Electrically Driven Microcavity Exciton-Polariton Optomechanics at 20 GHz

Microcavity exciton polaritons enable the resonant coupling of excitons and photons to vibrations in the super-high-frequency (SHF, 3–30 GHz) domain. We introduce here a novel platform for coherent SHF optomechanics based on the coupling of polaritons and electrically driven SHF longitudinal acoustic phonons confined in a planar Bragg microcavity. The highly monochromatic phonons with tunable amplitudes are excited over a wide frequency range by piezoelectric transducers, which also act as efficient phonon detectors with a very large dynamical range. The microcavity platform exploits the long coherence time of polaritons as well as their efficient coupling to phonons. Furthermore, an intrinsic property of the platform is the backfeeding of phonons to the interaction region via reflections at the sample boundaries, which leads to quality factor $\times$ frequency products ($Q\times f$) exceeding ${10}^{14}\mathrm{Hz}$ as well as huge modulation amplitudes of the optical transition energies exceeding 8 meV. We show that the modulation is dominated by the phonon-induced energy shifts of the excitonic polariton component. Thus, the large modulation leads to a dynamical switching of light-matter nature of the particles from a mixed (i.e., polaritonic) one to photonlike and excitonlike states at frequencies up to 20 GHz. On the one hand, this work opens the way for electrically driven polariton optomechanics in the nonadiabatic, sideband-resolved regime of coherent control. Here, the bidirectionality of the transducers can be exploited for light-to-sound-to-rf conversion. On the other hand, the large phonon frequencies and $Q\times f$ products enable phonon control with optical readout down to the single-particle regime at relatively high temperatures (of 1 K).

Popular Summary

Coherent phonons—collective vibrations of a lattice—with frequencies in the 3–30 GHz range are an important tool for the coherent manipulation of solid-state excitations, an application relevant to several aspects of quantum information processing. In this work, we tackle two main challenges in this field: the on-demand generation and detection of coherent gigahertz phonons and their coupling to optoelectronic systems. In particular, we introduce a novel platform for electrical excitation of phonons with frequencies up to 20 GHz as well as their efficient coupling to photons.

Our platform exploits hybrid optomechanical microcavities with semiconductor quantum wells, which simultaneously confine near-infrared photons, quantum-well excitons, and gigahertz phonons. Using piezoelectric transducers that also act as phonon detectors, we inject coherent vibrations into the microcavities, a few-hundred-nanometers-thick “spacer” sandwiched between stacks of acoustic and optical mirrors. The vibrations travel into the spacer region, which encloses the quantum well. Here, strong coupling between photons and excitons—bound states of electrons and electron holes—gives rise to exciton polaritons, hybrid particles of light and matter. Thus, the electrically generated phonons allow for tunable modulation of polariton energy, which leads to the modulation of the energy of the emitted photons. Furthermore, the low acoustic losses enable high acoustic intensities as well as long phonon lifetimes, which are important considerations for coherent control.

This work opens the way toward electrically driven polariton optomechanics at gigahertz frequencies with an intrinsic interface to near-infrared photons. Furthermore, our results can be extended to the control of a single polariton by a single phonon and vice versa, by laterally confining the excitations in structured microcavities with intracavity traps.

Figure 1

Hybrid MC for polaritons and phonons. (a) Schematic cross section of sample $A$ showing the spatial distribution of photon (red-shaded region) and exciton-polariton fields (yellow). ODBR and AODBR stand for the distributed Bragg reflectors (DBRs) acting as optical and acoustic mirrors, respectively. Longitudinal bulk acoustic waves (BAWs) are generated by a ring-shaped bulk acoustic wave resonator (BAWR) driven by rf voltage. The ring-shaped BAWR has an aperture for laser excitation of the MC. (b),(c) Profiles for the acoustic displacement field $|\mathbf{u}|$ calculated for the mode localized (b) at the sample surface (mode with $f_S=6.36\mathrm{GHz}$) and (c) within the MC spacer [$f_{\mathrm{MC}}=6.83\mathrm{GHz}$; cf. thick arrows in (d)]. (d) Measured $s_{11}$ rf-scattering parameter of the BAWR (thick red curve) and calculated $s_{11}$ profiles for different thicknesses $d_{\mathrm{ZnO}}$ of the piezoelectric ZnO layer of the BAWR varying from 300 nm (bottom curve) to 180 nm (top curve) in steps of 20 nm (thin black lines). The calculations are done according to the procedure outlined in Ref. [43]. The colored area in (d) indicates the spectral extent of the acoustic stop band of the MC.

