Abstract
Strongly confined photonic modes can couple to quantum emitters and mechanical excitations. To harness the full potential in quantum photonic circuits, interactions between different constituents have to be precisely and dynamically controlled. Here, a prototypical coupled element, a photonic molecule defined in a photonic crystal membrane, is controlled by a radio frequency surface acoustic wave. The sound wave is tailored to deliberately switch on and off the bond of the photonic molecule on subnanosecond timescales. In timeresolved experiments, the acoustooptically controllable coupling is directly observed as clear anticrossings between the two nanophotonic modes. The coupling strength is determined directly from the experimental data. Both the time dependence of the tuning and the intercavity coupling strength are found to be in excellent agreement with numerical calculations. The demonstrated mechanical technique can be directly applied for dynamic quantum gate operations in stateoftheartcoupled nanophotonic, quantum cavity electrodynamic and optomechanical systems.
Introduction
Twodimensional photonic crystal membranes provide a versatile planar architecture for integrated photonics to control the propagation of light on a chip using highquality optical cavities, waveguides, beamsplitters or dispersive elements^{1}. When combined with highly nonlinear quantum emitters, quantum photonic networks^{2,3} operating at the singlephoton level^{4} come within reach. Towards largescale quantum photonic networks^{5,6}, selective dynamic control of individual components and deterministic interactions between different constituents are of paramount importance^{7}. This indeed calls for switching speeds ultimately on the system’s native timescales to enable Landau–Zener nonadiabatic control schemes^{8,9}. For example, manipulation via electric fields or alloptical means have been used for switching in nanophotonic circuits^{10,11} and cavity quantum electrodynamics studies^{12,13,14}.
Here, we demonstrate dynamic control of the coherent interaction between two coupled photonic crystal (PhC) nanocavities forming a photonic molecule (PM)^{15,16,17}. By using an electrically generated radio frequency (RF) surface acoustic wave (SAW), we achieve optomechanical tuning^{18}. SAWs have been used to dynamically control nanophotonic^{18,19,20}, plasmonic^{21,22,23}, integrated optical devices^{24,25} and quantum dot (QD) emitters^{26,27,28,29} at frequencies up to several GHz. The tuning range of our method is sufficiently large to compensate for the inherent fabricationrelated cavity mode detuning and the operation speed exceeds that of typical^{30} and downscaled^{31} resonant mechanical approaches. Our findings open a route towards nanomechanically gated protocols^{9}, which hitherto have inhibited the realization in alloptical schemes^{32,33}. Moreover, the mechanical nature of the SAW makes them ideally suited to generate tailored classical phonon fields^{34}. The GHz frequencies accessible by SAWs perfectly match that of the mechanical modes in membranetype PhC photonic^{35} and optomechanical cavities^{36}. Thus, our results pave the way towards native mechanical control in these scaled onchip optomechanical systems.
Results
Implementation of acoustically tunable PM
The onchip PM studied here consists of two L3type missing hole cavities^{37}, labelled C_{1} and C_{2}, defined in a twodimensional PhC membrane. Its static coupling strength J is known to depend exponentially on the separation between the two cavities^{17}. In our sample, the cavities are offset symmetrically by d=5 lattice constants (a=260 nm) along each primitive direction of the PhC lattice (Supplementary Fig. 1), as can be seen in the scanning electron micrograph in Fig. 1a. The finite coupling strength J leads to the formation of two normal modes; a bonding mode M_{−} and an antibonding mode M_{+}. Note that the mode indices in M_{±} refer to the respective normal mode frequencies ω_{±}, and thus are opposite to the spatial symmetry of the mode. In the most general case, the two cavities C_{1} and C_{2} exhibit resonance frequencies ω_{1} and ω_{2}, split by a finite detuning Δ=ω_{2}−ω_{1}. Thus, the normal mode frequencies can be expressed by:
