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Physics-Uspekhi

Time, tunneling and turbulence

M. Ya. Azbel

Published Jun 30, 1998• 13 citations
Publisher

Abstract

This paper considers tunneling traversal time; tunneling through an alternating potential, its enhancement and its fractal (Hofstadter butterfly) and chaotic resonances; and Hartree liquid resonance tunneling and its (specifically quantum) instability and turbulence.
DOI
10.1070/pu1998v041n06abeh000402

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Tunneling of the Hartree liquid through opaque potential barriers separated by a well is considered. It is always unstable and is related to three distinctly different time scales. The shortest one is the period of classical oscillations in the well. It determines the period of tunneling current oscillations. Instability and specifically quantum turbulence develop on the scale of the quantum dwell time in the well. Dissipation yields the largest time scale. Analytical and numerical solutions are presented, and possible experiments are discussed.
Motivated by recent realizations of two-dimensional (2D) superconducting-qubit lattices, we propose a protocol to simulate Hofstadter butterfly with synthetic gauge fields in superconducting circuits. Based on the existing 2D superconducting-qubit lattices, we construct a generalized Hofstadter model on zigzag lattices, which has a fractal energy spectrum similar to the original Hofstadter butterfly. By periodically modulating the resonant frequencies of qubits, we engineer a synthetic gauge field to mimic the generalized Hofstadter Hamiltonian. A spectroscopic method is used to demonstrate the Hofstadter butterfly from the time evolutions of experimental observables. We numerically simulate the dynamics of the system with realistic parameters, and the results show a butterfly spectrum clearly. Our proposal provides a promising way to realize the Hofstadter butterfly on the latest 2D superconducting-qubit lattices and will stimulate the quantum simulation of novel properties induced by magnetic fields in superconducting circuits.