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Physica Scripta

Chaos generation of superconducting quantum bits coupled with LC resonant circuits

Lian-E Lu, Jian-Zhuang Wu, Yonghong Ma

Published May 2, 2024• 4 citations
Publisher

Abstract

Abstract The dynamics of chaos have been widely used in nonlinear science, such as neural networks, extreme event statistics, and the biophysics of chaos self-organization. Superconducting qubits are artificial atoms based on the Josephson junction structure of nonlinear superconducting devices, offering high design flexibility and ease of coupling and control. In this paper, the generation of chaos through the coupling between superconducting qubits and LC resonant circuits is investigated. By varying the ratio of Josephson energy to charge energy, the coupling coefficient, and the energy of the external driving field, the generation and control of chaos within the system are numerically analyzed. This study provides theoretical support for parameter selection ensuring the confidentiality and fidelity of quantum information transmission based on the chaotic dynamics of superconducting qubits.

DOI
10.1088/1402-4896/ad468f

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Abstract The dynamics of chaos have been widely used in nonlinear science, such as neural networks, extreme event statistics, and the biophysics of chaos self-organization. Superconducting qubits are artificial atoms based on the Josephson junction structure of nonlinear superconducting devices, offering high design flexibility and ease of coupling and control. In this paper, the generation of chaos through the coupling between superconducting qubits and LC resonant circuits is investigated. By varying the ratio of Josephson energy to charge energy, the coupling coefficient, and the energy of the external driving field, the generation and control of chaos within the system are numerically analyzed. This study provides theoretical support for parameter selection ensuring the confidentiality and fidelity of quantum information transmission based on the chaotic dynamics of superconducting qubits.
In this thesis, measurements on superconducting electrical circuits that exhibit quantum mechanical effects are presented. Nonlinear superconducting circuits can be regarded as artificial atoms with energy spectra that can be engineered. The artificial atoms can be used as quantum bits for quantum computation. By coupling the artificial atoms to the electromagnetic field inside a transmission line resonator, quantum optical effects can be studied in these electrical circuits.The possibility of using a frequency tunable transmission line resonators for coupling of superconducting quantum bits is investigated. Tunable superconducting resonators consisting of coplanar waveguide structures, terminated to ground in one end via a superconducting quantum interference device (SQUID), are characterized. By applying a magnetic field to the SQUID loop, the boundary condition of the resonator changes leading to a change in resonance frequency.A change of the resonance frequency by more than 250 linewidths is demonstrated. It is also demonstrated that the resonator can be tune by several hundred MHz on a time scale that is much shorter than the photon lifetime of the resonator.Circuits containing both one and two transmon qubits coupled to the resonator are characterized. Quantum mechanical interactions between the resonator and the qubits, in form of vacuum Rabi splitting, are observed. Coherent control of a single qubit coupled to the resonator is demonstrated by performing Rabi oscillations of the qubit. In the two qubit case, coherent interaction between the qubits is observed in terms of a nonlinear scaling of the coupling strength between the resonator and the collective two qubit system.Measurements on a strongly driven single Cooper-pair box, using a quantum capacitance readout, are also presented. A rich structure in the response is well explained in terms of longitudinal dressed states of the single-Cooper pair box.When measuring the response of a single-electron box, a gate dependent excess dissipation is observed. The dissipation is understood by considering the internal dynamics of the single electron box. The excess dissipation is modeled as an effective resistance named the Sisyphus resistance.
A novel configuration is proposed to study optical bistability (OB) and optical multistability (OM) in a superconducting quantum circuit with a tunable V-type artificial molecule constructed by two superconducting Josephson charge qubits coupled with each other through a superconducting quantum interference device. We find that the ratio of the Josephson coupling energy to the capacitive coupling strength has a significant impact on creating optical bistability. The influence of other system parameters on bistable behavior of the artificial medium is then discussed. In particular, it is found that applying an incoherent pumping field can noticeably reduce the bistable threshold. We also realize a switch from OB to OM through proper tuning of detuning parameters. The controllability of OB and OM of this artificial molecule may be useful in building logic-gate devices for optical computing and quantum information processing and provide some new possibilities for solid-state quantum information science.
