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Physical Review B

Vacuum Rabi splitting due to strong coupling of a flux qubit and a coplanar-waveguide resonator

A. A. Abdumalikov, O. V. Astafiev, Yasunobu Nakamura, Yu. A. Pashkin, Jaw-Shen Tsai

Published Nov 10, 2008• 126 citations
Publisher

Abstract

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.

DOI
10.1103/physrevb.78.180502

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We demonstrate amplification of a microwave signal by a strongly driven two-level system in a coplanar waveguide resonator. The effect, similar to the dressed-state lasing known from quantum optics, is observed with a single quantum system formed by a persistent current (flux) qubit. The transmission through the resonator is enhanced when the Rabi frequency of the driven qubit is tuned into resonance with one of the resonator modes. Amplification as well as linewidth narrowing of a weak probe signal has been observed. The stimulated emission in the resonator has been studied by measuring the emission spectrum. We analyzed our system and found an excellent agreement between the experimental results and the theoretical predictions obtained in the dressed-state model.
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.
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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 study the response of a magnetic-field-driven superconducting qubit strongly coupled to a superconducting coplanar waveguide resonator. We observed a strong amplification/damping of a probing signal at different resonance points corresponding to a one and two-photon emission/absorption. The sign of the detuning between the qubit frequency and the probe determines whether amplification or damping is observed. The larger blue detuned driving leads to two-photon lasing while the larger red detuning cools the resonator. Our experimental results are in good agreement with the theoretical model of qubit lasing and cooling at the Rabi frequency.