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arXiv:2511.06533 · Physical Review Research

Flux-modulated tunable interaction regimes in two strongly nonlinear oscillators

J. D. Koenig, G. Barbieri, F. Fani Sani, C. A. Potts, M. Kounalakis, G. A. Steele

quant-phcond-mat.mes-hallSubmitted Nov 9, 2025• Announced Nov 11, 2025• 1 citation
arXivHTMLPDF

Abstract

The ability to efficiently simulate a variety of interacting quantum systems on a single device is an overarching goal for digital and analog quantum simulators. In circuit quantum electrodynamical systems, strongly nonlinear superconducting oscillators are typically realized using transmon qubits, featuring a wide range of tunable couplings that are mainly achieved via flux-dependent inductive elements. Such controllability is highly desirable both for digital quantum information processing and for analog quantum simulations of various physical phenomena, such as arbitrary spin-spin interactions. Furthermore, broad tunability facilitates the study of driven-dissipative oscillator dynamics in previously unexplored parameter regimes. In this work, we demonstrate the ability to selectively activate different dynamical regimes between two strongly nonlinear oscillators using parametric modulation. In particular, our scheme enables access to regimes that are dominated by photon-hopping, two-mode squeezing, or cross-Kerr interactions. Finally, we observe level repulsion and attraction between Kerr-nonlinear oscillators in regimes where the nonlinearities exceed the coupling strengths and decay rates of the system. Our results could be used for realizing purely analog quantum simulators to study arbitrary spin systems as well as for exploring strongly nonlinear oscillator dynamics in previously unexplored interaction regimes.

