Bose-Einstein Condensate Achieved in 10-Qubit Superconducting Network with Resonator

Researchers are increasingly exploring superconducting qubit networks as a pathway to macroscopic quantum phenomena and enhanced detector sensitivity. Patrick Navez (Université de Montpellier), Valentina Di Meo (CNR SPIN), and Berardo Ruggiero (CNR ISASI), alongside colleagues including C Gatti, F Chiarello and A D’Elia, demonstrate a novel approach using resonator-embedded networks to induce and observe Bose-Einstein condensation of microwave photons. Their two-tone spectroscopy experiment reveals a striking bistability in the photon number within the resonator, evidenced by an abrupt shift in resonant dip position when a critical pump power is reached. This observation , tunable with an applied magnetic field , confirms theoretical predictions and signifies a crucial step towards harnessing strong nonlinear interactions for advanced quantum technologies and ultra-sensitive microwave photon detection.

Experiments involved a two-tone spectroscopy technique, utilising a network of 10 flux qubits coupled to both an input resonator and an output transmission line, to probe these nonlinear interactions. An external microwave pump field, tuned close to the resonator’s resonance frequency, was used to populate the resonator mode as a Bose-Einstein condensate, while a second probe beam scanned for resonances, specifically Bogoliubov-like excitations.

This sharp shift, occurring within a narrow frequency range and tunable via an applied magnetic field, serves as a definitive signature of the bistability. The observed bistability aligns perfectly with theoretical predictions, confirming the successful implementation of this novel approach to manipulating microwave photons. This work opens exciting possibilities for advanced quantum technologies and highly sensitive detection systems. The research builds upon years of investigation into Josephson junction circuits, which have long served as a unique platform for studying fascinating physical phenomena, including magnetic Josephson vortices and superconductor-insulator quantum phase transitions.
The explosive growth of quantum technologies has driven the development of SQNs, whose dynamics are governed by quantum-mechanical laws on a macroscopic scale, enabling the creation of quantum processors and sensitive photon detectors. Crucially, even weak coupling of SQNs to high-quality resonators produces a non-negligible qubit-qubit coupling via resonator modes, leading to the emergence of collective quantum states. This team successfully harnessed this principle, leveraging the ac Stark effect to establish a strong interaction between microwave photons and the collective quantum states of the SQN. The experimental setup involved a device comprising two resonators, a T-resonator and an R-resonator, coupled through the SQN, which consisted of 10 capacitively-shunted superconducting flux qubits, each containing three Josephson junctions.

The SQN exhibited a coupled resonant frequency of approximately 7.7GHz and a coupling quality factor of around 105. Measurements were conducted at a cryogenic temperature of 15 mK within a dilution refrigerator at the Laboratori Nazionali di Frascati in Italy. The results definitively demonstrate the predicted bistability and pave the way for future advancements in quantum photonics and sensitive microwave detection.

Two-tone Spectroscopy of Superconducting Qubit Networks reveals valuable

The study pioneered a method for probing nonlinear interactions between microwave photons by coupling a set of ten flux qubits to both an input R-resonator and an output T-transmission line. Researchers populated the resonator mode with a Bose-Einstein condensate using an external microwave pump field, then scanned a second probe beam to excite Bogoliubov-like excitations within the system. This approach enables precise measurement of resonant frequencies and reveals subtle changes in the system’s behaviour under varying pump power. Experiments employed a Leiden Cryogenics CF-CS110-1000 dilution refrigerator, maintained at 15 mK,. Scientists also harnessed a static magnetic field of 0.489 G, observing a shift of the pump power threshold, Pcr, to lower values, further demonstrating control over the system’s bistable behaviour. This innovative methodology, combining precise spectroscopic measurements with controlled pump power and magnetic field manipulation, provides a powerful platform for exploring macroscopic quantum phenomena and enhancing the sensitivity of microwave photon detectors.

Bistability Observed in Superconducting Qubit Network

Experiments revealed that the SQN, comprising 10 capacitively-shunted flux qubits, exhibited a coupled resonant frequency of approximately 7.7GHz with a coupling quality factor, Qc, of around 105. Researchers implemented the device using two resonators, a T-resonator and an R-resonator, coupled through the SQN. The fabrication process, conducted at 15 mK temperature, allowed for strong suppression of parasitic coupling between the resonators in the absence of microwave photons, ensuring electrodynamic isolation. Two-tone spectroscopy was employed, measuring the transmission coefficient S21(fp) between ports of the T-resonator while injecting microwave photons at port 3 of the R-resonator.

The dependence of the dip frequency position on pump power, Ppump, was carefully mapped for various pump signal frequencies, fpump, revealing a pronounced effect within the narrow range of 7.743GHz to 7.746GHz. Measurements confirm that the magnitude of the frequency drop decreased and the threshold power, Pcr, shifted downwards as the pump frequency increased slightly. This behaviour strongly suggests the presence of a bistable regime, where the system exhibits two stable states for the same input conditions. By fitting experimental data, scientists deduced the photon number within the cavity, demonstrating its behaviour in both lower and higher branches of the bistable regime. The derived time-dependent non-linear Schrodinger-like equation remarkably reproduces the experimental data, solidifying the understanding of this complex quantum phenomenon and paving the way for advanced detector technologies.

Macroscopic Quantum Dynamics in Superconducting Networks

This shift, observed across a narrow range of pump frequencies and tunable with a magnetic field, provides experimental evidence for collective quantum dynamics on a macroscopic scale. The research team identified a significant frequency shift of approximately 200MHz per Gauss in the qubit frequency, aligning with theoretical predictions. They attribute this phenomenon to a nonlinear, multiphoton interaction between the pump microwave signal and the qubits of the SQN, showing good agreement between their experimental results and the theoretical model. The authors acknowledge that interpreting the dependence of the critical pump power on the magnetic field remains challenging, as they did not observe substantial changes in the bistability region when tuning the qubit frequency.

Future investigations could focus on elucidating this relationship further. These findings are significant as they demonstrate a pathway towards realising quantum threshold detectors or bistable memory elements within circuit quantum electrodynamics architectures. The observed bistability and hysteretic behaviour offer potential for advanced quantum information processing applications. However, the authors note limitations in fully understanding the magnetic field dependence of the critical pump power, suggesting a need for more detailed analysis in future work.