with ω_{0}=(ω_{1}+ω_{2})/2 being the centre frequency. In Fig. 1b, we present two emission spectra (see Methods section) recorded for spatially exciting either C_{1} (blue) or C_{2} (red) of a typical PM, denoted as PM1. For PM1, each cavity exhibits a distinct single mode, split by , with Δ_{0} being the static detuning. Such distinct and localized mode patterns are found for the majority of the PMs. This suggests that Δ_{0}>J, and that the intercavity coupling is strongly suppressed. Therefore, asfabricated and nominally identical cavities are only weakly interacting due to Δ_{0}≠0, which arises from inevitable imperfections during nanofabrication. To overcome this fundamental limitation and achieve dynamic control of the individual cavity resonances, we use an optomechanical approach using RF SAWs^{18,19}. As indicated in the schematic illustration of Fig. 1a, these quasimonochromatic acoustic phonons are generated by an interdigital transducer (IDT; see Methods section), propagate along the x axis of the PM and dynamically deform the individual cavities. The amplitude of this mechanism, ℏA>1 meV, exceeds both the static detuning, Δ_{0}, and the coupling strength, J, which enables us to dynamically tune the PM completely in and out of resonance. For our chosen geometric arrangement, the cavities are separated by a distance Δx along the SAW propagation direction, the modulations of ω_{1} and ω_{2} are phase shifted (in unit radians) by φ_{12}=Δx × ω_{SAW}/c_{SAW}, with ω_{SAW} and c_{SAW} being the SAW angular frequency and speed of sound, respectively. We deliberately set the acoustic wavelength, λ_{SAW}, such that it is commensurate with the spatial separation of the two cavity centres 2Δx=λ_{SAW}. As illustrated in the schematic in Fig. 1c, for the selected phase, the maximum (minimum) of the SAW expands C_{1} (compresses C_{2}), which in turn gives rise to a red (blue) shift of their respective resonances^{18}. The propagation of the sound wave along the x axis of the PM leads to a timedependent detuning of the two cavities
The amplitude of this modulation, , depends on the amplitudes of the modulations of the individual cavities, A_{1} and A_{2}, and is maximum for φ_{12}=180°. For Δ_{mod}>Δ_{0}, the detuning passes through zero, which results according to equation (1) in an avoided crossing of the normal modes. In Fig. 1d, the resulting temporal evolutions of the normalized mode frequencies (ωω_{0})/J obtained using equations (1) and (2) are evaluated over one acoustic cycle of T_{SAW} for a typical set of experimentally achievable parameters (J=1.2 Δ_{0}, A_{1}=1.5 Δ_{0}, A_{2}=1.9 Δ_{0} and φ_{12}=162°). The dashed lines show the time evolution of the noninteracting (J=0) modes M_{1} (blue) and M_{2} (red). In strong contrast, the normal modes M_{+} and M_{−} start with initially M_{1}like (blue) and M_{2}like (red) singlecavity character, and develop to fully mixed symmetric (bonding) and antisymmetric (antibonding) character (green) at resonance. At this point, the coupling strength J of the PM can be deduced directly from the splitting of the avoided crossing. After traversing through the avoided crossing, the initial character of the modes is exchanged, with M_{+} and M_{−} possessing M_{2}like (blue) and M_{1}like character, respectively. Over the duration of one full acoustic cycle, the two modes are brought into resonance at two distinct times, giving rise to two avoided crossings, restoring the initial configuration. We performed full finite difference timedomain (FDTD) simulations to confirm and, in particular, quantitate the dynamic coupling. The evaluation for the used sample geometry is shown in Supplementary Fig. 2. We evaluate the calculated profiles of the electric field component in the plane of the PhC membrane and perpendicular to the SAW propagation (E_{y}) in Fig. 1e. In the two left panels, the detuning is set to three times the coupling strength (Δ=3J), and thus the two modes remain well localized in one of the two cavities. For the resonance case, Δ=0, shown in the two right panels of Fig. 1e, the E_{y} exhibit the characteristic symmetric and antisymmetric superpositions for the M_{−} and M_{+} modes, respectively. For our sample geometry, the FDTD simulations predict ℏJ_{sim}=0.71 meV. This value is set by the chosen separation, that is, barrier thickness, between the two cavities.