Figure 2

(a) Electrical response of a BAWR on sample $A$ at 300 K. The red curve shows the $s_{11}$ scattering parameter for a BAWR on a bare GaAs substrate, while the blue one gives the response of a device on a MC (sample $A$). Both devices have nominally identical ZnO thickness of 260 nm. The gray-shaded area designates the spectral range of acoustic stop band created by the AODBR displayed in Fig. 1. The two modes within the stop band correspond to the MC acoustic mode with $f_{\mathrm{MC}}=6.9\mathrm{GHz}$ and the surface mode $f_S=6.4\mathrm{GHz}$ confined between the BAWR surface and the upper AODBR. (b) Simulated acoustic reflectivity of the MC with a BAWR device on its surface. (c) Electrical response of a BAWR on sample $B$ measured at 10 K, as given by the $s_{11}$ scattering parameter recorded as a function of the frequency. The curves are acquired using a BAWR with circular (rather than ring-shaped) contacts with a diameter of $20\mu \mathrm{m}$.

Figure 3

Acoustoelectric response of sample $A$ [panels (a), (c), (e)–(g)] and sample $B$ [panels (b), (d), (h)–(j)] at 10 K. (a) Time dependence of the rf BAWR reflection of sample $A$ determined from the spectral response of the $s_{11}$ rf-scattering parameter in the (5.5–7.5)-GHz spectral range. The multiple acoustic echoes ${\text{r}}_{\text{i}}$ ($i=1$ to 5) result from acoustic reflections at the back surface of the substrate. (c) Spectral dependence of the echoes within the time ranges ${\mathrm{TG}}_1$ (0–100 ns, pink) and ${\mathrm{TG}}_2$ (150–550 ns, green, encompassing three acoustic echoes) defined in (a). The gray area is the stop-band range. Two acoustic modes can be seen within the stop band for the ${\mathrm{TG}}_2$ (see text for discussion). (e)–(g) Enlargements of the green curve in (c) highlighting the frequency comb with spacing $\mathrm{\Delta }{f}_{\mathrm{sub}}=6.4\mathrm{MHz}$. (b) Time dependence of BAWR rf reflection of sample $B$ determined from the spectral response of the $s_{11}$ rf-scattering parameter in the (17–22)-GHz spectral range of Fig. 2. Similar to sample $A$, the multiple acoustic echoes ${\text{r}}_{\text{i}}$ ($i=1$ to 5) are observed due to the acoustic reflections at the back surface of the substrate. (d) Spectral dependence of the echoes within the time ranges ${\mathrm{TG}}_1$ (0–100 ns, pink) and ${\mathrm{TG}}_2$ (270–600 ns, green, encompassing three acoustic echoes) defined in (b). Again, two acoustic modes can be seen within the stop band for the ${\mathrm{TG}}_2$. (h)–(j) Enlargements of the green curve in (d) highlighting the frequency comb with spacing $\mathrm{\Delta }{f}_{\mathrm{sub}}=6.9\mathrm{MHz}$.

Figure 4

(a) Optical micrograph of a ring-shaped BAWR. The vertical dashed lines delimit the surface imaged on the slit of the spectrograph for PL spectral analysis. (b),(c) Maps of PL intensity as a function of the energy (horizontal axis) and position along the slit (vertical axis) without (b) and under BAW excitation of the acoustic MC mode $f_{\mathrm{MC}}=6.9247\mathrm{GHz}$ and rf power $P_{\mathrm{rf}}=14\mathrm{dBm}$ (c). These maps are recorded by collecting the PL emitted within the dashed rectangle in (a), excited by the 635-nm laser focused at the center of the BAWR aperture. (d) Comparison of PL spectra recorded in the center of the BAWR aperture in the absence (blue) and in the presence of the BAW (red). The spectra are produced by spatial integration over the regions delimited by the horizontal dashed lines in (b) and (c), respectively. $\mathrm{\Delta }E$ is the amplitude of the energy modulation of the excitonic resonances.

