Macroscopic quantum tunneling in quartic and sextic potentials: application to a phase qubit

TL;DR

This paper derives an analytical formula for macroscopic quantum tunneling rates in quartic and sextic potentials, crucial for understanding and designing phase qubits in superconducting circuits.

Contribution

It introduces a new instanton-based derivation of escape rates in complex potentials relevant to noise-insensitive phase qubits.

Findings

Derived explicit formulas for tunneling rates in quartic and sextic potentials.

Applied the formulas to potentials realized in phase qubits.

Enhanced understanding of quantum tunneling control in superconducting circuits.

Abstract

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 camel-back potential of a dc SQUID.