Direct observation of SAWcontrolled intercavity coupling
To experimentally verify the dynamic control of a PM by a ω_{SAW}/2π=800 MHz SAW, we performed timeresolved spectroscopy with optical excitation at a welldefined time during the acoustic cycle. The emission of the PM was analysed in the time domain and as a function of relative emission frequency ωω_{0}. We measured timedependent emission spectra of the two cavities of PM1 for three characteristic modulation amplitudes. For a weak modulation, Δ_{mod}<Δ_{0}, shown in Fig. 2a, C_{1} and C_{2} show the expected phaseshifted sinusoidal spectral modulations centred (dashed horizontal lines) at their unperturbed resonances, which decay with a characteristic time constant of ∼1.3 ns. As the modulation is increased to Δ_{mod}=Δ_{0} (Fig. 2b), the two singlecavity modes are brought into resonance at one distinct time t_{0}=0.6 ns during the acoustic cycle. At this time, coherent coupling leads to the formation of bonding and antibonding normal modes. This directly manifests itself in the experimental data due to the emergence of new emission features stemming from the spatial delocalization of the bonding and antibonding modes. For the initially lower frequency cavity (C_{1}), a new signal appears at the frequency of the normal mode M_{+}, which was initially confined within the other cavity (C_{2}). The initially higherfrequency cavity (C_{2}) exhibits precisely the opposite behaviour, with the normal mode M_{−} appearing at time t_{0}. The normal modes are split by the coupling strength ℏJ=(0.68±0.04) meV, very close to the value expected from our FDTD simulations. For further increased detuning Δ_{mod}>Δ_{0}, the two modes are brought into resonance at two distinct times, t_{1} and t_{2}, during the acoustic cycle. After the first resonance at t_{1}, coupling is suppressed, Δ>J, both modes are effectively decoupled and their singlecavity characters are exchanged compared with the initial configuration. The lower frequency mode M_{−}, which is initially C_{1}like, is switched to C_{2}like character after t_{1}, and vice versa. At the second resonance at t_{2}, the system is reverted to its original configuration at the beginning of the acoustic cycle. This sequence of two timeoffset coupling events gives rise to the experimentally observed anticorrelated time evolutions of the emission of C_{1} and C_{2}. We extracted the timedependent emission frequencies detected from the two cavities of PM1 and plotted them (C_{1} circles, C_{2} triangles) for the three modulation amplitudes in Fig. 2d–f.
From the set of measurements with varying tuning amplitude, we obtain mean values for the free parameters of the model, ℏ〈J〉_{PM1}=(0.70±0.04) meV, 〈A_{1}/A_{2}〉_{PM1}=0.75±0.05 and 〈φ_{12}〉_{PM1}=(155±10)°. Moreover, we note that the observed phase shift unambiguously confirms efficient coupling of the SAW into the subλ_{SAW} membrane. Its small deviation from the ideal value of 180° arises from the finite difference in the phase velocity of the acoustic wave within the membrane and the region of the transducer. The results from this model are plotted as lines and the character of the mode are colour coded. Clearly, our experimental data are in excellent agreement with the normal mode model detailed in the Methods section for all three modulation amplitudes. Both the timedependent spectral modulation as well as the switching of the character of the modes are nicely reproduced.
Statistical analysis and comparison with FDTD simulation
Such behaviour was experimentally confirmed for five different, nominally identical PMs for which we evaluated the mean of their respective key parameters. The experimentally observed static detuning Δ_{0} and coupling strength J are summarized in Fig. 3a. While the coupling strength, ℏJ=(0.8±0.1) meV, (blue) does not vary from PM to PM, the values of the static detuning, Δ_{0}, shows a pronounced scatter ranging between −1.2 and +3.7 meV. These observations are in fact expected. J exponentially depends on the symmetric intercavity offset, d, and is thus robust and insensitive to small deviations from the ideal geometry due to fabrication imperfections. In strong contrast, the absolute resonance frequencies of the two cavities forming the PM are highly sensitive to these inherent and inevitable deviations from the nominal geometry. The resulting fluctuations of the cavity resonances reflect themselves in the observed variation of Δ_{0}. Indeed, we observe pronounced static coupling (J≫Δ_{0}) only for one single asfabricated PM, labelled PM5. The corresponding experimental data are presented in Supplementary Note 1 and Supplementary Figs 3 and 4. The exponential dependence of J as a function of d is nicely confirmed by a best fit (line) to values calculated by FDTD (symbols) presented in Fig. 3b. The experimentally observed distribution of J_{exp} and the intercavity separation d_{exp} derived from J_{exp} and the FDTD simulation are indicated by the shaded horizontal and vertical bars. Clearly, the measured J_{exp} and its derived d_{exp} match perfectly the calculated value of ℏJ_{sim}=0.71 meV and the nominally set d=5a. These narrow distributions centred around the calculated and nominal values are expected since d is large compared with typical imperfections in the nanofabrication.
