Enhanced electron-phonon coupling for a semiconductor charge qubit in a surface phonon cavity

www.nature.com/scientificreports OPEN received: 15 June 2015 accepted: 18 September 2015 Published: 15 October 2015 Enhanced electron-phonon coupling for a semiconductor charge qubit in a surface phonon cavity J. C. H. Chen1, Y. Sato1, R. Kosaka1, M. Hashisaka1, K. Muraki2 & T. Fujisawa1 Electron-phonon coupling is a major decoherence mechanism, which often causes scattering and energy dissipation in semiconductor electronic systems. However, this electron-phonon coupling may be used in a positive way for reaching the strong or ultra-strong coupling regime in an acoustic version of the cavity quantum electrodynamic system. Here we propose and demonstrate a phonon cavity for surface acoustic waves, which is made of periodic metal fingers that constitute Bragg reflectors on a GaAs/AlGaAs heterostructure. Phonon band gap and cavity phonon modes are identified by frequency, time and spatially resolved measurements of the piezoelectric potential. Tunneling spectroscopy on a double quantum dot indicates the enhancement of phonon assisted transitions in a charge qubit. This encourages studying of acoustic cavity quantum electrodynamics with surface phonons. Coupling of electrons to intrinsic phonons has been known to cause scattering1 or energy relaxation2–4 in semiconductor electronic systems. Previous studies2,3 showed that spontaneous emission of energies into the phonon bath is a major dissipation mechanism in charge and spin qubits in GaAs/AlGaAs systems. However, this negative effect can be applied in a constructive way to realise an acoustic analog of cavity quantum electrodynamic (cQED) system5–8 for reaching the strong or ultra-strong coupling regime in cQED. It will be advantageous to fabricate an acoustic cQED system because it traps phonons with wavelengths in the nanometer regime, which is smaller than the microwave cavities used in conventional cQED systems. Smaller wavelengths allow for the fabrication of a smaller cavity with the potential of achieving a larger electron-cavity coupling9. Previously phonon cavities have been demonstrated on suspended nanowires10–13 however it is challenging to confine intrinsic crystallographic phonons6–8. Acoustic waves in piezoelectric materials, such as GaAs, has a large coupling to quantum dots14–17 or superconducting qubits18,19, and are advantageous for realising strong or ultra-strong coupling regimes with a small cavity9. In this study we demonstrate phonon cavities for surface acoustic waves (SAW) on a GaAs/AlGaAs heterostructure. Brag reflectors (BR) deposited onto the surface of the heterostructure are used as mirrors to reflect and trap SAW. By observing the piezoelectric potential of the SAW through time, spatial and frequency measurements, we identify the phonon band gap and cavity modes of our phonon cavities. Furthermore coupling of the cavity mode to a charge qubit is demonstrated through phonon assisted transport measurements on a double quantum dot and observe to be enhanced at the resonant frequency of the cavity. The coupling frequency g between a qubit and a cavity mode can be enhanced by reducing the mode volume V of the cavity. For standard cQED with electromagnetic waves, g normalized by the resonant 1 Department of Physics, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro, 152-8551, Japan. 2NTT Basic Research Laboratories, NTT Corporation, 3-1 Morinosato-Wakamiya, Atsugi, 243-0198, Japan. Correspondence and requests for materials should be addressed to J.C.H.C. (email: ) or T.F. (email: ) Scientific Reports | 5:15176 | DOI: 10.1038/srep15176 1 www.nature.com/scientificreports/ BR λBR a cavity: D BR r cavity mode d DQD AlGaAs GaAs 1 µm Figure 1. A SAW phonon cavity. (a) A schematic of the proposed phonon cavity. Two arrays of BRs for λBR determined by the period a are placed at the distance D. A DQD is formed at a distance d beneath the sample surface. SAWs are reflected at metal edges with a reflection coefficient r. Cavity mode is indicated by the standing wave beneath the schematic with a node in the middle of the DQD so maximum electronphonon coupling can be obtained. (b) A scanning electron micrograph (SEM) of a control device with identical design to Device B. Metal layers with the thickness of 10 nm for Ti and 30 nm for Au are patterned. Periodic arrays serve as BRs for forming a phonon cavity and IDT for generating SAWs. Fine metal fingers in the middle of the cavity are used to define point contacts for the phase-sensitive local potential measurements or a DQD for studying phonon assisted tunneling. frequency ω is bounded by the fine structure constant α ~ 1 , as seen in the form g = α l λ for an ω 137 V electric dipole of the length l and the wavelength λ5,20. Since geometric constraints require V to be greater than l2λ, g is practically limited by α . The phonon cavity is attractive for overcoming this limitation ω by taking advantage of its small mode volume associated with the slow speed v compared with the light speed c. Considering the electromechanical coupling K2 (0.07% for GaAs SAW)21,22, the normalized coupling for acoustic cQED is bounded by the effective fine structure constant αeff = αK 2c / v εr (εr being the relative dielectric constant). This can be greater than α in some piezoelectric materials (αeff / α ~ 10 for GaAs SAW and potentially greater than 100 for ZnO SAW and other piezoelectric materials23), and thus attractive for reaching the ultra-strong coupling regime. We show that GaAs SAW phonons are successfully confined in a cavity for enhancing the electron-phonon coupling. The coupling between SAW and a charge qubit in two-dimensional electron gas (2DEG) of a GaAs/ AlGaAs heterostructure is significant even without forming a cavity24. SAW is a Rayleigh wave localized near the surface within the penetration length (≈ 0.3 λ) comparable to the SAW wavelength λ, which provides a large piezoelectric field at the 2DEG located near the surface25. A charge qubit, in which an excess electron occupies one of the two dots, has an electric dipole (el) for the dot distance l26. The coupling can be maximized when l is comparable to λ/2 of SAW that resonate with the level spacing of the qubit (typically a few GHz)2. Typical GaAs DQDs approximately meet this condition (λ =  800 nm for the SAW frequency f =  3.2 GHz, 2DEG depth d =  95 nm and l =  240 nm in our device). We show that SAW can be confined in a cavity and the coupling can be further enhanced by designing a SAW cavity. A SAW cavity can be formed by two BRs made of periodic metal arrays with a period a, shown by the schematic in Fig. 1a. Metallization of the semiconductor surface decreases the SAW velocity by about 10% and causes a small reflection with a coefficient r (≈ 1%) at the metal edges27. With a large number NBR ( 1/r) of the array, the total reflection coefficient approaches unity for a specific wavelength λBR close to 2a. When two BRs are separated by a gap distance D which equals an odd int (...truncated)