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arXiv:1012.5599 · Low Temperature Physics

Quantum behavior of a flux qubit coupled to a resonator

A. N. Omelyanchouk, S. N. Shevchenko, Ya. S. Greenberg, O. V. Astafiev, E. Il’ichev

Published Oct 1, 2010• 39 citations
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Abstract

A detailed theory for a system of a superconducting qubit coupled to a transmission line resonator is presented. We describe the system by solving analytically and numerically the master equation for the density matrix, which includes a dissipative Lindblad term. We calculate the transmission coefficient, which provides a way to probe the dressed states of a qubit. The theoretical results are related to experiments with intermediate coupling between a qubit and a resonator when the coupling energy is of the same order as the qubit relaxation rate.

DOI
10.1063/1.3515520

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A detailed theory for a system of a superconducting qubit coupled to a transmission line resonator is presented. We describe the system by solving analytically and numerically the master equation for the density matrix, which includes a dissipative Lindblad term. We calculate the transmission coefficient, which provides a way to probe the dressed states of a qubit. The theoretical results are related to experiments with intermediate coupling between a qubit and a resonator when the coupling energy is of the same order as the qubit relaxation rate.
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.
Abstract We calculate the transmission spectra of a flux qubit coupled to a dissipative resonator in the ultrastrong coupling regime. Such a qubit-oscillator system constitutes the building block of superconducting circuit QED platforms. The calculated transmission of a weak probe field quantifies the response of the qubit, in frequency domain, under the sole influence of the oscillator and of its dissipative environment, an Ohmic heat bath. We find the distinctive features of the qubit-resonator system, namely two-dip structures in the calculated transmission, modified by the presence of the dissipative environment. The relative magnitude, positions, and broadening of the dips are determined by the interplay among qubit-oscillator detuning, the strength of their coupling, and the interaction with the heat bath.
We calculate the transmission spectra of a flux qubit coupled to a dissipative resonator in the ultrastrong coupling regime. Such a qubit-oscillator system constitutes the building block of superconducting circuit QED platforms. The calculated transmission of a weak probe field quantifies the response of the qubit, in frequency domain, under the sole influence of the oscillator and of its dissipative environment, an Ohmic heat bath. We find the distinctive features of the qubit-resonator system, namely two-dip structures in the calculated transmission, modified by the presence of the dissipative environment. The relative magnitude, positions, and broadening of the dips are determined by the interplay among qubit-oscillator detuning, the strength of their coupling, and the interaction with the heat bath.
The superconducting qubits are nowadays considered as good candidates both for building a quantum computer and for the study of the quantum erects in macroscopic systems. The system of two coupled qubits can be described by the Liouville equation. We convert the Liouville equation in the system of real equations by making use of the convenient parametrization of the reduced density matrix. Phenomenological inclusion of the relaxation is presented. The time evolution of the levels population in coupled flux qubits is calculated by solving the Bloch-Redfield equations.
We analyze a system composed of a qubit coupled to the electromagnetic fields in two high quality quantum oscillators. A particular realization of such a system is the superconducting qubit coupled to a transmission-line resonator driven by two signals with frequencies close to the resonator's harmonics. This doubly driven system can be described in terms of the doubly dressed qubit states. Our calculations demonstrate the possibility to change the number of photons in the resonator and the transmission of the fundamental-mode signal over a wide parameter range exploiting resonances with the dressed qubit. Experiments show that in the case of high quality resonators the dressed energy levels and corresponding resonance conditions can be probed, even for high driving amplitudes. The interaction of the qubit with photons of two harmonics can be used for the creation of quantum amplifiers or attenuators.
We present theoretical transmission spectra of a strongly driven, damped flux qubit coupled to a dissipative resonator in the ultrastrong-coupling regime. Such a qubit-oscillator system, described within a dissipative Rabi model, constitutes the building block of superconducting circuit QED platforms. The addition of a strong drive allows one to characterize the system properties and study novel phenomena, leading to a better understanding and control of the qubit-oscillator system. In this work, the calculated transmission of a weak probe field quantifies the response of the qubit, in frequency domain, under the influence of the quantized resonator and of the strong microwave drive. We find distinctive features of the entangled driven qubit-resonator spectrum, namely resonant features and avoided crossings, modified by the presence of the dissipative environment. The magnitude, positions, and broadening of these features are determined by the interplay among qubit-oscillator detuning, the strength of their coupling, the driving amplitude, and the interaction with the heat bath. This work establishes the theoretical basis for future experiments in the driven ultrastrong-coupling regime.