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arXiv:1207.6825 · Physical Review B

Large dispersive shift of cavity resonance induced by a superconducting flux qubit in the straddling regime

K. Inomata, Tsuyoshi Yamamoto, P.-M. Billangeon, Yasunobu Nakamura, J. S. Tsai

Published Oct 26, 2012• 64 citations
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Abstract

We demonstrate enhancement of the dispersive frequency shift in a coplanar waveguide resonator induced by a capacitively coupled superconducting flux qubit in the straddling regime. The magnitude of the observed shift, 80 MHz for the qubit-resonator detuning of 5 GHz, is quantitatively explained by the generalized Rabi model which takes into account the contribution of the qubit higher energy levels. By applying the enhanced dispersive shift to the qubit readout, we achieved $90%$ contrast of the Rabi oscillations, which is mainly limited by the energy relaxation of the qubit.

DOI
10.1103/physrevb.86.140508

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We demonstrate enhancement of the dispersive frequency shift in a coplanar waveguide resonator induced by a capacitively coupled superconducting flux qubit in the straddling regime. The magnitude of the observed shift, 80 MHz for the qubit-resonator detuning of 5 GHz, is quantitatively explained by the generalized Rabi model which takes into account the contribution of the qubit higher energy levels. By applying the enhanced dispersive shift to the qubit readout, we achieved 9090%90 contrast of the Rabi oscillations, which is mainly limited by the energy relaxation of the qubit.
We study the system where a superconducting flux qubit is capacitively coupled to an LC resonator. In three devices with different coupling capacitance, the magnitude of the dispersive shift is enhanced by the third level of the qubit and quantitatively agrees with the theory. We show by numerical calculation that the capacitive coupling plays an essential role for the enhancement in the dispersive shift. We investigate the coherence properties in two of these devices, which are in the strong-dispersive regime, and show that the qubit energy relaxation is currently not limited by the coupling. We also observe the discrete ac-Stark effect, a hallmark of the strong-dispersive regime, in accordance with the theory.
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 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.
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.
The hybridization of distinct quantum systems is now seen as an effective way to engineer the properties of an entire system leading to applications in quantum metamaterials, quantum simulation, and quantum metrology. Recent improvements in both fabrication techniques and qubit design have allowed the community to consider coupling large ensembles of artificial atoms, such as superconducting qubits, to a resonator. Here, we demonstrate the coherent coupling between a microwave resonator and a macroscopic ensemble composed of several thousand superconducting flux qubits, where we observe a large dispersive frequency shift in the spectrum of 250 MHz. We achieve the large dispersive shift with a collective enhancement of the coupling strength between the resonator and qubits. These results represent the largest number of coupled superconducting qubits realized so far.