Distinguishing quantum from classical oscillations in a driven phase qubit

S N Shevchenko,Franco Nori,A M Zagoskin,S Savel'Ev,A N Omelyanchouk

doi:10.1088/1367-2630/10/7/073026

Abstract

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 ω10 (multiphoton processes), the classical effect also exists when the system is excited at the overtones, nω10. 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.

Highlights

Classical regimeThe phase qubit can be described by the RSJJ
New Journal of Physics 10 (2008) 073026 1367-2630/08/073026+10$30.00. Are possible, even their simplified versions (e.g. [13]) are demanding. This motivated us to further investigate the classical behaviour of a phase qubit and find that there is a possibility to distinguish the quantum Rabi oscillations from their classical double, by the shape of the resonance, by the fact that the classical effect can be produced by the overtones, nω10, of the resonance frequency, and by the sign of the resonant frequency shift
A symmetric versus asymmetric Stark shift in a qubit playing the role of a detector was proposed to distinguish the classical and quantum behaviours of a nanomechanical oscillator [11].) Classical and quantum resonances, as a function of applied drives, are studied in [17]

Summary

Classical regime

The phase qubit can be described by the RSJJ (ii) The amplitude b of the small driven oscillations at the main resonance is bmax = /(γ0α) When this amplitude is not small, the phase-locked ansatz becomes invalid. The solution of equation (5) describes the escape from the phase-locked state, which means the appearance of a nonzero average voltage on the contact. This voltage is proportional to the average derivative of the phase, φ ̇. We note that for the anharmonic driven oscillator, described by equation (10), both the resonances at γ0/2 and 2γ0 appear due to the anharmonicity of the potential energy and are of the same order. The classical Rabi-like oscillations are displayed in figure 2

Quantum regime

Conclusions