Universal Quantum Transducers Based on Surface Acoustic Waves The Harvard community has made this article openly available. Please share how this access benefits you. Your story matters Citation Schuetz, M. J. A., E. M. Kessler, G. Giedke, L. M. K. Vandersypen, M. D. Lukin, and J. I. Cirac. 2015. Universal Quantum Transducers Based on Surface Acoustic Waves. Physical Review X 5, 3. doi:10.1103/physrevx.5.031031. Published Version doi:10.1103/PhysRevX.5.031031 Citable link http://nrs.harvard.edu/urn-3:HUL.InstRepos:30361315 Terms of Use This article was downloaded from Harvard University’s DASH repository, and is made available under the terms and conditions applicable to Other Posted Material, as set forth at http:// nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of- use#LAA PHYSICAL REVIEW X 5, 031031 (2015) Universal Quantum Transducers Based on Surface Acoustic Waves M. J. A. Schuetz,1 E. M. Kessler,2,3 G. Giedke,1,4,5 L. M. K. Vandersypen,6 M. D. Lukin,2 and J. I. Cirac1 1Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Strasse 1, 85748 Garching, Germany 2Physics Department, Harvard University, Cambridge, Massachusetts 02318, USA 3ITAMP, Harvard-Smithsonian Center for Astrophysics, Cambridge, Massachusetts 02318, USA 4Donostia International Physics Center, Paseo Manuel de Lardizabal 4, E-20018 San Sebastián, Spain 5Ikerbasque Foundation for Science, Maria Diaz de Haro 3, E-48013 Bilbao, Spain 6Kavli Institute of NanoScience, TU Delft, P.O. Box 5046, 2600 GA Delft, Netherlands (Received 22 April 2015; published 10 September 2015) We propose a universal, on-chip quantum transducer based on surface acoustic waves in piezoactive materials. Because of the intrinsic piezoelectric (and/or magnetostrictive) properties of the material, our approach provides a universal platform capable of coherently linking a broad array of qubits, including quantum dots, trapped ions, nitrogen-vacancy centers, or superconducting qubits. The quantized modes of surface acoustic waves lie in the gigahertz range and can be strongly confined close to the surface in phononic cavities and guided in acoustic waveguides. We show that this type of surface acoustic excitation can be utilized efficiently as a quantum bus, serving as an on-chip, mechanical cavity-QED equivalent of microwave photons and enabling long-range coupling of a wide range of qubits. DOI: 10.1103/PhysRevX.5.031031 Subject Areas: Condensed Matter Physics, Quantum Physics, Quantum Information I. INTRODUCTION the surface of a solid and are widely used in modern electronic devices, e.g., as compact microwave filters The realization of long-range interactions between [14,15]. Inspired by two recent experiments [16,17], where remote qubits is arguably one of the greatest challenges the coherent quantum nature of SAWs has been explored, towards developing a scalable, solid-state spin-based quan- here we propose and analyze SAW phonon modes in tum information processor [1]. One approach to address piezoactive materials as a universal mediator for long- this problem is to interface qubits with a common quantum bus that distributes quantum information between distant range couplings between remote qubits. Our approach qubits. The transduction of quantum information between involves qubits interacting with a localized SAW phonon stationary and moving qubits is central to this approach. A mode, defined by a high-Q resonator, which in turn can be particularly efficient implementation of such a quantum bus coupled weakly to a SAW waveguide (WG) serving as a can be found in the field of circuit QED where spatially quantum bus; as demonstrated below, the qubits can be separated superconducting qubits interact via microwave encoded in a great variety of spin or charge degrees of photons confined in transmission line cavities [2–4]. In this freedom. We show that the Hamiltonian for an individual way, multiple qubits have been coupled successfully over node (for a schematic representation see Fig. 1) can take on ℏ 1 relatively large distances of the order of millimeters [5,6]. the generic Jaynes-Cummings form ð ¼ Þ, Fueled by dramatic advances in the fabrication and ω manipulation of nanomechanical systems [7], an alternate q σz ω † σþ σ− † Hnode ¼ 2 þ ca a þ gð a þ a Þ; ð1Þ line of research has pursued the idea of coherent, long- range interactions between individual qubits mediated by where σ~ refers to the usual Pauli matrices describing the mechanical resonators, with resonant phonons playing the qubit with transition frequency ω and a is the bosonic role of cavity photons [8–13]. q operator for the localized SAW cavity mode of frequency In this paper, we propose a new realization of a quantum ω 2π ∼ transducer and data bus based on surface acoustic waves c= GHz [18]. The