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arXiv:cond-mat/0405430 · Physical Review Letters

Coherent Oscillations in a Superconducting Multilevel Quantum System

Julien Claudon, Franck Balestro, F. W. J. Hekking, O. Buisson

Published Oct 26, 2004• 108 citations
arXivHTMLPDF

Abstract

We have observed coherent oscillations in a multilevel quantum system, formed by a current-biased dc SQUID. These oscillations have been induced by applying resonant microwave pulses of flux. Quantum measurement is performed by a nanosecond flux pulse that projects the final state onto one of two different voltage states of the dc SQUID, which can be read out. The number of quantum states involved in the coherent oscillations increases with increasing microwave power. The dependence of the oscillation frequency on microwave power deviates strongly from the linear regime expected for a two-level system and can be very well explained by a theoretical model taking into account the anharmonicity of the multilevel system.

DOI
10.1103/physrevlett.93.187003

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We have observed coherent oscillations in a multilevel quantum system, formed by a current-biased dc SQUID. These oscillations have been induced by applying resonant microwave pulses of flux. Quantum measurement is performed by a nanosecond flux pulse that projects the final state onto one of two different voltage states of the dc SQUID, which can be read out. The number of quantum states involved in the coherent oscillations increases with increasing microwave power. The dependence of the oscillation frequency on microwave power deviates strongly from the linear regime expected for a two-level system and can be very well explained by a theoretical model taking into account the anharmonicity of the multilevel system.
This paper presents our procedure to measure the quantum state of a dc superconducting quantum interference device (SQUID) within a few nanoseconds, using an adiabatic dc flux pulse. Detection of the ground state is governed by standard macroscopic quantum tunneling (MQT) theory, with a small correction due to residual noise in the bias current. In the two-level limit, where the SQUID constitutes a phase qubit, an observed contrast of 0.54 indicates a significant loss in contrast compared to the MQT prediction. It is attributed to spurious depolarization (loss of excited state occupancy) during the leading edge of the adiabatic flux measurement pulse. We give a simple phenomenological relaxation model which is able to predict the observed contrast of multilevel Rabi oscillations for various microwave amplitudes.
A current biased dc superconducting quantum interference device behaves as an anharmonic quantum oscillator controlled by a bias current and an applied magnetic flux. We consider here its two level limit consisting of the two lower energy states \ensuremath{\mid}0⟩ and \ensuremath{\mid}1⟩. We have measured energy relaxation times and microwave absorption for different bias currents and fluxes in the low microwave power limit. Decoherence times are extracted. The low frequency flux and current noise have been measured independently by analyzing the probability of current switching from the superconducting to the finite voltage state, as a function of applied flux. The high frequency part of the current noise is derived from the electromagnetic environment of the circuit. The decoherence of this quantum circuit can be fully accounted for by these current and flux noise sources.
We have observed Rabi-like oscillations in a current-biased dc superconducting quantum interference device presenting enhanced coherence times compared to our previous realization [J. Claudon et al., Phys. Rev. Lett. 93, 187003 (2004)]. This Josephson device behaves as an anharmonic oscillator which can be driven into a coherent superposition of quantum states by resonant microwave flux pulses. Increasing the microwave amplitude, we study the evolution of the Rabi frequency from the two-level regime to the regime of multilevel dynamics. When up to three levels are involved, the Rabi frequency is a clear signature of a quantum behavior. At higher excitation amplitude, classical and quantum predictions for the Rabi frequency converge. This result is discussed in the light of a calculation of the Wigner function. In particular, our analysis shows that pronounced quantum interferences always appear in the course of the Rabi-like oscillations.
We have observed coherent time evolution between two quantum states of a superconducting flux qubit comprising three Josephson junctions in a loop. The superposition of the two states carrying opposite macroscopic persistent currents is manipulated by resonant microwave pulses. Readout by means of switching-event measurement with an attached superconducting quantum interference device revealed quantum-state oscillations with high fidelity. Under strong microwave driving, it was possible to induce hundreds of coherent oscillations. Pulsed operations on this first sample yielded a relaxation time of 900 nanoseconds and a free-induction dephasing time of 20 nanoseconds. These results are promising for future solid-state quantum computing.
We present Rabi oscillation measurements of a Nb/AlOx/Nb\text{Nb}/{\text{AlO}}_{\text{x}}/\text{Nb}Nb/AlOx​/Nb dc superconducting quantum interference device (SQUID) phase qubit with a $100\text{ }\ensuremath{\mu}{\text{m}}^{2}$ area junction acquired over a range of microwave drive power and frequency detuning. Given the slightly anharmonic level structure of the device, several excited states play an important role in the qubit dynamics, particularly at high power. To investigate the effects of these levels, multiphoton Rabi oscillations were monitored by measuring the tunneling escape rate of the device to the voltage state, which is particularly sensitive to excited state population. We compare the observed oscillation frequencies with a simplified model constructed from the full phase qubit Hamiltonian and also compare time-dependent escape rate measurements with a more complete density-matrix simulation. Good quantitative agreement is found between the data and simulations, allowing us to identify a shift in resonance (analogous to the ac Stark effect), a suppression of the Rabi frequency, and leakage to the higher excited states.