We study a phononic crystal interacting with an articial atom - a superconducting quantum system - in the quantum regime. The phononic crystal is made of a long lattice of narrow metallic stripes on a quatz surface. The articial atom in turn interacts with a transmission line. Therefore, two degrees of freedom of different nature, acoustic and electromagnetic, are coupled with a single quantum object. A scattering spectrum of propagating electromagnetic waves on the articial atom visualizes acoustic modes of the phononic crystal. We simulate the system and found quasinormal modes of our phononic crystal and their properties. The calculations are consistent with the experimentally found modes, which are tted to the dispersion branches of the phononic crystal near the rst Brillouin zone edge. Our geometry allows to realize effects of quantum acoustics on a simple and compact phononic crystal.

Here we present an experimental data used for ploting the figures: 2a, 2b, 2c, 3 and for Fig4c inset. 

All datasets are titled according to the corresponding figure number in the manuscript:

data_for_Fig_2a.csv

data_for_Fig_2b.pkl

data_for_Fig_2c.csv

data_for_Fig_3.csv

data_for_Fig4c_inset.csv

Our experiment is performed at a base temperature T = 15 mK of a dilution refrigerator, so that the thermal uctuations are well below the energy of surface acoustic phonons, which are in the gigahertz range of frequencies. We implement the measurement setup typically used for quantum optics experiments with superconducting arti cial atoms. The electromagnetic waves are transmitted from a vector network analyzer (VNA) through coaxial cables and a set of attenuators at different cooling stages, for suppressing room temperature blackbody radiation. Atom-wave interaction results in the scattering of the propagated through a transmission line waves, detected as a change in phase and amplitude of the transmitted signal close to the qubit resonance frequency. The transmitted signal is then amplied by cryogenic and room-temperature ampliers and measured by the VNA. The data for the Figures 2a, 2b, 2c and 3 by using the method described above.  The corresponding data files are: data_for_Fig_2a.csv, data_for_Fig_2b.pkl, data_for_Fig_2c.csv, data_for_Fig_3.csv. In measurements for Figures 2b, 2c and 3, we changed the magnetic field by applying current to the coil. Therefore, there is a current column in the data. Figure 2a is a measurement of signal transmission versus frequency for a fixed magnetic field. Accordingly, there is no current column in this data(data_for_Fig_3.csv). 

In order to get the data for Fig.4c inset we measured the reflection coefficient of the microwave signal applied directly to the interdigital transducer, which has the same geometry as the phononic crystal. The resonance dips found in this experimental plot correspond to the excitation of quasi-normal modes

All data can be easily visualized. For example, by using the library matplotlib in python. Other standard software tools for data visualization can also be used as the data in the files is presented as columns with obvious headers. Particulary, the table of each dataset can be opened in Microsoft Excel.