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arXiv:2601.15101

Bose condensation and Bogoliubov excitation in resonator-embedded superconducting qubit network

Patrick Navez, Valentina Di Meo, Berardo Ruggiero, Claudio Gatti, Fabio Chiarello, Alessandro D'Elia, Alessio Rettaroli, Emanuele Enrico, Luca Fasolo, Mikhail Fistul, Ilya Eremin, Alexandre Zagoskin, Paolo Vanacore, Paolo Silvestrini, Mikhail Lisitskiy

quant-phSubmitted Jan 21, 2026• Announced Jan 22, 2026• 0 citations• Revised Jan 26, 2026 (v2)
v1 · Jan 21, 2026v2 · Jan 26, 2026
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Abstract

Superconducting qubit networks (SQNs) embedded in a low-dissipative resonator is a promising device allowing one not only to establish the collective quantum dynamics on a macroscopic scale but also to greatly enhance the sensitivity of detectors of microwave photons. A quantum ac Stark effect provided by coupling between an SQN and microwave photons of a resonator, leads to a strong nonlinear interaction between photons. Here, we present a two-tone spectroscopy experiment in which a set of 10 superconducting flux qubits is coupled to the input R- resonator and the output T- transmission line. An external microwave pump field close to the resonance frequency populates macroscopically the resonator mode as a Bose-Einstein condensate, while a second probe beam scans the resonances referred also as Bogoliubov-like excitations. The corresponding excitation frequency measured from the transmission coefficient, |S21(f)| displays an abrupt change of the resonant dip position once the power of the pump field overcomes a critical value Pcr. This sharp shift occurs in a narrow region of pump frequencies, and can be tuned by an applied magnetic field. It is a signature of bistability of the photon number inside the resonator, in agreement with theory.

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Superconducting qubit networks (SQNs) embedded in a low-dissipative resonator is a promising device allowing one not only to establish the collective quantum dynamics on a macroscopic scale but also to greatly enhance the sensitivity of detectors of microwave photons. A quantum ac Stark effect provided by coupling between an SQN and microwave photons of a resonator, leads to a strong nonlinear interaction between photons. Here, we present a two-tone spectroscopy experiment in which a set of 10 superconducting flux qubits is coupled to the input R- resonator and the output T- transmission line. An external microwave pump field close to the resonance frequency populates macroscopically the resonator mode as a Bose-Einstein condensate, while a second probe beam scans the resonances referred also as Bogoliubov-like excitations. The corresponding excitation frequency measured from the transmission coefficient, |S21(f)| displays an abrupt change of the resonant dip position once the power of the pump field overcomes a critical value Pcr. This sharp shift occurs in a narrow region of pump frequencies, and can be tuned by an applied magnetic field. It is a signature of bistability of the photon number inside the resonator, in agreement with theory.
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We have performed spectroscopic measurements of a superconducting qubit dispersively coupled to a nonlinear resonator driven by a pump microwave field. Measurements of the qubit frequency shift provide a sensitive probe of the intracavity field, yielding a precise characterization of the resonator nonlinearity. The qubit linewidth has a complex dependence on the pump frequency and amplitude, which is correlated with the gain of the nonlinear resonator operated as a small-signal amplifier. The corresponding dephasing rate is found to be close to the quantum limit in the low-gain limit of the amplifier.
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Experimental search of galactic axions requires detection of single photons in the microwave range. We work on a novel approach to detect single microwave photons based on a coherent collective response of quantum states occurring in a superconducting qubit network (SQN) embedded in a lowdissipative superconducting resonator. We propose a two resonators detector configuration with two parallel resonators without common part and with separated input and output terminals. The device consists of a low-dissipative resonator with embedded SQN in which microwave photons arrive (“signal resonator”), and a transmission line for measuring the frequency dependent transmission coefficient demonstrating resonant drops at the qubit frequencies (“readout resonator”). In comparison with T-type three terminal device recently proposed and investigated by us, the device with two resonators with separated input and output terminals doesn't contain common part of both resonators and exclude an unwanted noise from measurement readout circuits to the signal resonator. A layout of two resonators four terminal SQN detectors containing 5 flux qubits weakly coupled to a low-dissipative signal and readout resonator was developed and optimized. The samples were fabricated by Manhattan Al-based technology with Nb resonator circuits. The SQN detector was experimentally tested in terms of microwave measurements of scattering parameters of both resonators, and crosstalk properties. Comparison of experimental data with results of the simulations permits one to conclude that the electromagnetic conditions of the fundamental resonant peak of 8.5 GHz of both resonators aren't affected by the crosstalk phenomenon and their performances provided by the design remain not altered for correct device operation
We propose a novel approach to detect a low power microwave signal with a frequency of the order of several GHz based on a coherent collective response of quantum states occurring in a superconducting qubits network (SQN). An SQN composes of a large number of superconducting qubits embedded in a low-dissipative superconducting resonator. Our theory predicts that an SQN interacting with the off-resonance microwave radiation, demonstrates the collective alternating current Stark effect that can be measured even in the limit of single photon counting. A design of the layout of three terminals SQN detectors containing 10 flux qubits weakly coupled to a low-dissipative R-resonator and T-transmission line was developed. The samples were fabricated by Al-based technology with Nb resonator. The SQN detector was tested in terms of microwave measurements of scattering parameters and two-tone spectroscopy. A substantial shift of the frequency position of the transmission coefficient drop induced by a second tone pump signal was observed, and this effect clearly manifests a nonlinear multiphoton interaction between the second-tone microwave pump signal and an array of qubits.