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.
In quantum optics, light-matter interaction has conventionally been studied using small atoms interacting with electromagnetic fields with wavelength several orders of magnitude larger than the atomic dimensions [1, 2]. In contrast, here we experimentally demonstrate the vastly different giant atom regime, where an artificial atom interacts with acoustic fields with wavelength several orders of magnitude smaller than the atomic dimensions. This is achieved by coupling a superconducting qubit [3] to surface acoustic waves at two points with separation on the order of 100 wavelengths. This approach is comparable to controlling the radiation of an atom by attaching it to an antenna. The slow velocity of sound leads to a significant internal time-delay for the field to propagate across the giant atom, giving rise to non-Markovian dynamics [4]. We demonstrate the non-Markovian character of the giant atom in the frequency spectrum as well as nonexponential relaxation in the time domain. Following studies of the interaction between atoms and photons in cavity Quantum Electrodynamics (cavity QED) configurations, where the atom is placed inside a cavity to enhance the interaction strength with the radiation field [5,6], superconducting circuit quantum electrodynamics emerged in the last 15 years as an analogue to the cavity QED experiments. This has enabled probing the strong coupling regime of atom -light interaction to study exotic phenomena including vacuum Rabi splitting [7] and the controlled generation of non-classical photon states [8,9]. A later development was waveguide QED where superconducting circuits where coupled to open transmission lines [10,11,12]. These experiments replace natural atoms and optical cavities with Josephson junction-based superconducting circuits behaving 1 arXiv:1812.01302v1 [quant-ph]
A novel way to create a band structure of the quasienergy spectrum for driven systems is proposed based on the discrete symmetry in phase space. The system, e.g., an ion or ultracold atom trapped in a potential, shows no spatial periodicity, but it is driven by a time-dependent field coupling highly nonlinearly to one of its degrees of freedom (e.g., ∼q(n)). The band structure in quasienergy arises as a consequence of the n-fold discrete periodicity in phase space induced by this driving field. We propose an explicit model to realize such a phase space crystal and analyze its band structure in the frame of a tight-binding approximation. The phase space crystal opens new ways to engineer energy band structures, with the added advantage that its properties can be changed in situ by tuning the driving field's parameters.
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