Journal reference
Phys. Rev. Research 8, 013192 (2026)
DOI
10.1103/3pf2-8n9b

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The ability to efficiently simulate a variety of interacting quantum systems on a single device is an overarching goal for digital and analog quantum simulators. In circuit quantum electrodynamical systems, strongly nonlinear superconducting oscillators are typically realized using transmon qubits, featuring a wide range of tunable couplings that are mainly achieved via flux-dependent inductive elements. Such controllability is highly desirable both for digital quantum information processing and for analog quantum simulations of various physical phenomena, such as arbitrary spin-spin interactions. Furthermore, broad tunability facilitates the study of driven-dissipative oscillator dynamics in previously unexplored parameter regimes. In this work, we demonstrate the ability to selectively activate different dynamical regimes between two strongly nonlinear oscillators using parametric modulation. In particular, our scheme enables access to regimes that are dominated by photon-hopping, two-mode squeezing, or cross-Kerr interactions. Finally, we observe level repulsion and attraction between Kerr-nonlinear oscillators in regimes where the nonlinearities exceed the coupling strengths and decay rates of the system. Our results could be used for realizing purely analog quantum simulators to study arbitrary spin systems as well as for exploring strongly nonlinear oscillator dynamics in previously unexplored interaction regimes.
Abstract Analog quantum simulations offer rich opportunities for exploring complex quantum systems and phenomena through the use of specially engineered, well-controlled quantum systems. A critical element, increasing the scope and flexibility of such experimental platforms, is the ability to access and tune in situ different interaction regimes. Here, we present a superconducting circuit building block of two highly coherent transmons featuring in situ tuneable photon hopping and nonlinear cross-Kerr couplings. The interactions are mediated via a nonlinear coupler, consisting of a large capacitor in parallel with a tuneable superconducting quantum interference device (SQUID). We demonstrate the working principle by experimentally characterising the system in the single-excitation and two-excitation manifolds, and derive a full theoretical model that accurately describes our measurements. Both qubits have high coherence properties, with typical relaxation times in the range of 15 to 40 μs at all bias points of the coupler. Our device could be used as a scalable building block in analog quantum simulators of extended Bose-Hubbard and Heisenberg XXZ models, and may also have applications in quantum computing such as realising fast two-qubit gates and perfect state transfer protocols.
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Precise control of mechanical modes in the quantum regime is a key resource for quantum technologies, offering promising pathways for quantum sensing with macroscopic systems and scalable architectures for quantum simulation. In this work, we realize a multimode mechanical cavity coupled to a superconducting Kerr resonator, which induces nonlinearity in the mechanical modes. The Kerr mode is realized by a flux-tunable superconducting quantum interference device (SQUID) array resonator, while the mechanical modes are implemented by a surface acoustic wave cavity. Both mechanical and electromagnetic modes are individually addressable via dedicated measurement lines, enabling full spectroscopic characterization. We introduce a straightforward protocol to measure the SQUID array resonator’s participation ratio in the hybrid acoustic modes, quantifying the degree of hybridization. The participation ratio reveals that our device operates at the onset of the multimode coupling regime, where multiple acoustic modes simultaneously interact with the nonlinear superconducting element. Furthermore, this platform allows controllable Kerr-type nonlinearities in multiple acoustic modes, with the participation ratio serving as the key parameter determining both the dissipation rates and nonlinear strengths of these hybridized modes. Close to the resonant regime, we measure a cross-Kerr interaction between seven pairs of mechanical modes, which is controllable via the SQUID array resonator detuning. Finally, we apply a two-photon parametric drive to the SQUID array resonator and observe the resulting parametric down-conversion and metastable state switching in a mechanical mode. These results establish a platform for engineering nonlinear multimode mechanical interactions, offering potential for future integration with superconducting qubits and implementation of multiple mechanical qubits.
Parametric modulation, valued for its versatility, is widely employed in superconducting circuits for quantum simulations and high-fidelity two-qubit gates. Conventionally, the qubit coupling strength is determined by the amplitude of the parametric flux pulse, which affects the qubit parameters dramatically. In this paper, we propose and implement a phase-modulation scheme to tune the interaction strength via adjustment of the relative phase between the parametric flux pulses applied to two coupled qubits. We characterize this modulation for sideband couplings, at both sweet and off-sweet spots, achieving a broad range of coupling strengths, as confirmed by both population dynamics and spectroscopy methods. This approach enables phase-controlled modulation of coupling strength, providing a promising candidate for parametrically driven quantum simulations and gate operations.
We report the experimental realization of strong longitudinal (ZZ) coupling between two superconducting transmon qubits achieved solely through capacitive engineering. By systematically varying the qubit frequency detuning, we measure cross-Kerr inter-qubit interaction strengths ranging from 10 MHz up to 350 MHz, more than an order of magnitude larger than previously observed in similar capacitively coupled systems. In this configuration, the qubits enter a strong-interaction regime in which the excitation of one qubit inhibits that of its neighbor, demonstrating a dynamical blockade mediated entirely by the engineered ZZ coupling. Circuit quantization simulations accurately reproduce the experimental results, while perturbative models confirm the theoretical origin of the energy shift as a hybridization between the computational states and higher-excitation manifolds. We establish a robust and scalable method to access interaction-dominated physics in superconducting circuits, providing a pathway towards solid-state implementations of globally controlled quantum architectures and cooperative many-body dynamics.
This thesis explores nonlinear couplings in superconducting circuits with the purpose of achieving quantum control over the elementary excitations of light and motion. It consists mainly of three research themes. The first theme concerns the experimental realisation of a tuneable coupling scheme, giving rise to different interactions with adjustable ratios, between two transmon qubits. The tuneable capabilities of the device together with its versatile geometry and high coherence make it an interesting building block for analog quantum simulators of certain classes of complex problems. The second theme concerns two theoretical proposals for controlling mechanical resonators using transmon qubits. In the first part we analyse an electromechanical circuit architecture giving rise to tuneable three-body interactions between two qubits and a mechanical beam. Several protocols are performed numerically demonstrating ground-state cooling and the creation of mechanical quantum states, such as single-phonon and multi-phonon superposition states as well as qubit-phonon entanglement. Additionally, schemes for generating arbitrary quantum states are explored. The second part relies on the same concept for coupling a mechanical resonator to a transmon qubit and explores the qubit-resonator system in the ultrastrong coupling regime, where the optomechanical coupling approaches or even exceeds the mechanical frequency. We find that for certain coupling strengths ground-state cooling is possible and devise a protocol for generating macroscopic quantum superposition states, known as “Shrödinger cats”, on the mechanical resonator. Finally, the third research theme presented in the thesis concerns an experiment where a cold superconducting qubit is employed to readout and control a thermally populated radio-frequency resonator coupled via a strong dispersive coupling. By means of reservoir engineering, ground-state cooling as well as stabilisation of Fock states in the resonator are demonstrated reaching a new operating regime for circuit quantum electrodynamics.