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We investigate the quantum dynamics of a single transmon qubit coupled tosurface acoustic waves (SAWs) via two distant connection points. Since theacoustic speed is five orders of magnitude slower than the speed of light, thetravelling time between the two connection points needs to be taken intoaccount. Therefore, we treat the transmon qubit as a giant atom with adeterministic time delay. We find that the spontaneous emission of the system,formed by the giant atom and the SAWs between its connection points, initiallydecays polynomially in the form of pulses instead of a continuous exponentialdecay behaviour, as would be the case for a small atom. We obtain exactanalytical results for the scattering properties of the giant atom up totwo-phonon processes by using a diagrammatic approach. We find that two peaksappear in the inelastic (incoherent) power spectrum of the giant atom, aphenomenon which does not exist for a small atom. The time delay also givesrise to novel features in the reflectance, transmittance, and second-ordercorrelation functions of the system. Furthermore, we find the short-timedynamics of the giant atom for arbitrary drive strength by a numerically exactmethod for open quantum systems with a finite-time-delay feedback loop.

The giant acoustic atom -- a single quantum system with a deterministic time delay