Discussion
In summary, we demonstrated dynamic optomechanical control of coherent interactions in a prototypical coupled nanophotonic system. When combined with optical nonlinearities, our tunable PM paves the way to dynamically controlled highfidelity entanglement generation^{38} and distribution on a chip^{39,40}. For larger switching rates, as required for Landau–Zener transitionbased gates^{9}, the underlying optomechanical coupling could be enhanced further by direct antiphased SAW excitation of localized vibronic modes of either nanocavity^{35}. Since SAWs represent nanomechanical waves, Fourier synthesis allows to shape waveforms^{34}. This paradigm in turn can be used to deliberately speed up or slow down switching as required for static or dynamic control schemes. Moreover, SAWs or SAW waveforms can be interfered generating one or twodimensional nanomechanical strain fields^{41}. Thus, our approach could be directly scaled up to large arrays of coupled cavities^{42,43} or waveguides^{44}. The coherent phononic nature of SAWs was verified by Metcalfe et al.^{27} who demonstrated resolved sidebands in the emission of a SAWdriven QD and performed optomechanical cooling and heating in this system. For the GaAsbased nanocavities, the cavity linewidth exceeds the sideband splitting set by ω_{SAW}. Our approach can be readily transferred to silicon (Si)based PhC membranes and optomechanical crystals using piezoelectric coupling layers^{45}. On this platform, cavity photon loss rates of <1 GHz have been achieved^{11}. Therefore, our approach is ideally suited to perform optomechanically driven allphotonic Landau–Zenerbased entangling quantum gates with high fidelity, even for moderate SAW frequencies. The performance of this type of quantum gates can be drastically increased using higher SAW frequencies as demonstrated for instance by Tadesse and Li (ref. 25) and weaker cavity coupling rates. The exponential dependence of the coupling strength shown in Fig. 3b predicts a decrease from J∼170 to J<20 GHz when the offset is increased from 5a to 7a. This value of J is indeed compatible with stateoftheart IDTs on Si (ref. 46). We note that our method is compatible with superconducting twolevel systems and circuit electrodynamics. In particular, the geometry of transmontype superconducting qubits matches that of IDTs. In a recent experiment by Gustafsson et al., these highly coherent twolevel systems have been strongly coupled to single SAW quanta^{47}. Finally we note that resonant frequencies of vibronic modes in optomechanical crystals^{36,48} match well with the frequency band covered by SAWs. The tight confinement of photonic and vibronic excitations in these structures gives rise to large optomechanical couplings^{49}. In recent theoretical work, Ludwig and Marquart^{50} show a rich phase diagram for arrays of such optomechanical cavities, which delicately depends on the intercavity coupling. Thus, our method provides a tantalizing avenue to deliberately switch on and off the interaction or drive such systems allmechanically.
Methods
Optical spectroscopy
For photoluminescence spectroscopy of the PM, the sample is cooled to T=5 K in a Heliumflow cryostat with custombuiltintegrated RF connections. Offresonant QDs are excited by an externally triggered diode laser emitting ∼90 ps pulses at a wavelength of 850 nm, which is focused to a 1.5μm spot by a NIR × 50 microscope objective. The train of laser pulses is actively locked to the RF signal exciting the SAW to ensure optical excitation at an arbitrary but welldefined time during the acoustic cycle.^{51} The emission from the sample is dispersed by a 0.75m imaging grating monochromator. A fast (<50 ps rise time) Si singlephoton avalanche detector is used for timeresolved singlechannel detection of the spectral modulation of the optical modes^{52}. Details of the phaselocked excitation scheme and additional data on singlecavity measurements are discussed in Supplementary Note 2 and Supplementary Fig. 5.
