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Applied Physics Letters

Quantum state characterization of a fast tunable superconducting resonator

Z. L. Wang, Youpeng Zhong, L. J. He, H. Wang, John M. Martinis, Andrew N. Cleland, Qiwei Xie

Published Apr 22, 2013• 74 citations
Publisher

Abstract

We demonstrate a frequency-tunable superconducting coplanar waveguide resonator, with a tuning range of half a gigahertz and a switching time of 1 ns. The resonator is made tunable by inserting a superconducting quantum interference device in the center strip of the resonator. Quantum measurements are made by probing the resonator with a superconducting qubit, allowing us to use microwave photon Fock states to benchmark the resonator performance. Using the resonator, we shuttle energy quanta between the qubit and a microscopic two-level state. The tunable resonator can, therefore, serve as a communication bus or memory element in a prototype quantum processor.

DOI
10.1063/1.4802893

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We demonstrate a frequency-tunable superconducting coplanar waveguide resonator, with a tuning range of half a gigahertz and a switching time of 1 ns. The resonator is made tunable by inserting a superconducting quantum interference device in the center strip of the resonator. Quantum measurements are made by probing the resonator with a superconducting qubit, allowing us to use microwave photon Fock states to benchmark the resonator performance. Using the resonator, we shuttle energy quanta between the qubit and a microscopic two-level state. The tunable resonator can, therefore, serve as a communication bus or memory element in a prototype quantum processor.
We have fabricated and characterized systems consisting of superconducting quantum bits (qubits) of the transmon type, coupled to a tunable transmission line resonator. The resonator consists of a superconducting quarter wavelength coplanar waveguide (CPW) resonator that is made tunable by terminating the transmission line to ground through a superconducting quantum interference device (SQUID). Here we present measurements on two devices where we observe Rabi oscillations as we drive the qubit, and vacuum Rabi splitting both as we tune the qubits into resonance with the resonator and as we tune the resonator into resonance with the qubits. We also observe coherent interaction between two resonant qubits. In addition, we demonstrate that we can calculate the response very accurately using a multilevel Hamiltonian.
Superconducting microwave resonators play a pivotal role in superconducting quantum circuits. The ability to fine-tune their resonant frequencies provides enhanced control and flexibility. Here, we introduce a frequency-tunable superconducting coplanar waveguide resonator. By applying electrical currents through specifically designed ground wires, we achieve the generation and control of a localized magnetic field on the central line of the resonator, enabling continuous tuning of its resonant frequency. We demonstrate a frequency tuning range of 54.85 MHz in a 6.21-GHz resonator. This integrated and tunable resonator holds great potential as a dynamically tunable filter and as a key component of communication buses and memory elements in superconducting quantum computing.
In this licentiate thesis design, fabrication, and measurements of tunable superconducting microwave transmission line resonators are described. The resonators are of quarter wavelength type were the tuning is achieved by changing one of the boundary conditions of the resonator through a tunable impedance. As tunable impedance the Josephson inductance in form of SQUIDs is used. The Josephson inductance can then be tuned by applying a magnetic field to the SQUID loop. A tuning range of 750 MHz for a 5 GHz resonator is achieved, and as a figure of merit it can be tuned over 200 line widths. The purpose of the tunable resonators is to use them for dynamic coupling of superconducting quantum bits, this requires that the resonators can be tuned fast on the timescale of the resonator-qubit coupling. To measure tuning speeds faster then the ring up time of the resonators a method that measures the leakage of energy out of a detuned resonator was developed. With this method a frequency shift of the energy stored in the resonator can be measured. A detuning of 330 MHz in less than 10 ns is demonstrated for a 4.5 GHz resonator with a quality factor of 104^44. Working in the few photon limit indicates that the devices can be used to change the frequency of individual photons, this is however still to be demonstrated. As a part of this work the dressed states of a superconducting charge qubit was also studied.
Superconducting coplanar microwave resonators may serve as a quantum bus to transfer information from superconducting qubits to natural spin systems, such as ultracold atomic vapors, for long-lived quantum memory. The authors investigate a stacked two-chip superconducting device, consisting of a lumped-element resonator side-coupled to a coplanar-waveguide transmission line. By moving the chips relative to each other, the device can be operated in different regimes, enabling control over both the resonance frequency and the coupling. This system has the advantage of providing tunable coupling to clouds of ultracold atoms that must be operated at millitesla-level magnetic fields.
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.
We realize on-demand storage and retrieval of weak coherent microwave photon pulses at the single-photon level. A superconducting multiresonator system which is composed of a set of frequency-tunable coplanar waveguide resonators is implemented as the quantum memory. By dynamically tuning the resonant frequencies of the resonators, we achieve tunable memory bandwidth from 10 to 55 MHz, with well preserved phase coherence. We further demonstrate on-demand storage and retrieval of a time-bin flying qubit. This result opens up a prospect to integrate our chip-based quantum memory with the state-of-the-art superconducting quantum circuit technology for quantum information processing.