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arXiv:1209.0321

The dynamics of a qubit coupled strongly with a quantum oscillator

Guihua Tian

Published Sep 3, 2012• 0 citations
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Abstract

The dynamics of a qubit coupled with a quantum oscillator is re-studied in the region of strong coupling. The non-degenerate perturbation is added to the usual degenerate one and new results are given.
DOI
10.48550/arxiv.1209.0321

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Environmental influences on the dynamics of a coupled qubit-oscillator system are studied analytically in a regime where deviations from the exactly solvable Jaynes–Cummings model are important. We investigate the case of a quasi-degenerate qubit within the ultra-strong coupling regime for which the qubit frequency is much smaller than the frequency of the oscillator, and the coupling between the qubit and the oscillator is large, both of which invalidate the usually employed rotating wave approximation. In contrast to the standard quantum optics master equation, we explicitly take the qubit-oscillator coupling into account while microscopically deriving a dressed state master equation. Using the derived master equation, we discuss a spectroscopic technique which can be used to probe the dressed energy-level structure of the qubit-oscillator system.
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The entanglement of two qubits is investigated in the range of their ultra-strongly coupling with a quantum oscillator. The two qubits are initially in four Bell states and they are under the control mechanism of the coherent state of the quantum oscillator. There are four parameters: the average number of the coherent state, the ultra-strong coupling strength, the ratio of two frequencies of qubit and oscillator, and the inter-interaction coupling of the two qubits in the mechanism, and they all are influential parameters on the entanglement of the two qubits. One Bell state |0〉 is easyily kept and is trivial case. The novel results show that there is one state | I 0 〉 among the other three Bell states which the entanglement of the two qubits could be almost completely preserved. The possibility is made into reality by the appropriate choice of the four influential parameters. We give two different schemes to choose the respective parameters to maintain the entanglment of | I 0 〉 almost undiminished. The results will be useful for the quantum information process.
Using adiabatic approximation, a two arbitrary qubits Rabi model has been studied in ultra-strong coupling. The analytical expressions of the eigenvalues and the eigenvalues are obtained. They are in accordance with the numerical determined results. The dynamical behavior of the system and the evolution of entanglement have also been discussed. The collapse and revival phenomena has garnered particular attention. The influence of inconsistent coupling strength on them is studied. These results will be applied in quantum information processing.
We revisit the analytic solution of the two-qubit quantum Rabi model with inhomogeneous coupling and transition frequencies using a displaced oscillator basis. This approach enables us to apply the same truncation rules and techniques adopted in the Rabi model to the two qubits system. The derived analytical spectra match perfectly with the numerical solutions in the parameter regime where the qubits’ transition frequencies are far off-resonance with the field frequency and the interaction strengths reach the ultrastrong coupling regime. We further explore the dynamical behavior of the two qubits as well as the evolution of entanglement. The analytical methods provide unexpectedly accurate results in describing the dynamics of the two qubits in the present experimentally accessible coupling regime. The time evolutions of the probability for the qubits show that the collapse-revival phenomena emerge, survive and finally disappear when one coupling strength increases from weak to strong coupling regimes and the other coupling strength is well into the ultrastrong coupling regime. The inhomogeneous coupling system exhibits new dynamics, which are different from the homogeneous coupling case.