Periodic Reporting for period 2 - SUPERGALAX (Highly sensitive detection of single microwave photons with coherent quantum network of superconducting qubits for searching galactic axions) Reporting period: 2021-05-01 to 2022-12-31 Summary of the context and overall objectives of the project The overall objectives of the project are to develop and realize conceptually novel and practical quantum limited superconducting qubits network (SQN) detector capable to reveal single microwave (MW) photons for a photon frequency of ~10 GHz (with the energy 32000 times less than the energy of infrared visible photons) with a view to apply it to a search for galactic axions –cold dark matter candidates- by means of a “haloscopes”- the laboratory converter of axions to MW photons. The context objectives of the project are: -to develop a single MW photon detector based on moderate size networks of interacting superconducting qubits;-to develop an heralded microwave single photon source based on the Traveling Wave Josephson Parametric Amplifier (TWJPA);-to develop the single photon SQN detector integrated with the single photon source;-experimental study of feasibility of the single photon SQN detector for the “haloscope” type of axion searching. Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far The fabrication of photolithography masks and layouts for chips containing superconducting qubit network (SQN) detectors based on 5 and 10 flux qubits and 8 transmons qubits has been realized. The SQNs formed by an array of 8 transmon qubits coupled to the coplanar waveguide were fabricated and used to experimental study of the waveguide induced long-range interaction between qubits (Fig. 1). The qubits were consecutively tuned to a common resonance frequency at 7.898 GHz. Our spectroscopic test measurements (Fig. 2) has given an experimental evidence for a stable collective quantum state in the SQN up to 8 qubits. In addition, time resolved experiments showed reduced group velocities down to a factor of about 1500 smaller than in vacuum.We have elaborated the quantitative numerical model of an SQN interacting with a weak microwave (MW) radiation. The Heisenberg limit of sensitivity is reached in the presence of a strong long-range interaction between qubits. A comprehensive theoretical framework describing the interaction of single microwave photons with an array of superconducting transmon qubits in a waveguide cavity resonator has been developed. The coherent collective quantum states have been theoretically studied in disordered SQNs coupled to a low-dissipative resonator and a transmission line. An inductive coupling of SQN to a low-dissipative resonator provides an effective long-range interaction between all qubits. Coupling of an SQN to the transmission line allows one to experimentally access the temporal correlation function of equilibrium/non-equilibrium total polarization (Fig. 3). The collective quantum dynamics occurring in SQNs in presence of a spread of individual qubit frequencies has been studied theoretically. An amplitude of the main resonance drastically increases as the interaction overcomes the disorder, and the collective state is formed. In the presence of a weak non-resonant photon field, the positions of resonances depend on the number of photons, i.e. the collective ac Stark effect is obtained (Fig.4). Traveling Wave Josephson Parametric Amplifier (TWJPA)-the core of the heralded single MW photon source-was designed and fabricated (Fig.5) . A preliminary measurements of the correlated signals at the output of JTWPA were performed at T=100 mK.T-type three terminal SQNs with 10 c-shunted flux qubits have been fabricated (Fig. 6)A new dilution refrigerator able to reach T= 8 mK was installed in the Laboratori Nazionali di Frascati of the INFN, Italy. Scattering parameters measurements and two-tone spectra experiment were carried out on the T-type three terminal SQNs with 10 c-shunted flux qubits (Fig. 6) at zero magnetic field and at T=15 mK. A substantial shift of the resonant drop in the transmission coefficient induced by the pump second-tone signal was observed (Fig.7) and this effect presents experimental evidence of a non-linear multiphoton interaction between the pump signal and flux qubits of the SQN.The Workshop "Searching for Galactic Axions and Superconducting Devices with Quantum Efficiency" have been organised on October 25-29,2021 with the help of SUPERGALAX consortium. Special Session on Quantum Detection in the framework of the 14th Workshop on Low Temperature Electronics (WOLTE14) has been organized. The SUPERGALAX activity has been presented on the Applied Superconductivity Conference 2022 – ASC 22 , 23-28 October, 2022, Honolulu, US. Several scientific seminars hosted the talks about SUPERGARAX activities have been periodically hold. Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far) Proposed in this project the detection principle based on interacting superconducting qubit networks (SQNs) will outperform state-of-the-art of currently existing single qubit detectors in:- high efficiency of detection of single microwave (MW) photons.- in sensitivity reaching the Heisenberg limit - a quantum non-demolition measurement and therefore, probe spatial correlations of photon states.- detecting the signal even against the background of strong local ambient noise.Expected results:- design and technology: design and fabrication of SQNs embedded in a low-disipative resonator and coupled to a transmission line; design and fabrication of the heralded single MW photon source; -theory: a theoretical study of temporal and spatial correlations of single photons interacting with an SQN; theory of a Heisenberg limited superconducting quantum detector; theory of the collective AC Stark effect. -experimental technique: experimental evidences of the collective states in SQN; experimental detection of low MW power signals by SQNsThe potential impact of the project is-technology:. Design and fabrication of a single microwave photon detector based on SQNs embedded in a cavity; Josephson travelling wave parametric amplifier based on a large number (up to 900) Josephson junctions;-metrology:. The SQN detector presents a novel quantum detector of single quantum-limited MW signal.-quantum technologies. Proposed SQN detector with quantum limit sensitivity is an essential device for quantum modelling with solid-state circuits and MW photons, ultrasensitive analysis of MW components, and non-classical photon states; - MW quantum photonic circuits. High fidelity of the developed single MW photon source will permit to realize photonic circuits with synchronized multiple single photon sources;- quantum simulators. The elaborated SQN detector serves as a prototype of quantum analogous simulator. - theoretical physics. a quantitative theory for modelling of large networks of strongly coupled superconducting qubits- fundamental physics knowledge. The novel SQN detector with quantum limit sensitivity will be employed in the experimental search of axions in the universe.-world-wide scientific collaboration. The successful realization of the Project and dissemination of the results will maintain the existing and create new valuable scientific collaborations between prominent international groups working in the field of quantum information and physics of elementary particles.-education in quantum technology. Seminars in the Bochum University (Germany) and in the Center for Theoretical Physics of Complex Systems, Institute for Basic Science, Daejeon (Republic of Korea). Bachelor and master student’s research activity.-social impact. Financial support of 5 young PhD fellow researchers. Setup of the SQN composed of 8-transmon qubits for microwave transmission measurements. Shift of the resonant drop in the transmission coefficient on the two-tone experiment. Schematic of experimental setup composed of a flux-qubits SQN coupled to a low-dissipative resonato SEM images of fabricated T-type three terminal SQN with 10 c-shunted flux qubits. Heralded single MW photon source based on TWJPA. Frequency dependent transmission coefficient for N resonant qubits tuned to the frequency 7.898GHz. Dominant resonance frequency positions versus interaction strength for different Fock states.