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arXiv:0810.2372 · Physical Review Letters

Quantum Dynamics in a Camelback Potential of a dc SQUID

Emile Hoskinson, Florent Lecocq, Nicolas Didier, Aurélien Fay, F. W. J. Hekking, Wiebke Guichard, O. Buisson, R. Dolata, Brigitte Mackrodt, Alexander B Zorin

Published Mar 6, 2009• 32 citations
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Abstract

We investigate a quadratic-quartic anharmonic oscillator formed by a potential well between two potential barriers. We realize this novel potential with a dc SQUID at near-zero current bias and flux bias near half a flux quantum. Escape out of the central well can occur via tunneling through either of the two barriers. We find good agreement with a generalized double-path macroscopic quantum tunneling theory. We also demonstrate an "optimal line" in current and flux bias along which the oscillator, which can be operated as a phase qubit, is insensitive to decoherence due to low-frequency current fluctuations.

DOI
10.1103/physrevlett.102.097004

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We investigate a quadratic-quartic anharmonic oscillator formed by a potential well between two potential barriers. We realize this novel potential with a dc SQUID at near-zero current bias and flux bias near half a flux quantum. Escape out of the central well can occur via tunneling through either of the two barriers. We find good agreement with a generalized double-path macroscopic quantum tunneling theory. We also demonstrate an "optimal line" in current and flux bias along which the oscillator, which can be operated as a phase qubit, is insensitive to decoherence due to low-frequency current fluctuations.
Macroscopic quantum tunneling of the phase is a fundamental phenomenon in the quantum dynamics of superconducting nanocircuits. The tunneling rate can be controlled in such circuits, where the potential landscape for the phase can be tuned with different external bias parameters. Precise theoretical knowledge of the macroscopic quantum tunneling rate is required in order to simulate and understand the experiments. We present a derivation, based on the instanton technique, of an analytical expression of the escape rate in general quartic and symmetric sextic potentials comprising two escape paths. These new potentials were recently realized when creating a noise-insensitive phase qubit in the camelback potential of a dc SQUID.
The escape probability out of the superconducting state of a hysteretic dc SQUID has been measured at different values of the applied magnetic flux. At low temperatures, the escape current and the width of the probability distribution are temperature independent but they depend on flux. Experimental results do not fit the usual one-dimensional macroscopic quantum tunneling (MQT) law but are perfectly accounted for by the two-dimensional MQT behavior as we propose here. Near zero flux, our data confirms the recent MQT observation in a dc SQUID [Phys. Rev. Lett. 89, 98301 (2002)]].
The authors report measurements of the transition rate from zero-voltage metastable minima in the two-dimensional potential of a DC SQUID (superconducting quantum interference device) as a function of applied flux and temperature. A crossover is observed from thermally activated escape to macroscopic quantum tunneling at a critical temperature that is a strong function of the bias flux. The macroscopic quantum tunneling rate is substantially reduced by damping, which also broadens the crossover region. The authors unexpectedly observed thermal rates that are significantly suppressed from those predicted by the classical two-dimensional thermal activation model, as if the potential barrier for activation were effectively enhanced. They discuss possible explanations for this result, based on the interaction of the macroscopic degrees of freedom in the device and energy level quantization effects.>
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.
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.