Dynamical properties of a resonator can be analyzed using the Rayleigh-Lorentz invariant which is not an exact constant but varies more or less over time. We investigate the time behavior of this invariant for a flux qubit resonator in order for better understanding of qubit-information detection with the resonator. Flux qubit resonators can be utilized in implementing diverse next generation nano-optic and nano-electronic devices such as quantum computing systems. Through the analyses of the temporal evolution of the invariant, we derive a condition for optimal adiabatic qubit-information detection with the resonator. This condition is helpful for controlling the dynamics of qubit resonators over long periods of time. It is necessary to consider it when designing a nano-resonator used for quantum nondemolition readouts of qubit states, crucial in quantum computation.
Dynamical properties of a resonator can be analyzed using the Rayleigh-Lorentz invariant which is not an exact constant but varies more or less over time. We investigate the time behavior of this invariant for a flux qubit resonator in order for better understanding of qubit-information detection with the resonator. Flux qubit resonators can be utilized in implementing diverse next generation nano-optic and nano-electronic devices such as quantum computing systems. Through the analyses of the temporal evolution of the invariant, we derive a condition for optimal adiabatic qubit-information detection with the resonator. This condition is helpful for controlling the dynamics of qubit resonators over long periods of time. It is necessary to consider it when designing a nano-resonator used for quantum nondemolition readouts of qubit states, crucial in quantum computation.
Dynamical properties of a resonator can be analyzed using the Rayleigh-Lorentz invariant which is not an exact constant but varies more or less over time depending on variations of parameters. We investigate the time behavior of this invariant for a superconducting nano-resonator in order for better understanding of qubit-information detection with the resonator. Superconducting resonators which uses parametric resonance in a Josephson junction circuit can be utilized in implementing diverse next generation nano-optic and nano-electronic devices such as quantum computing systems. Through the analyses of the temporal evolution of the invariant, we derive a condition for optimal adiabatic qubit-information detection with the resonator. This condition is helpful for controlling the dynamics of the resonators over long periods of time. It is necessary to consider it when designing a nano-resonator used for quantum nondemolition readouts of qubit states, crucial in quantum computation.
An adiabatic invariant, which is a conserved quantity, is useful for studying quantum and classical properties of dynamical systems. Adiabatic invariants for time-dependent superconducting qubit-oscillator systems and resonators are investigated using the Liouville-von Neumann equation. At first, we derive an invariant for a simple superconducting qubit-oscillator through the introduction of its reduced Hamiltonian. Afterwards, an adiabatic invariant for a nanomechanical resonator linearly interfaced with a superconducting circuit, via a coupling with a time-dependent strength, is evaluated using the technique of unitary transformation. The accuracy of conservation for such invariant quantities is represented in detail. Based on the results of our developments in this paper, perturbation theory is applicable to the research of quantum characteristics of more complicated qubit systems that are described by a time-dependent Hamiltonian involving nonlinear terms.
Superconducting flux qubits have many advantages as a storage of quantum information, such as broad range tunability of frequency, small-size fabricability, and high controllability. In the flux qubit-oscillator, qubits are connected to SQUID resonators for the purpose of performing dispersive non-destructive readouts of qubit signals with high fidelity. In this work, we propose a theoretical model for analyzing quantum characteristics of a flux qubit-oscillator on the basis of quantum solutions obtained using a unitary transformation approach. The energy levels of the combined system (qubit + resonator) are analyzed in detail. Equally spaced each energy level of the resonator splits into two parts depending on qubit states. Besides, coupling of the qubit to the resonator brings about an additional modification in the split energy levels. So long as the coupling strength and the tunnel splitting are not zero but finite values, the energy-level splitting of the resonator does not disappear. We conclude that quantum nondemolition dispersive measurements of the qubit states are possible by inducing bifurcation of the resonator states through the coupling.
This thesis presents circuit quantum electrodynamic (cQED) experiments done with artificial atoms coupled to a high quality factor superconducting microwave resonator. This work discusses the theoretical framework, design, fabrication, implementation and characterization of a multi-qubit system using superconducting persistent current qubits, often referred as flux qubits. \n \nWe developed a new type of cryogenic aid for fast turnaround microwave experiments. The minimum turnaround time to perform microwave experiments in dilution refrigerators is typically a few days, as required by cooling down and warming up the entire refrigerator. The cryogenic microwave payload and wiring needed for each qubit and resonator add a significant heat load to \nthe system which typically only has a few µW s of cooling power at millikelvin temperatures. We present a new experimental approach we developed in which a suitable sample holder is attached to a cold-insertable probe and brought in contact with transmission lines permanently mounted inside the cryostat. The total turnaround time is reduced to 8 hours if the target temperature is 80 mK. This new measurement method increased our ability to successfully identify good devices with fast design-characterization iterations, while allowing months-long measurements at 30 mK. \n \nOur device architecture uses several qubits, each of which is controlled via on-chip fast flux bias lines. Readout of the qubit’s quantum state is performed by homodyne detection of the resonator field at large driving power. We observe long coherence times at the optimal bias point of the flux qubits and present decoherence measurements around this optimal point, where the \nflux qubits couple mostly to magnetic flux noise. Dynamical decoupling techniques employing fast microwave pulses are used to protect the qubit’s coherence and allow calculating the magnetic flux noise power spectral density of the qubit’s environment. Photon-mediated interaction between distant qubits in the resonator allows the implementation of a two-qubit controlled-NOT gate \nusing the selective darkening technique. \n \nThis multi-qubit superconducting design is an interesting platform to study the decoherence properties of flux qubits, the properties of strong interaction of electromagnetic radiation with macroscopic quantum systems. These results demonstrate the potential of cQED as a platform for fundamental investigations of decoherence and quantum dynamics of flux qubits.
Quantum technologies, including those based on superconducting quantum circuits, require high-fidelity high-speed detection of the quantum state of a qubit. Standard quantum nondemolition readout of a superconducting qubit is based on its dispersive coupling to a resonator, but this method suffers from the Purcell effects: Purcell decay, critical photon number, and qubit-dependent Kerr nonlinearity. The authors propose a method in which both speed and fidelity of flux-qubit readout can avoid all three Purcell limitations.
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.