arXiv:2004.02519 · Physical Review Research

Dissipative Rabi model in the dispersive regime

Clemens Müller

Published Jul 9, 2020• 9 citations

Abstract

This paper presents analytic results on the dispersive regime of the dissipative Rabi model, without taking the rotating wave approximation of the underlying Hamiltonian. The analytic expressions for all dynamical parameters show qualitative differences at intermediate and large detuning, which allows the author to update the model of the interaction between qubits and resonators.

DOI: 10.1103/physrevresearch.2.033046

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arXiv:2004.02519 · Physical Review Research

Dissipative Rabi model in the dispersive regime

Clemens Müller

Published Jul 9, 2020• 9 citations

arXiv HTML PDF

Abstract

DOI: 10.1103/physrevresearch.2.033046

Related papers

Qubit-oscillator dynamics in the dispersive regime: Analytical theory beyond the rotating-wave approximation

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We generalize the dispersive theory of the Jaynes-Cummings model beyond the frequently employed rotating-wave approximation (RWA) in the coupling between the two-level system and the resonator. For a detuning sufficiently larger than the qubit-oscillator coupling, we diagonalize the non-RWA Hamiltonian and discuss the differences to the known RWA results. Our results extend the regime in which dispersive qubit readout is possible. If several qubits are coupled to one resonator, an effective qubit-qubit interaction of Ising type emerges, whereas RWA leads to isotropic $XY$ interaction. This impacts on the entanglement characteristics of the qubits.We generalize the dispersive theory of the Jaynes-Cummings model beyond the frequently employed rotating-wave approximation (RWA) in the coupling between the two-level system and the resonator. For a detuning sufficiently larger than the qubit-oscillator coupling, we diagonalize the non-RWA Hamiltonian and discuss the differences to the known RWA results. Our results extend the regime in which dispersive qubit readout is possible. If several qubits are coupled to one resonator, an effective qubit-qubit interaction of Ising type emerges, whereas RWA leads to isotropic $XY$ interaction. This impacts on the entanglement characteristics of the qubits.

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XY

interaction. This impacts on the entanglement characteristics of the qubits.

We study the coherent dynamics of relaxing qubits driven by a bichromatic radiation in the dispersive regime, when detuning of the frequency

ω_{rf}

of a longitudinal radiofrequency field from the Rabi frequency

ω_{1}

in a transverse microwave field is comparable in magnitude to

ω_{rf}

and

ω_{1}

. We analytically describe this regime beyond the rotating wave approximation and find that the dominant feature of dynamics of qubits is the shift of the Rabi frequency caused by the dynamical Zeeman and Bloch-Siegert-like effects. These fundamental effects can be experimentally separated because, unlike the Bloch-Siegert effect, the dynamical Zeeman effect depends on the detuning sign. Our theoretical results are in a good agreement with the experimental data obtained in pulse EPR for the

E'_{1}

centers in crystalline quartz.

n

, as the driving intensity increases from weak to deep-strong. In addition, we further explore the Floquet dynamics of the dissipative open Rabi model. Remarkably, the dissipations are tunable in the rotating frame, and the approximate analytical results obtained by our method are in good agreement with the numerical results in the strong driving regime. These results pave the way to quantum control using strong and deep-strong driving with applications in quantum technologies.