Sample structure
We start by fabricating the PhC membranes from a semiconductor heterostructure grown by molecular beam epitaxy (MBE). This heterostructure consists of a 170nm GaAs layer with selfassembled InGaAs QDs at its centre, on top of a 725nmthick Al_{0.8}Ga_{0.2}As sacrificial layer. The PM structure is defined by electron beam lithography and transferred into the heterostructure by inductively coupled plasma reactive ion etching (ICPRIE) etching. In a wet chemical etching step using hydrofluoric acid, we removed the sacrificial layer to release a fully suspended membrane. The PMs are deliberately designed to be offresonant with the QD emission to achieve a sufficiently long decay time of the cavity emission. The cavity resonance is detuned by several meV from the QD emission band. Thus, no Purcellenhanced spontaneous emission with fast radiative rates occurs^{53}. In turn, the cavity mode emission arises from phonon or Coulombassisted feeding mechanisms on a ∼1ns timescale^{54,55,56}. These long timescales set the experimental time window over which the cavity mode can be detected using timeresolved photoluminescence spectroscopy. Additional data of timeresolved experiments of the cavity emission are shown in Supplementary Fig. 5d.
IDTs were defined using electron beam lithography and metallized with 5 nm Ti and 50 nm Al in a liftoff process. The finger period is 3.83 μm, resulting in a resonance frequency of 800 MHz at the measurement temperature of 5 K. The IDTs consist of 80 pairs of 185μmlong fingers and are located at a distance of 800 μm from the array of PhCs. The PhCs are arranged in a staggered pattern, that is, offset in the direction perpendicular to the SAW propagation. This arrangement ensures comparable SAW coupling to each PhC device. A schematic of this layout is included as Supplementary Fig. 6.
Coupled mode model
We treat the PM as a model system of two coupled cavities. The singlecavity modes M_{1,2} have the complex amplitudes a_{1,2} and the frequencies ω_{1,2}. In the presence of finite coupling and the absence of dissipation, the time evolution is given by
and
with a real coupling constant J.
The resulting normal modes have the frequencies given by equation (1) with centre frequency and detuning Δ=ω_{2}ω_{1}. We note that since J>0, the lowfrequency mode, ω_{−}, and the highfrequency mode, ω_{+}, correspond to symmetric and antisymmetric superpositions of the uncoupled, singlecavity modes, respectively.
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How to cite this article: Kapfinger, S. et al. Dynamic acoustooptic control of a strongly coupled photonic molecule. Nat. Commun. 6:8540 doi: 10.1038/ncomms9540 (2015).
References
Notomi, M. Manipulating light with strongly modulated photonic crystals. Rep. Prog. Phys. 73, 096501 (2010).
O'Brien, J. L., Furusawa, A. & Vuckovic, J. Photonic quantum technologies. Nat. Photon. 3, 687–695 (2009).
Faraon, A. et al. Integrated quantum optical networks based on quantum dots and photonic crystals. New. J. Phys. 13, 055025 (2011).
Volz, T. et al. Ultrafast alloptical switching by single photons. Nat. Photon. 6, 605–609 (2012).
Hartmann, M. J., Brandao, F. & Plenio, M. B. Strongly interacting polaritons in coupled arrays of cavities. Nat. Phys. 2, 849–855 (2006).
Yang, X., Yu, M., Kwong, D.L. & Wong, C. W. Alloptical analog to electromagnetically induced transparency in multiple coupled photonic crystal cavities. Phys. Rev. Lett. 102, 173902 (2009).
Grillet, C. et al. Reconfigurable photonic crystal circuits. Laser Photonics. Rev. 4, 192–204 (2010).
Shevchenko, S. N., Ashhab, S. & Nori, F. LandauZenerStückelberg interferometry. Phys. Rep. 492, 1–30 (2010).
Blattmann, R., Krenner, H. J., Kohler, S. & Hänggi, P. Entanglement creation in a quantumdotnanocavity system by Fouriersynthesized acoustic pulses. Phys. Rev. A 89, 012327 (2014).
Vlasov, Y. A., O'Boyle, M., Hamann, H. F. & McNab, S. J. Active control of slow light on a chip with photonic crystal waveguides. Nature 438, 65–69 (2005).
Tanabe, T., Notomi, M., Kuramochi, E., Shinya, A. & Taniyama, H. Trapping and delaying photons for one nanosecond in an ultrasmall highQ photoniccrystal nanocavity. Nat. Photon. 1, 49–52 (2007).
Laucht, A. et al. Electrical control of spontaneous emission and strong coupling for a single quantum dot. New. J. Phys. 11, 023034 (2009).
Jin, C.Y. et al. Ultrafast nonlocal control of spontaneous emission. Nat. Nanotechnol. 9, 886–890 (2014).
Pagliano, F. et al. Dynamically controlling the emission of single excitons in photonic crystal cavities. Nat. Commun. 5, 5786 (2014).
