Superconducting chip shows quantum phase shift across 21 modes

Researchers at Chalmers University of Technology have observed a simultaneous frequency jump across 21 superconducting resonators, demonstrating a multi-mode dissipative first-order phase transition within a one-dimensional Bose-Hubbard chain. This experiment provides a platform to study quantum phase transitions in systems that lose energy, unlike most theoretical work focused on equilibrium conditions. The work characterizes a phase transition, with switching times measured from a few milliseconds up to 143 seconds.

The team reports that these results “open a new window into non-equilibrium quantum many-body physics” and advance the understanding of these transitions using superconducting circuits.

Multimode Phase Transition in 21-Resonator Superconducting Chain A chain of 21 superconducting resonators has demonstrated a synchronized quantum phase transition, where a shift in frequency occurred simultaneously across all elements when subjected to a changing pump tone. This experiment marks a significant increase in scale for observing such transitions, moving beyond individual resonators or small arrays towards a system approaching the thermodynamic limit, a regime where collective quantum effects become dominant. The observed phase transition manifested as a distinct jump in the frequency of each resonator mode as the frequency or power of the applied pump tone was altered. This “all-at-once” shift indicates a strong interconnectedness within the system, where the state of one resonator directly influences the others. By meticulously measuring the system’s emission spectrum during this transition, the team was able to map out the complete phase diagram, delineating the conditions under which the shift occurs. The experimental setup utilized a chain of lumped-element nonlinear resonators, each incorporating an array of 10 Josephson junctions to create a nonlinear inductance. These resonators were coupled to each other, forming a one-dimensional Bose-Hubbard chain, and accessed via input and output ports for both pumping and probing. Characterization of the chain at low power revealed 21 discernible peaks in the transmission spectrum, each corresponding to a hybridized mode of the resonators. From these measurements, the team estimated a nearest-neighbor coupling strength of J, providing key parameters for understanding the system’s behavior. The core of the experiment involved applying a coherent pump tone and sweeping its frequency while monitoring the transmission through the metamaterial. As the pump frequency approached the resonant frequency of a specific mode, a frequency shift was observed. This shift abruptly ceased when the detuning became sufficiently large, causing the mode to return to its original state. The researchers write that this behavior has previously been observed in other systems and characterizes a first-order phase transition. This observation confirms the emergence of a distinct phase transition within the superconducting chain.

The team’s model, based on single-mode mean-field theory and cross-Kerr interactions, successfully captured the observed features at moderate pump powers. This theoretical framework, incorporating self- and cross-Kerr nonlinearities, quantitatively reproduced the transition line, validating the experimental findings. The ability to accurately model the system’s behavior with a relatively simple theoretical approach suggests a deeper understanding of the underlying physics governing the phase transition. The researchers emphasize that this work explores a system not previously studied, approaching the thermodynamic limit, and opening possibilities for future investigations into more complex quantum systems. The implications of this research extend beyond the immediate demonstration of a multimode phase transition. The ability to control and observe such transitions in a large-scale superconducting circuit provides a platform for exploring fundamental questions in quantum many-body physics. Specifically, the study addresses the ongoing debate regarding the correspondence between driven-dissipative quantum systems and their equilibrium counterparts. These dissipative systems, which lose energy to their environment, often exhibit behaviors that differ from traditional equilibrium systems, and understanding these differences is crucial for developing new quantum technologies. The precision of the measurements, combined with the theoretical validation, establishes a robust foundation for future studies. The 21-resonator chain provides a scalable platform for investigating more complex quantum phenomena, potentially leading to advancements in areas such as quantum sensing and computation. By pushing the boundaries of what can be observed and controlled in superconducting circuits, this research contributes to a deeper understanding of the quantum world and its potential applications. Bose-Hubbard System Hamiltonian & Device Implementation Superconducting circuits at Chalmers University of Technology are revealing new insights into quantum phase transitions, with a recent experiment demonstrating a synchronized shift in frequency across 21 interconnected superconducting resonators. This achievement, detailed in a new study, moves beyond previous investigations of isolated quantum systems by creating a large-scale, one-dimensional Bose-Hubbard chain capable of exhibiting collective quantum behavior. The device, fabricated with lumped-element resonators and incorporating an array of Josephson junctions to create nonlinearity, allows researchers to explore the behavior of many-body quantum systems in a way previously limited by technological constraints. Researchers induced this transition by sweeping the frequency or power of a pump tone applied to the system, observing a simultaneous frequency jump across all 21 modes. The observed phase transition manifests as a dim-to-bright transition, where the system shifts from a state of low photon occupation to one with a significantly increased number of photons. Complementary time-dependent measurements, tracking the switching speed between the dim and bright phases, corroborated the transition line and revealed transition times ranging from a few milliseconds up to 143 seconds. This wide range in switching times suggests a complex interplay of factors influencing the dynamics of the phase transition. The researchers are investigating whether a correspondence can be drawn between these non-equilibrium systems and their equilibrium analogs, a pressing question in contemporary physics. By demonstrating a multimode first-order dissipative phase transition in a well-controlled superconducting circuit, they provide valuable data for testing theoretical predictions and refining our understanding of these complex systems. The ability to observe this synchronized behavior across multiple modes is a key achievement, demonstrating the effectiveness of the device and the underlying physics. Frequency-Dependent Transitions via Pump Tone Sweeps Claudia Castillo-Moreno of the Department of Microtechnology and Nanoscience at Chalmers University of Technology led a study demonstrating a synchronized quantum shift across a surprisingly large array of superconducting resonators.

