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Physics of the Solid State

Measurement of the superconducting flux qubit parameters in the quasi-dispersive regime

Ilya L. Novikov, Boris I. Ivanov, A. N. Sultanov, Ya. S. Greenberg, Evgeni V. Il’ichev

Published Nov 1, 2016• 7 citations
Publisher

Abstract

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.

DOI
10.1134/s1063783416110287

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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.
The properties of a superconducting flux quantum bit (qubit) in the quasidispersive mode, where the frequency of a probe signal is lower than the qubit excitation frequency but is close to it, have been experimentally studied. It has been shown that all parameters of the qubit inductively coupled to a coplanar resonator can be determined at the single-frequency excitation from the analysis of the frequency responses of the transmission of the probe signal at the output of this resonator. Under the additional excitation of the qubit by the signal at the second harmonic of the cavity, resonance dips have been observed because of resonance between the probe signal and induced Rabi splitting. It has been shown that the positions of these dips are in good agreement with the parameters of the qubit that are obtained by analyzing the amplitude–frequency response within the width of the fundamental resonance frequency.
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.
We measured the relaxation and decoherence rates of a superconducting transmon qubit in a resonator-free setting. In our experiments, the qubit is coupled to an open coplanar waveguide such that the transmission of microwaves through this line depends on the qubit's state. To determine the occupation of the first excited qubit energy level, we introduced a two-pulse technique. The first applied pulse, at a frequency close to the eigenfrequency of the qubit, serves to excite the qubit. A second pulse is then used for probing the transition between the first and second excited energy levels. Utilizing this measurement technique allowed for the reconstruction of the relaxation dynamics and Rabi oscillations. Furthermore, we demonstrate the consistency between the extracted parameters and the corresponding estimations from frequency-domain measurements.
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 analyze a system composed of a superconducting flux qubit coupled to a transmission-line resonator driven by two signals with frequencies close to the resonator's harmonics. The first strong signal is used for exciting the system to a high energetic state while a second weak signal is applied for probing effective eigenstates of the system. In the framework of doubly dressed states we showed the possibility of amplification and attenuation of the probe signal by direct transitions at the Rabi frequency. We present a brief review of theoretical and experimental works where a direct resonance at Rabi frequency have been investigated in superconducting flux qubits. The interaction of the qubit with photons of two harmonics has prospects to be used as a quantum amplifier (microwave laser) or an attenuator.