Bayer, M. et al. Optical modes in photonic molecules. Phys. Rev. Lett. 81, 2582–2585 (1998).
Cai, T., Bose, R., Solomon, G. S. & Waks, E. Controlled coupling of photonic crystal cavities using photochromic tuning. Appl. Phys. Lett. 102, 141118 (2013).
Chalcraft, A. R. A. et al. Mode structure of coupled L3 photonic crystal cavities. Opt. Express 19, 5670–5675 (2011).
Fuhrmann, D. A. et al. Dynamic modulation of photonic crystal nanocavities using gigahertz acoustic phonons. Nat. Photon. 5, 605–609 (2011).
de Lima, M. M. & Santos, P. V. Modulation of photonic structures by surface acoustic waves. Rep. Prog. Phys. 68, 1639–1701 (2005).
de Lima, M. M., van der Poel, M., Santos, P. V. & Hvam, J. M. Phononinduced polariton superlattices. Phys. Rev. Lett. 97, 045501 (2006).
Ruppert, C. et al. Surface acoustic wave mediated coupling of freespace radiation into surface plasmon polaritons on plain metal films. Phys. Rev. B 82, 081416 (R) (2010).
Schiefele, J., Pedros, J., Sols, F., Calle, F. & Guinea, F. Coupling light into graphene plasmons through surface acoustic waves. Phys. Rev. Lett. 111, 237405 (2013).
Ruppert, C. et al. Radio frequency electromechanical control over a surface plasmon polariton coupler. ACS Photon. 1, 91–95 (2014).
Beck, M. et al. Acoustooptical multiple interference switches. Appl. Phys. Lett. 91, 061118 (2007).
Tadesse, S. A. & Li, M. Suboptical wavelength acoustic wave modulation of integrated photonic resonators at microwave frequencies. Nat. Commun. 5, 5402 (2014).
Gell, J. R. et al. Modulation of single quantum dot energy levels by a surfaceacousticwave. Appl. Phys. Lett. 93, 081115 (2008).
Metcalfe, M., Carr, S. M., Muller, A., Solomon, G. S. & Lawall, J. Resolved sideband emission of InAs/GaAs quantum dots strained by surface acoustic waves. Phys. Rev. Lett. 105, 037401 (2010).
Völk, S. et al. Enhanced sequential carrier capture into individual quantum dots and quantum posts controlled by surface acoustic waves. Nano Lett. 10, 3399–3407 (2010).
Weiß, M. et al. Dynamic acoustic control of individual optically active quantum dotlike emission centers in heterostructure nanowires. Nano Lett. 14, 2256–2264 (2014).
Li, H. & Li, M. Optomechanical photon shuttling between photonic cavities. Nat. Nanotechnol. 9, 913–919 (2014).
Sun, X., Zhang, X., Poot, M., Xiong, C. & Tang, H. X. A superhighfrequency optoelectromechanical system based on a slotted photonic crystal cavity. Appl. Phys. Lett. 101, 221116 (2012).
Sato, Y. et al. Strong coupling between distant photonic nanocavities and its dynamic control. Nat. Photon. 6, 56–61 (2012).
Bose, R., Cai, T., Choudhury, K. R., Solomon, G. S. & Waks, E. Alloptical coherent control of vacuum Rabi oscillations. Nat. Photon. 8, 858–864 (2014).
Schülein, F. J. R. et al. Fouriersynthesis of radio frequency nanomechanical pulses with different shapes. Nat. Nanotechnol. 10, 512–516 (2015).
Gavartin, E. et al. Optomechanical coupling in a twodimensional photonic crystal defect cavity. Phys. Rev. Lett. 106, 203902 (2011).
Eichenfield, M., Chan, J., Camacho, R. M., Vahala, K. J. & Painter, O. Optomechanical crystals. Nature 462, 78–82 (2009).
Akahane, Y., Asano, T., Song, B.S. & Noda, S. HighQ photonic nanocavity in a twodimensional photonic crystal. Nature 425, 944–947 (2003).
Liew, T. C. H. & Savona, V. Single photons from coupled quantum modes. Phys. Rev. Lett. 104, 183601 (2010).
