A 1D Optomechanical crystal with a complete phononic band gap

Recent years have witnessed the boom of cavity optomechanics, which exploits the confinement and coupling of optical and mechanical waves at the nanoscale. Amongst their physical implementations, optomechanical (OM) crystals 4,5 built on semiconductor slabs enable the integration and manipulation of multiple OM elements in a single chip and provide GHz phonons suitable for coherent phonon manipulation. Different demonstrations of coupling of infrared photons and GHz phonons in cavities created by inserting defects on OM crystals have been performed. However, the considered structures do not show a complete phononic bandgap, which should allow longer dephasing time, since acoustic leakage is minimized. We demonstrate the excitation of acoustic modes in a 1D OM crystal properly designed to display a full phononic bandgap for acoustic modes at 4 GHz. The modes inside the complete bandgap are designed to have mechanical Q factors above 10 and invariant to fabrication imperfections. Optomechanical (OM) coupling, the direct interaction of electromagnetic radiation and mechanical vibrations of matter, can be greatly enhanced by confining electromagnetic radiation in a cavity. Since the establishment of cavity optomechanics the transduction of phonons through light has led to a wide variety of applications in sensing and communications. Moreover, the manipulation of the mechanical degrees of freedom with light, with the demonstrations of energy transfer from photons to phonons (amplification) and from phonons to photons (sideband resolved OM cooling) has paved the way towards the coherent quantum control of a mechanical oscillator. Recent experimental demonstration of cooling down to the ground state of a mechanical resonator with less than a single confined phonon in average, and coherent effects like optomechanically induced transparency and coherent coupling in the well resolved sideband regime (OM normal mode splitting ) confirm OM cavities as ideal building blocks for quantum computation using phonons. But the conditions that a cavity OM system, which range from the macroscopic to the atomic domain and make use of radiation covering the microwave to the visible domain, must fulfil to allow phonon coherent manipulation are strongly restrictive. The OM vacuum coupling (g) strength is one of the key factors, with the highest reports giving g/2 rates in the MHz range 5,26–28 and reports of GHz in extended systems. This g factor multiplied by the photon lifetime in the cavity (cav ) gives an important figure of merit (g/where  is the optical cavity decay rate, cav), which can be related with the interaction strength per photon inside the cavity. Ground state cooling, that is, average phonon population below 1 at the ground state, requires that the OM system is within the side band resolved limit. In other words, the lifetime in the cavity must exceed the mechanical oscillation period . In addition, it is important to preserve the phonon mode from the interaction with thermally populated acoustic phonons that dephase the system. High frequency phononic modes (mec in the GHz) are less populated for the same temperature ( ), and can be cooled down to the ground state even without OM assisted cooling. The quality of the mechanical cavity (Qmec), a signature of the level of isolation reached in the phonon confinement, can be compensated by the intrinsic weight of the phonon frequency, so Qmec· mecis considered a good figure of merit for quantum coherent phonon manipulation. Goryachev et al reached with a microwave system 7.8·10 Hz whereas Chan et al reached 3.9·10 Hz with an OM crystal. OM crystals are simultaneously photonic and phononic crystals that confine in the same structure photons and phonons, so that when engineered properly they can lead to strong photon-phonon interaction. A practical advantage remarks them over the rest of OM systems: ease of integration in chip platforms allows the design of multiple OM elements as circuits. But they have also an edge on the fundamental physical limits attainable in phonon isolation, as their typical phonon frequency lies in the high GHz range and phononic band gaps can be design to prevent phonon propagation at certain frequency ranges. A complete phononic band gap is defined by the absence of any phononic band in a given frequency range, meanwhile, a pseudo-band gap is defined by the absence of bands of a particular symmetry in the frequency range of definition, even if there are still bands of other symmetries at that frequencies. In Chang et al 8,27 , the Q mechanical factor of the confined phononic mode at cryogenic temperatures is limited by unwanted fabrication imperfections that break the perfect symmetry of the ideal (as designed) structure and allow coupling among different symmetry phononic propagative bands inside the pseudo-bandgaps. This loss is partly mitigated by surrounding the structure with a phononic radiation shell (a 2D phononic crystal with a complete band gap). By means of that approach, the energy coupled to the unwanted propagative modes of other symmetries does not leak out to the substrate, but is indeed lost by the confined phononic mode and spread around the full nanobeam. This leaking mechanism could be completely avoided by using a structure with a complete phononic band gap, but in practice the design of a 1D cavity that is at the same time photonic and phononic is even more restrictive and has not been accomplished so far. Limiting the losses would increase the dephasing time and allow multiple coherent phonon operations in a quantum computing scheme based in phonons and controlled/read out by light. As shown in a really recent work by Safavi-Naeini et al, the use of a full phononic bandgap is essential to reduce the loss channels in a 2D optomechanical crystal, in that case they are capable of limiting the coupling of their confined phonon mode to a single band in the Gamma-X direction of the waveguide used to create the defect. In this paper we present a silicon 1D OM crystal built up so that it displays a dual absolute band gap for both phonons and photons, as proposed by Maldovan and Thomas in ref 33, what has been named a phoXonic crystal. Figure 1a sketches the top view of the unit cell of the proposed OM crystal, a 220 nm thick nanobeam. The key advantage of this cell over previous approaches is that optical properties are mainly determined by the inner beam width and the hole size and spacing whilst the mechanical properties are specially affected by the stub width and size. Such approach uncouples effectively the design of the optical and the mechanical cavities which allows achieving a full 1D phononic band gap for propagative modes and a photonic bandgap for TE-like (even parity) optical modes. Figure 1. Description of the 1D OM crystal with a full phononic bandgap. a), Ideal unit cell with the parameters that define it, adapted from reference 32 and tilted SEM image of typical fabricated device. b) Parameter variation to build up the OM defect crystal cavity. On top of the graph we show a SEM image of the fabricated OM cavity with dimensions corresponding one to one to the ordinate axis. The red contour of the SEM image corresponds to the profile used in the FEM calculations to model the real structure. The cavity is built by varying in a parabolic way towards the centre of the structure the cell width (a, pitch), hole radius (r) and stub width (d) the same percentage (Percentage of Reduction (PR)), meanwhile the beam width (w) is increased towards the centre. In the OM cavity presented in Figure 1 b), PR is 72%. These parameters and others (hole to ellipse, stub shape...) could be varied in an independent way at the expense of a numerically complex optimization process, what gives a taste of the room for improvement in the OM coupling still to explore. On top of the graph, we present a Scanning Electron Microscope (SEM) image of the OM cavity discussed onwards. The fabrication imperfections are taken into account in the simulations along the paper (see supplementary information). We draw in red the contour of the structure obtained rendering the SEM image. This contour is used to calculate the optical and mechanical properties of the structure using finite a