coupling g between the qubit and (SAWs). SAWs involve phononlike excitations bound to the acoustic cavity mode is mediated intrinsically by the piezoproperties of the host material, it is proportional to the electric or magnetic zero-point fluctuations associated with a single SAW phonon and, close to the surface, can reach Published by the American Physical Society under the terms of ∼ 400 the Creative Commons Attribution 3.0 License. Further distri- values of g MHz, much larger than the relevant bution of this work must maintain attribution to the author(s) and decoherence processes and sufficiently large to allow for the published article’s title, journal citation, and DOI. quantum effects and coherent coupling in the spin-cavity 2160-3308=15=5(3)=031031(30) 031031-1 Published by the American Physical Society M. J. A. SCHUETZ et al. PHYS. REV. X 5, 031031 (2015) electromagnetic devices: (i) SAW resonators, the mechani- cal equivalents of Fabry-Perot cavities, with low-temper- ature measurements reaching quality factors of Q ∼ 105 even at gigahertz frequencies [22–24], and (ii) acoustic waveguides as analog to optical fibers [14]. (4) For a given frequency in the gigahertz range, due to the slow speed of sound of ∼103 m=s for typical materials, device dimen- sions are in the micrometer range, which is convenient for fabrication and integration with semiconductor compo- nents, and about 105 times smaller than corresponding electromagnetic resonators. (5) Since SAWs propagate FIG. 1. SAW as a universal quantum transducer. Distributed elastically on the surface of a solid within a depth of Bragg reflectors made of grooves form an acoustic cavity for approximately one wavelength, the mode volume is surface acoustic waves. The resonant frequency of the cavity is intrinsically confined in the direction normal to the surface. 2 determined by the pitch p, fc ¼ vs= p. Reflection occurs Further surface confinement then yields large zero-point effectively at some distance inside the grating; the fictitious fluctuations. (6) Yet another inherent advantage of our mirrors above the surface are not part of the actual experimental system is the intrinsic nature of the coupling. In piezo- setup, but are shown for illustrative purposes only. Red arrows indicate the relevant decay channels for the cavity mode: leakage electric materials, the SAW is accompanied by an electrical ϕ through the mirrors, internal losses due to, for example, surface potential , which has the same spatial and temporal imperfections, and conversion into bulk modes. Qubits inside and periodicities as the mechanical displacement and provides outside of the solid can be coupled to the cavity mode. In more an intrinsic qubit-phonon coupling mechanism. For exam- complex structures, the elastic medium can consist of multiple ple, recently, qubit lifetimes in GaAs singlet-triplet qubits layers on top of some substrate. were found to be limited by the piezoelectric electron- phonon coupling [25]. Here, our scheme provides a new system as evidenced by cooperativities [19] of C ∼ 10–100 paradigm, where coupling to phonons becomes a highly (see Sec. IV and Table I for definition and applicable valuable asset for coherent quantum control rather than a values). For ω ≈ ω , H allows for a controlled map- liability. q c node In what follows, we first review the most important ping of the qubit state onto a coherent phonon super- features of surface acoustic waves, with a focus on the position, which can then be mapped to an itinerant SAW associated zero-point fluctuations. Next, we discuss the phonon in a waveguide, opening up the possibility to different components making up the SAW-based quantum implement on-chip many quantum communication proto- transducer and the acoustic quantum network it enables: cols well known in the context of optical quantum SAW cavities, including a detailed analysis of the achiev- networks [13,20]. able quality factor Q, SAW waveguides, and a variety of The most pertinent features of our proposal can be different candidate systems serving as qubits. Lastly, as summarized as follows. (1) Our scheme is not specific exemplary application, we show how to transfer quantum to any particular qubit realization, but—thanks to the states between distant nodes of the network under realistic plethora of physical properties associated with SAWs in conditions. Finally, we draw conclusions and give an piezoactive materials (strain and electric and magnetic outlook on future directions of research. fields)—provides a common on-chip platform accessible to various different implementations of qubits, comprising II. SAW PROPERTIES both natural (e.g., ions) and artificial candidates, such as quantum dots (QDs) or superconducting qubits. In particu- Elastic