Cirac, J. I., Zoller, P., Kimble, H. J. & Mabuchi, H. Quantum state transfer and entanglement distribution among distant nodes in a quantum network. Phys. Rev. Lett. 78, 3221–3224 (1997).
Vasco, J. P., Guimarães, P. S. S. & Gerace, D. Longdistance radiative coupling between quantum dots in photonic crystal dimers. Phys. Rev. B 90, 155436 (2014).
Stotz, J. A. H., Hey, R., Santos, P. V. & Ploog, K. H. Coherent spin transport through dynamic quantum dots. Nat. Mater. 4, 585–588 (2005).
Notomi, M., Kuramochi, E. & Tanabe, T. Largescale arrays of ultrahighQ coupled nanocavities. Nat. Photon. 2, 741–747 (2008).
Liew, T. H. C. & Savona, V. Multimode entanglement in coupled cavity arrays. New J. Phys. 15, 025015 (2013).
Gersen, H. et al. Direct observation of bloch harmonics and negative phase velocity in photonic crystal waveguides. Phys. Rev. Lett. 94, 123901 (2005).
Batista, P. D. et al. ZnO/SiO2 microcavity modulator on silicon. Appl. Phys. Lett. 92, 133502 (2008).
Büyükköse, S. et al. Ultrahighfrequency surface acoustic wave transducers on ZnO/SiO2/Si using nanoimprint lithography. Nanotechnology 23, 315303 (2012).
Gustafsson, M. V. et al. Propagating phonons coupled to a superconducting qubit. Science 346, 207–211 (2014).
Eichenfield, M., Chan, J., SafaviNaeini, A. H., Vahala, K. J. & Painter, O. Modeling dispersive coupling and losses of localized optical and mechanical modes in optomechanical crystals. Opt. Express 17, 20078–20098 (2009).
SafaviNaeini, A. H. et al. Twodimensional phononicphotonic band gap optomechanical crystal cavity. Phys. Rev. Lett. 112, 153603 (2014).
Ludwig, M. & Marquart, F. Quantum manybody dynamics in optomechanical arrays. Phys. Rev. Lett. 111, 073603 (2013).
Völk, S. et al. Direct observation of dynamic surface acoustic wave controlled carrier injection into single quantum posts using phaseresolved optical spectroscopy. Appl. Phys. Lett. 98, 023109 (2011).
Schülein, F. J. R. et al. Acoustically regulated carrier injection into a single optically active quantum dot. Phys. Rev. B 88, 085307 (2013).
Kress, A. et al. Manipulation of the spontaneous emission dynamics of quantum dots in two dimensional photonic crystals. Phys. Rev. B 71, 241304 (R) (2005).
Winger, W. et al. Explanation of photon correlations in the faroffresonance optical emission from a quantumdotcavity system. Phys. Rev. Lett. 103, 207403 (2009).
Laucht, A. et al. Temporal monitoring of nonresonant feeding of semiconductor nanocavity modes by quantum dot multiexciton transitions. Phys. Rev. B 81, 241302(R) (2010).
Florian, M., Gartner, P., Steinhoff, A., Gies, C. & Jahnke, F. Coulombassisted cavity feeding in nonresonant optical emission from a quantum dot. Phys. Rev. B 89, 161302(R) (2014).
Acknowledgements
This work was supported by the Deutsche Forschungsgemeinschaft (DFG) via the Emmy Noether Programme (KR 3790/21), Sonderforschungsbereich 631 and the Cluster of Excellence Nanosystems Initiative Munich (NIM). K.M. acknowledges support by the Alexander von Humboldt Foundation.
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H.J.K. and S.K. designed the study. S.K. built the experimental setup and performed the experiments. S.K., T.R. and S.L. designed, fabricated and characterized the devices, and performed 3DFDTD simulations. K.M. fabricated and characterized the MBE material. S.K. and H.J.K. performed the data analysis and modelling. All authors discussed the results. S.K. and H.J.K. wrote the manuscript with contributions from all other authors. H.J.K. proposed, initiated and coordinated research. H.J.K., M.K., J.J.F. and A.W. inspired and supervised the project.
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Kapfinger, S., Reichert, T., Lichtmannecker, S. et al. Dynamic acoustooptic control of a strongly coupled photonic molecule. Nat Commun 6, 8540 (2015). https://doi.org/10.1038/ncomms9540
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DOI: https://doi.org/10.1038/ncomms9540
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