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arXiv:0910.4739 · Physical Review B

Weak continuous monitoring of a flux qubit using coplanar waveguide resonator

G. Oelsner, S. H. W. van der Ploeg, P. Macha, Uwe Hübner, Detlef Born, Solveig Anders, Evgeni V. Il’ichev, H.‐G. Meyer, M. Grajcar, S. Wünsch, M. Siegel, A. N. Omelyanchouk, O. V. Astafiev

Published May 26, 2010• 45 citations
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Abstract

We study a flux qubit in a coplanar waveguide resonator by measuring transmission through the system. In our system with the flux qubit decoupled galvanically from the resonator, the intermediate coupling regime is achieved. In this regime, dispersive readout is possible with weak back action on the qubit. The detailed theoretical analysis and simulations give good agreement with the experimental data and allow us to make the qubit characterization.

DOI
10.1103/physrevb.81.172505

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We study a flux qubit in a coplanar waveguide resonator by measuring transmission through the system. In our system with the flux qubit decoupled galvanically from the resonator, the intermediate coupling regime is achieved. In this regime, dispersive readout is possible with weak back action on the qubit. The detailed theoretical analysis and simulations give good agreement with the experimental data and allow us to make the qubit characterization.
We have experimentally studied a superconducting flux qubit strongly coupled to a single mode of a high-quality transmission-type coplanar-waveguide resonator. The qubit-resonator coupling is revealed in the resonator transmission spectrum as a vacuum Rabi splitting. In the dispersive regime the qubit energy levels are spectroscopically probed. We observe a shift in the qubit transition frequency that linearly depends on the number of photons in the resonator, which is attributed to the ac-Zeeman shift. The observations are in agreement with the theoretical predictions.
This paper reports on the results of the investigation of a superconducting flux quantum bit (qubit) in the quasi-dispersive regime, where the frequency of a probe signal even though is lower than, but, nevertheless, close to the excitation frequency of the qubit. In this regime, in contrast to the known experiments, the interaction of the qubit with a waveguide leads not only to a shift of the resonance frequency, which is characteristic of the dispersive regime, but also to a significant broadening of the resonance line due to the spontaneous emission of the qubit. On the basis of the analysis of the amplitude–frequency characteristic of the transmission signal, this makes it possible to determine, under single-frequency excitation, the characteristic parameters of the qubit inductively coupled to the coplanar resonator.
We report experiments on superconducting flux qubits in a circuit quantum electrodynamics (cQED) setup. Two qubits, independently biased and controlled, are coupled to a coplanar waveguide resonator. Dispersive qubit state readout reaches a maximum contrast of 72%. We measure energy relaxation times at the symmetry point of 5 and $10\ensuremath{\mu}\mathrm{s}$, corresponding to 7 and $20\ensuremath{\mu}\mathrm{s}$ when relaxation through the resonator due to Purcell effect is subtracted out, and levels of flux noise of 2.6 and $2.7\phantom{\rule{0.222222em}{0ex}}\ensuremath{\mu}{\mathrm{\ensuremath{\Phi}}}_{0}/\sqrt{\text{Hz}}$ at 1 Hz for the two qubits. We discuss the origin of decoherence in the measured devices. The strong coupling between the qubits and the cavity leads to a large, cavity-mediated, qubit-qubit coupling. This coupling, which is characterized spectroscopically, reaches 38 MHz. These results demonstrate the potential of cQED as a platform for fundamental investigations of decoherence and quantum dynamics of flux qubits.
We have investigated microwave response of a λ/4 superconducting coplanar waveguide resonator which is terminated by a DC-SQUID coupled with a flux qubit. The circuit is designed for non-destructive single-shot readout of a flux qubit based on dispersive interaction between the qubit and the resonator and switching between bistable states of the driven nonlinear resonator. A high-frequency (∼ 10 GHz) resonator is exploited for suppressing photon-number fluctuations which cause qubit dephasing even when the readout circuit is not activated. We observed bifurcation of the resonator in the nonlinear driving regime. In the linear regime, the degeneracy point of the qubit was detected as a shift of the resonant frequency.
A superconducting flux qubit is inductively coupled to a superconducting quantum interference device (SQUID) magnetometer, capacitively shunted to form a 1.294-GHz resonator. The qubit-state-dependent resonator frequency is weakly probed with a microwave signal and detected with a microstrip SQUID amplifier. At a mean resonator occupation n‾=1.5\overline{n}=1.5n=1.5 photons, the readout visibility is increased by a factor of 4.5 over that using a cryogenic semiconductor amplifier. As n‾\overline{n}n is increased from 0.008 to 0.1, no reduction in T1{T}_{1}T1​ is observed, potentially enabling continuous monitoring of the qubit state.