon processes. In contrast, the larger slope at ( A − ! )/2 (1) points towards a two-phonon process. In conclusion, we demonstrate the heterointegration of an (Al)GaAs based QD-heterostructure on a LiNbO3 SAW resonator. In our hybrid device we demonstrate strong optomechanical coupling between single QDs with the phononic modes of the SAW-resonator. Moreover, we identify fingerprints of nonlinear coupling in the dot's optomechanical response. Our platform represents an important step towards hybrid semiconductor-LiNbO3 quantum devices. In particular, our approach is fully compatible with emerging thin film LiNbO3 technology [35][36][37][38] and a wide variety of quantum emitters 39 . Moreover, it can be readily combined with electrical contacts 30 facilitating quasi-static Stark-tuning of the QD's optical transitions. Finally, small mode volume and high frequency (> 1 GHz) resonators may enable coherent optomechanical control in the resolved sideband regime which has been reached both for III-V QDs 13,40 and defect centers 10 . The demonstrated hybrid architecture promises a strong enhancement of the optomechanical coupling compared to traditional monolithic approaches 41 .
SFig 2 shows in (blue) the calculated phase velocity ./0,12*"%3 of the full stack as a function of acoustic frequency ./0 . Analogous calculations (not shown) have been performed for the LiNbO3 surface coated with 50 nm of Pd without the semiconductor. In addition, SFig 2 shows in (red) the optomechanical coupling parameter ,-for QDs located in the center of the membrane. v. Fitting procedure of data in Figure 4 SFig 3 -Best fits (lines) to the data (symbols) in Figure 4.
The optomechanical response of the QD Δ L "# M presented in Figure 4 of the main letter is fitted as a series of Lorentzian lines. SFig 3 shows the experimental data (symbols) and the best fit (lines). The area extracted for selected peaks is plotted in Figure 4 (c).