Two basic physical models, a two-level system and a harmonic oscillator, are realized on the mesoscopic scale as coupled qubit and resonator. The realistic system includes moreover the electronics for controlling the distance between the qubit energy levels and their populations and to read out the resonator’s state, as well as the unavoidable dissipative environment. Such rich system is interesting both for the study of fundamental quantum phenomena on the mesoscopic scale and as a promising system for future electronic devices. We present recent results for the driven superconducting qubit–resonator system, where the resonator can be realized as an LC circuit or a nanomechanical resonator. Most of the results can be described by the semiclassical theory, where a qubit is treated as a quantum two-level system coupled to the classical driving field and the classical resonator. Application of this theory allows to describe many phenomena for the single and two coupled superconducting qubits, among which are the following: the equilibrium-state and weak-driving spectroscopy, Sisyphus damping and amplification, Landau–Zener–Stückelberg interferometry, the multiphoton transitions of both direct and ladder-type character, and creation of the inverse population for lasing.
The leading approach to attempt quantum computing is based on superconductors. In particular, Circuit Quantum Electrodynamic systems (circuit QED) are used to couple photons stored in a microwave resonator to a quantum bit (qubit), allowing the qubit to be controlled and measured. A lumped element parallel RLC circuit will be used to model a superconducting coplanar microwave resonator, in order to gain an intuitive understanding of how various parameters affect its electromagnetic properties, and how they can be optimised to provide desired specifications. Resonator quality factors will also be realised, which describe the effects of coupling the microwave resonator to external input/output transmission lines. The qubit is generated by a superconducting capacitively shunted Josephson Junction; the transmon, and its operation and non-linear behaviour will be discussed in this report. The transmon is integrated with a microwave resonator to generate the circuit QED system, and the derivation of the systems Hamiltonian will allow us to determine the equations describing the behaviour of the system, and therefore how it may be controlled and measured. The Bloch sphere will be introduced, which provides a useful geometric representation of the state space of a two-level quantum system. Mapping the derived Hamiltonian to the time-dependent Schrodinger equation facilitates realisation of control mechanisms of the qubit based on rotations about the Bloch sphere.
Elastic scattering is one of the useful methods to control the transmission behaviors of microwave photons transporting in microwave quantum networks without energy consumption. Therefore, it is of practical significance for developing microwave quantum devices and constructing multi-node microwave quantum networks. The transmission line embedded by a single Josephson junction can be described by different circuit models (series and parallel). In this work, we first theoretically analyze the transmission characteristics of microwave photons scattered by different elastic scattering models described by series or parallel embedding models, generated by a single LC loop or a nonlinear Josephson junction device, respectively. The classical microwave transport theory predicts that the series LC loop and the parallel LC loop lead to different elastic scattering behaviors of microwave photons, i.e. the series LC circuit yields the resonant reflection and the parallel LC circuit leads alternatively to the resonant transmission. Recently, the transport properties of microwave photons scattered by a Josephson junction embedded in a transmission line have been discussed, and the results suggested that the Josephson junction embedded in the transmission line can be described by a series embedding circuit, which implies the resonant reflection. We argue here that if the Josephson junction is embedded in parallel in the transmission line, the elastically scattered microwave photons should be transmitted by resonant transmission. In order to test which of the above two different embedding circuit models yielding the completely different elastic scattering behaviors, is physically correct, we then fabricate such a device, i.e. a single Joseph junction device embedded in a transmission line, and measure its elastic scattering transmission coefficient at an extremely low temperature. The results are consistent with the expected effect of the parallel embedding circuit model, but inconsistent with the behaviors predicted by the series embedding circuit model in the literature. According to the above theoretical and experimental analyses of the elastic scattering of a single Josephson junction device, we further propose a scheme to control the elastic scattering behavior of microwave photons by modulating a DC superconducting quantum interference device with a bypass current, which can be applied to the construction of a microwave quantum network based on elastic scattering node controls.