The team’s experiment, detailed in recent findings, utilized a one-dimensional Bose-Hubbard chain fabricated from 21 interconnected superconducting resonators to observe a first-order dissipative phase transition. This configuration allows for the exploration of quantum phenomena in a system approaching a scale where collective behavior becomes more pronounced and predictable. The scale of the array is notable, representing a significant increase in complexity compared to previous experiments examining similar transitions with fewer interconnected elements. Characterizing the individual resonators revealed a decay rate of γ, the one directly targeted by the pump signal. This precise measurement of loss mechanisms is crucial for understanding the system’s behavior and validating the theoretical models used to interpret the observed transitions.

The team employed transmission measurements, specifically examining the S21 parameter, to map the phase transition as the pump frequency was swept. Further analysis involved constructing a complete phase diagram by measuring the system’s emission spectrum, allowing for detailed characterization of the dim-to-bright phase transition. The ability to map this diagram confirms the robustness of the observed phenomenon and provides a framework for future investigations. Time-dependent measurements were also performed to analyze the switching dynamics between the two phases of the transition.

Phase Diagram Extraction Using Power Spectral Density Researchers observed an instantaneous frequency shift across all resonators when altering the frequency or power of a driving signal, a behavior indicative of a collective quantum phenomenon. The observed transition isn’t a gradual drift, but a sudden, coordinated jump in the resonant frequency of each of the 21 resonators. By constructing a 1D Bose-Hubbard chain, the team created a system that, unlike many theoretical models, approaches the thermodynamic limit, a regime where the system’s behavior is governed by collective effects rather than individual component properties. Characterizing this transition required a detailed mapping of the system’s phase diagram, achieved through measurements of the emitted radiation spectrum. By analyzing the power spectral density, researchers were able to identify the boundaries between different quantum phases, regions where the system exhibits distinct behaviors. This process revealed a clear dim-to-bright phase transition, where the resonators switch from a state of minimal energy emission to one of maximal emission. This agreement provides a framework for understanding the behavior of similar systems and for developing more sophisticated quantum simulations. This theoretical framework provides a valuable tool for interpreting the experimental results and for predicting the system’s behavior under different conditions. Unlike traditional quantum systems which are isolated, these systems exchange energy with their environment, leading to unique dynamics and potential applications. The experiment’s scale, utilizing 21 interconnected superconducting elements, is particularly noteworthy. While theoretical studies have explored similar transitions in two-dimensional systems, this work demonstrates the feasibility of realizing and characterizing them in a one-dimensional chain. This achievement opens up new avenues for exploring the fundamental properties of quantum matter and for developing novel quantum technologies. 👉 More information🗞 Experimental Observation of Multimode Quantum Phase Transitions in a Superconducting Bose-Hubbard Simulator✍️ Claudia Castillo-Moreno, Théo Sépulcre, Timo Hillmann, Kazi Rafsanjani Amin, Mikael Kervinen and Simone Gasparinetti🧠 DOI: http://link.aps.org/doi/10.1103/rvhv-ms4t Stay currentSee today’s quantum computing news on Quantum Zeitgeist for the latest breakthroughs in qubits, hardware, algorithms, and industry deals. Tags: