Time-reversal-symmetry breaking (TRSB) has been central to detecting exotic phases of matter. Here, we leverage the circuit electrodynamics capabilities of superconducting devices to propose a scheme based on a multimode superconducting ring resonator for the sensitive probing of TRSB in quantum materials. A ring resonator enables nonlinear cross-interactions between the modes which act as built-in amplifiers to be harnessed for enhanced sensing. Using a driven-dissipative model, we explore the nonlinear dynamics of a two-mode superconducting circuit with self- and cross-Kerr nonlinearities under conditions near the bifurcation threshold. By mapping the optimal parameter regimes, we show that even when the photon occupation numbers are subjected to different initial conditions, they can be driven into a symmetric configuration which is broken even with weak TRSB. Through a full quantum analysis we demonstrate that the Kerr-nonlinear interactions up-convert the magnetic effects of the material-resonator hybrid system, enhancing the probing of TRSB. Our findings highlight the utility of superconducting microwave resonators outside of quantum information processing, as a tool for probing exotic states of matter.
Time-reversal-symmetry breaking (TRSB) has been central to detecting exotic phases of matter. Here, we leverage the circuit electrodynamics capabilities of superconducting devices to propose a scheme based on a multimode superconducting ring resonator for the sensitive probing of TRSB in quantum materials. A ring resonator enables nonlinear cross-interactions between the modes which act as built-in amplifiers to be harnessed for enhanced sensing. Using a driven-dissipative model, we explore the nonlinear dynamics of a two-mode superconducting circuit with self- and cross-Kerr nonlinearities under conditions near the bifurcation threshold. By mapping the optimal parameter regimes, we show that even when the photon occupation numbers are subjected to different initial conditions, they can be driven into a symmetric configuration which is broken even with weak TRSB. Through a full quantum analysis we demonstrate that the Kerr-nonlinear interactions up-convert the magnetic effects of the material-resonator hybrid system, enhancing the probing of TRSB. Our findings highlight the utility of superconducting microwave resonators outside of quantum information processing, as a tool for probing exotic states of matter.
We propose a scheme for dispersive readout of stored energy in one mode of a nonlinear-superconducting microwave ring resonator by detection of the frequency shift of a second mode coupled to the first via a Kerr nonlinearity. Symmetry is used to enhance the device responsivity while minimizing self-nonlinearity of each mode. Assessment of the signal to noise ratio indicates that the scheme will function at the single-photon level, allowing quantum nondemolition measurement of the photon-number state of one mode. Experimental data from a simplified version of the device demonstrating the principle of operation are presented.
Josephson junctions are a fundamental building block of superconducting quantum circuits. They provide the nonlinearity required to realize quantum bits and enable a wide range of nonlinear phenomena central to quantum technologies. This thesis explores two superconducting systems in which this nonlinearity plays a central role. In the first part, we investigate a superconducting resonator terminated by a superconducting quantum interference device (SQUID), an arrangement of two Josephson junctions connected in parallel. The SQUID provides a tunable Kerr nonlinearity and allows the resonator to be driven parametrically. Under the combined action of the parametric drive, Kerr nonlinearity, and dissipation to the environment, the state of the resonator can undergo abrupt changes as the pump frequency or amplitude is varied. We interpret these changes within the framework of dissipative phase transitions (DPTs). By implementing a finite-component thermodynamic limit, we experimentally and theoretically investigate both first- and second-order DPTs in this system. We characterize their steady-state and dynamical signatures, including squeezing below vacuum, phase coexistence, hysteresis, spontaneous symmetry breaking, and critical slowing down. Finally, we exploit the enhanced susceptibility near the second-order critical point to implement a frequency-estimation protocol. We show that the estimation precision scales quadratically with the effective system size, demonstrating that finite-component DPTs can provide a quantum advantage in a sensing protocol. In the second part, we investigate a novel architecture for the readout of superconducting qubits. Conventional dispersive readout relies on a transverse interaction between a transmon and a resonator, which can lead to Purcell decay and measurement-induced state transitions, ultimately limiting the readout fidelity. To overcome these limitations, we implement a nonlinear coupling by galvanically connecting the transmon and resonator through a Josephson junction. This interaction provides a strong cross-Kerr coupling for clear state discrimination, but also introduces a detrimental transverse interaction. We experimentally show that the exchange part of the transverse interaction can be suppressed by adding a capacitor in parallel with the coupling junction while preserving the strong cross-Kerr coupling. In addition, we show that the same circuit acts as an intrinsic Purcell filter, protecting the qubit against Purcell decay. The coupling junction also induces a Kerr nonlinearity in the resonator, which we exploit to implement a bifurcation readout with a 99.4 % fidelity in a 68 ns integration time. This performance is achieved without a dedicated Purcell filter or a near-quantum-limited amplifier. Overall, this thesis demonstrates the engineering of nonlinear superconducting circuits to investigate dissipative phase transitions, exploit criticality for enhanced quantum sensing, and develop a novel qubit readout architecture enabling fast, high-fidelity measurement.
