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

TL;DR

This paper studies a giant transmon qubit coupled to surface acoustic waves, revealing unique decay, scattering, and correlation phenomena caused by the deterministic time delay inherent to its large size.

Contribution

It introduces a quantum model of a giant atom with a time delay, providing exact analytical results and numerical methods for its scattering and dynamical properties.

Findings

Polynomial decay of spontaneous emission pulses

Appearance of two peaks in the inelastic power spectrum

Novel features in reflectance, transmittance, and correlation functions

Abstract

We investigate the quantum dynamics of a single transmon qubit coupled to surface acoustic waves (SAWs) via two distant connection points. Since the acoustic speed is five orders of magnitude slower than the speed of light, the travelling time between the two connection points needs to be taken into account. Therefore, we treat the transmon qubit as a giant atom with a deterministic time delay. We find that the spontaneous emission of the system, formed by the giant atom and the SAWs between its connection points, initially decays polynomially in the form of pulses instead of a continuous exponential decay behaviour, as would be the case for a small atom. We obtain exact analytical results for the scattering properties of the giant atom up to two-phonon processes by using a diagrammatic approach. We find that two peaks appear in the inelastic (incoherent) power spectrum of the giant atom, a phenomenon which does not exist for a small atom. The time delay also gives rise to novel features in the reflectance, transmittance, and second-order correlation functions of the system. Furthermore, we find the short-time dynamics of the giant atom for arbitrary drive strength by a numerically exact method for open quantum systems with a finite-time-delay feedback loop.