Distinguishing quantum from classical oscillations in a driven phase qubit

TL;DR

This paper identifies key differences between quantum and classical oscillations in phase qubits, providing criteria to reliably distinguish genuine quantum Rabi oscillations from classical effects.

Contribution

It offers a set of qualitative and quantitative criteria based on resonance shape, frequency shifts, and excitation conditions to differentiate quantum from classical oscillations in phase qubits.

Findings

Quantum Rabi oscillations can be driven by subharmonics, unlike classical oscillations.

Classical resonance exhibits asymmetric shape, whereas quantum resonance is symmetric.

Classical resonance shows a negative frequency shift, opposite to the positive Bloch-Siegert shift in quantum case.

Abstract

Rabi oscillations are coherent transitions in a quantum two-level system under the influence of a resonant perturbation, 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 [N. Gronbech-Jensen and M. Cirillo, Phys. Rev. Lett. 95, 067001 (2005)] 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 effect. First, while the quantum Rabi oscillations can be produced by the subharmonics of the resonant frequency (multiphoton processes), the classical effect also exists when the system is excited at the overtones. Second, the shape of the resonance is, in the classical case, characteristically asymmetric; while quantum resonances are described by symmetric Lorentzians. Third, 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 to confidently distinguish the bona fide Rabi oscillations from their classical Doppelganger.