Nonlinear microwave resonators are a versatile tool in quantum information processing, enabling parametric amplification, continuous variable quantum computing, and engineered mode interactions. Many of these applications especially benefit from cubic nonlinearities enabling three-wave mixing; at the same time, they are limited by quartic nonlinearities giving rise to undesired Kerr effects. A recurrent challenge is therefore to engineer resonators with a finite cubic nonlinearity while suppressing quartic terms. Here, we investigate a superconducting resonator hosting two weak links fabricated from an aluminum-capped indium arsenide nanowire. We characterize the Kerr nonlinearity as a function of magnetic flux and gate bias, showing that it can be tuned to zero with either control parameter. Furthermore, we experimentally demonstrate three-wave mixing in a semiconductor-superconductor hybrid device, establishing nonzero cubic nonlinearity. An effective model based on Andreev bound states qualitatively captures the observed trends. Our results validate semiconductor-superconductor hybrid devices as a promising platform for tunable nonlinear superconducting circuits, with applications in parametric amplification, quantum control of bosonic modes, and engineering interactions between microwave modes.
The quantum sensing landscape has been revolutionized by advanced technologies like superconducting circuits and qubit-based systems which have furthered the ability to probe and understand fundamental properties of quantum matter. Here, we propose an integrated photonic device where a transmon qubit capacitively couples to a microwave cross-resonator, and the setup is employed for sensing of time reversal broken order in materials. In this sensing scheme, the transmon qubit plays a dual role as both a control element and a passive detector, while the photonic cross-resonator serves as the host for the sample, enabling a contact-free spectroscopic method suitable for studying materials where reliable electrical contacts are challenging to obtain, e.g., in van der Waal 2D heterostructures. We show that by tuning the coupling strength and phase between the transmon and the cross-resonator, the system allows selective control over the interaction dynamics and leads to a highly sensitive detection method that can be compactly understood in terms of evolution of excited state population and quantum metric of the resonator-transmon hybrid state. This architecture has the potential to host a wide range of quantum phenomena that can be precisely encoded in the dynamics of the transmon qubit and, in this way, potentially allows access to elusive aspects of correlated materials.
Hybrid quantum systems play an essential role in efforts towards the advancements of quantum information technology and quantum sensing by bridging distinct technological platforms. In particular, hybrid systems comprising superconducting microwave circuits are being pursued intensely in light of existing achievements in superconducting qubits and precise quantum control in microwave circuits. Their realization relies on the design of superconducting resonators capable of coupling to an oscillatory mode of a second quantum system, facilitating the probing and manipulation of one via the other. In order to accommodate the coupled system, its particular constraints and requirements must be respected, which may be quite extreme from the perspective of established superconducting circuit design and operation. Overcoming this challenge has proved to be a substantial obstacle for the attainment of strongly coupled hybrid systems, despite spectacular advances in superconducting microwave circuits individually. In this work, we examine two approaches tackling this issue for different hybrid quantum systems, focusing on the optimization and characterization of the superconducting circuits. The first device aims at a superconductor-atom hybrid system through the coupling to Rydberg-Rydberg transitions in ultra-cold Rb-87 atoms trapped near the superconducting chip. Using simulations in conjunction with theoretical considerations, we demonstrate a comprehensive geometry parameter optimization procedure for maximum coupling rate. Presenting an experimental implementation of the resulting circuit, we validate its suitability for use under the intended operation conditions, including the option of tuning the electronic transition frequencies using a dc voltage. Secondly, we investigate a device designed for applications in large magnetic in-plane fields used to mediate coupling to integrated micromechanical oscillators; more specifically it is a flux-tunable SQUID resonator comprising Josephson nano-constrictions as nonlinear inductive components. Performing a thorough characterization of its frequency and Kerr anharmonicity tuning behavior at fields up to several hundred mT, we discover a pronounced asymmetry in its flux response at large fields. We show this asymmetry to be caused by the nano-constrictions turning into Josephson diodes, develop an intuitive macroscopic model for its field-induced emergence and reconstruct the diode current-phase relation from the flux tuning data. Several figures of merit informing the suitability of the SQUID resonators for optomechanical systems as well as other applications are improved by the diode effect, highlighting the potential of Josephson diodes in superconducting microwave circuits. Our results provide a promising stepping stone for the advancement of hybrid systems involving superconducting microwave circuits, putting new and exciting operation and coupling regimes within reach.
We propose a scheme to dissipatively stabilize superpositions of squeezed coherent states for single- and two-resonator modes in superconducting circuits, where a superconducting qubit is coupled to a single or two parametrically driven transmission-line resonators with different circuit designs. A modulated magnetic flux applied to the qubit can periodically break the inversion symmetry of the qubit and induce both the parametrically enhanced transverse and longitudinal couplings to the resonators, resulting in strong nonlinear two-photon interactions between the qubit and the resonators and enabling the scheme to be implemented in a relatively weak coupling regime. With an additional microwave drive applied to the qubit, the dissipation of the qubit used as a resource can help drive the resonators into the desired superpositions of squeezed coherent states at a steady state with high speed. Numerical simulations show that the target states with high fidelity and highly nonlinear properties can be created for a long time even in the presence of photon leakage out of the resonators. The scheme can be generalized to other quantum platforms and may have potential applications in the field of quantum information processing and the improvement of estimation precision in quantum metrology.