Figure 5

Polariton-phonon interaction in a hybrid microcavity. (a) Spectral dependence of the photoluminescence on the rf frequency for sample $A$ recorded at 10 K and the nominal rf power of 24 dBm. The acoustic stop-band limits are indicated by the vertical dashed lines. (b) Comparison of the time-gated $s_{11}$ parameter of a similar device with the acoustically induced energy modulation amplitude of the comb resonances $\mathrm{\Delta }E(f)$ calculated with respect to the $E_{\mathrm{ref}}=1464.3\mathrm{meV}$ [indicated in (a) with the horizontal black dashed line]. (c) The rf-frequency dependence of the PL recorded for a fixed rf power $P_{\mathrm{rf}}=14\mathrm{dBm}$ applied to the BAWR at 10 K corresponding the coupled linear power amplitude $P_{\mathrm{BAW}}^{0.5}=45{\mathrm{mW}}^{0.5}$ showing the effects of the frequency comb with $\mathrm{\Delta }{f}_{\mathrm{sub}}=6.4\mathrm{MHz}$. The inset displays the temperature ($T$) dependence of the energy modulation amplitude $\mathrm{\Delta }E$. The dashed line in the inset is a guide to the eye. (d) Dependence of the PL recorded for a fixed rf frequency $f_{\mathrm{rf}}=6.9312\mathrm{GHz}$ applied to the BAWR at 10 K on $P_{\mathrm{BAW}}^{0.5}$.

Figure 6

Modulation of polaritons by MC acoustic modes. Time-averaged PL spectra of sample $A$ recorded in the absence (thin blue lines) and in the presence (thick red lines) of a BAW with frequency $f_{\mathrm{BAW}}=6.931\mathrm{GHz}$ recorded at (a) 65, (b) 50, and (c) 10 K. $\mathrm{\Delta }E$ denotes the energy modulation amplitude of the excitonic levels in (a) and (b), and polariton states in (c).

Figure 7

Optomechanical response of a hybrid MC for 20-GHz BAWs. (a) The rf-frequency dependence of the PL recorded for a fixed rf power $P_{\mathrm{rf}}=24\mathrm{dBm}$ applied to the BAWR displaying the effect of the BAW on the PL emission. The red arrow points at one of the acoustic resonances. The LP and UP stand for the lower-polariton branch and the upper-polariton branch, respectively. (b) Time-averaged PL spectra recorded at 10 K in the absence (thin blue line) and presence (thick red line) of a BAW with frequency $f_{\mathrm{BAW}}=19.926\mathrm{GHz}$ [cf. red arrow in (a)]. The measurements are carried out at 10 K.

Figure 8

(a) Layer structure of the hybrid microcavity (sample $A$). Depth profiles within the spacer region of the hybrid microcavity of the (b) optical field $F_x$ at the photonic resonance energy, where $x$ is the polarization direction on the MC surface, (c) refractive index, $n$, and (d) normalized acoustic strain field $u_{zz}$ for the acoustic resonance frequency $f_{\mathrm{MC}}=6.9\mathrm{GHz}$. The green band designates depth of the two QWs.

Figure 9

Temperature dependence of the PL of the hybrid MC (sample $A$). (a) Temperature dependence of the PL spectrum. $X_1$ and $X_2$ are excitonic resonances of the coupled InGaAs QWs, which couple to the photonic ($C$) mode of the MC to form the lower (LP), middle (MP), and upper (UP) states at low temperatures. Momentum-resolved PL at (b) 10, (c) 30, (d) 55, and (e) 70 K. Below 50 K, the system is in the strong-coupling regime. The solid lines in (e) are three coupled oscillator fits to the data. The dashed lines are bare energies. The fitted Rabi splitting energy is ${\mathrm{\Omega }}_{\mathrm{Rabi}}=2\pm 0.3\mathrm{meV}$.

Figure 10

Spatial dispersion of photoluminescence of sample $B$ at 10 K. The white dashed lines represent calculated spatial dispersion of bare cavity ($C$) and exciton ($X$) modes. The solid yellow lines are fits using the two coupled oscillators model. The fitted Rabi splitting energy is ${\mathrm{\Omega }}_{\mathrm{Rabi}}=3\pm 0.5\mathrm{meV}$.

Figure 11

(a) Comparison of the PL under three different rf conditions: (i) rf off, (ii) rf out of phase, and (iii) rf in phase. The in phase and out of phase are measured at the same resonant rf frequency 6.944 GHz and the same applied rf power 14 dBm.