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arXiv:cond-mat/0501455 · Europhysics Letters (EPL)

Rabi oscillations of a qubit coupled to a two-level system

Y. M. Galperin, Daniil V. Shantsev, Joakim Bergli, B. L. Altshuler

Published May 26, 2005• 25 citations
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Abstract

The problem of Rabi oscillations in a qubit coupled to a fluctuator and in contact with a heath bath is considered. A scheme is developed for taking into account both phase and energy relaxation in a phenomenological way, while taking full account of the quantum dynamics of the four-level system subject to a driving AC field. Significant suppression of the Rabi oscillations is found when the qubit and fluctuator are close to resonance. The effect of the fluctuator state on the read-out signal is discussed. This effect is shown to modify the observed signal significantly. This may be relevant to recent experiments by Simmonds et al. ( Phys. Rev. Lett. 93 (2004) 077003).

DOI
10.1209/epl/i2005-10053-y

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The problem of Rabi oscillations in a qubit coupled to a fluctuator and in contact with a heath bath is considered. A scheme is developed for taking into account both phase and energy relaxation in a phenomenological way, while taking full account of the quantum dynamics of the four-level system subject to a driving AC field. Significant suppression of the Rabi oscillations is found when the qubit and fluctuator are close to resonance. The effect of the fluctuator state on the read-out signal is discussed. This effect is shown to modify the observed signal significantly. This may be relevant to recent experiments by Simmonds et al. ( Phys. Rev. Lett. 93 (2004) 077003).
We consider the problem of a qubit driven by a harmonically oscillating external field while it is coupled to a quantum two-level system (TLS). We perform a systematic numerical analysis of the problem by varying the relevant parameters. The numerical calculations agree with the predictions of a simple intuitive picture, namely one that takes into consideration the four-level energy spectrum, the simple principles of Rabi oscillations and the basic effects of decoherence. Furthermore, they reveal a number of other interesting phenomena. We provide explanations for the various features that we observe in the numerical calculations and discuss how they can be used in experiment. In particular, we suggest an experimental procedure to characterize an environment of TLSs.
Superconducting qubits often show signatures of coherent coupling to microscopic two-level fluctuators (TLFs), which manifest themselves as avoided level crossings in spectroscopic data. In this work we study a phase qubit, in which we induce Rabi oscillations by resonant microwave driving. When the qubit is tuned close to the resonance with an individual TLF and the Rabi driving is strong enough (Rabi frequency of order of the qubit-TLF coupling), interesting four-level dynamics are observed. The experimental data show a clear asymmetry between biasing the qubit above or below the fluctuator's level splitting. Theoretical analysis indicates that this asymmetry is due to an effective coupling of the TLF to the external microwave field induced by the higher qubit levels.
Coherent Rabi oscillations between quantum states of superconducting microcircuits have been observed in a number of experiments, albeit with a visibility that is typically much smaller than unity. Here, we show theoretically that the coherent coupling of superconducting phase qubits to background charge fluctuators [R. W. Simmonds et al., Phys. Rev. Lett., 93, 77003 (2004)] leads to a significantly reduced visibility if the Rabi frequency is comparable to the coupling energy of microcircuit and fluctuator. For larger Rabi frequencies, transitions to the second excited state of the superconducting microcircuit become dominant in suppressing the Rabi oscillation visibility.
We present an analytical and comprehensive description of the quantum dynamics of a microwave resonantly driven superconducting phase qubit coupled to a microscopic two-level system (TLS), covering a wide range of the external microwave field strength. Our model predicts several interesting phenomena in such an ac driven four-level bipartite system including anomalous Rabi oscillations, high-contrast beatings of Rabi oscillations, and extraordinary two-photon transitions. Our experimental results in a coupled qubit-TLS system agree quantitatively very well with the predictions of the theoretical model.
Noise and decoherence are major obstacles to the implementation of Josephson junction qubits in quantum computing. Recent experiments suggest that two-level systems (TLS) in the oxide tunnel barrier are a source of decoherence. We explore two decoherence mechanisms in which these two-level systems lead to the decay of Rabi oscillations that result when Josephson junction qubits are subjected to strong microwave driving. (A) We consider a Josephson qubit coupled resonantly to a two-level system, i.e., the qubit and TLS have equal energy splittings. As a result of this resonant interaction, the occupation probability of the excited state of the qubit exhibits beating. Decoherence of the qubit results when the two-level system decays from its excited state by emitting a phonon. (B) Fluctuations of the two-level systems in the oxide barrier produce fluctuations and 1∕f1∕f1∕f noise in the Josephson junction critical current I0{I}_{0}I0​. This in turn leads to fluctuations in the qubit energy splitting that degrade the qubit coherence. We compare our results with experiments on Josephson junction phase qubits.
Rabi oscillations are coherent transitions in a quantum two-level system under the influence of a resonant drive, with a much lower frequency dependent on the perturbation amplitude. These serve as one of the signatures of quantum coherent evolution in mesoscopic systems. It was shown recently (Grønbech-Jensen N and Cirillo M 2005 Phys. Rev. Lett. 95 067001) that in phase qubits (current-biased Josephson junctions) this effect can be mimicked by classical oscillations arising due to the anharmonicity of the effective potential. Nevertheless, we find qualitative differences between the classical and quantum effects. Firstly, while the quantum Rabi oscillations can be produced by the subharmonics of the resonant frequency ω 10 (multiphoton processes), the classical effect also exists when the system is excited at the overtones, n ω 10 . Secondly, the shape of the resonance is, in the classical case, characteristically asymmetric, whereas quantum resonances are described by symmetric Lorentzians. Thirdly, the anharmonicity of the potential results in the negative shift of the resonant frequency in the classical case, in contrast to the positive Bloch–Siegert shift in the quantum case. We show that in the relevant range of parameters these features allow us to distinguish confidently the bona fide Rabi oscillations from their classical Doppelgänger.