Non-linear coupling between the two oscillation modes of a dc-SQUID

TL;DR

This paper provides a detailed theoretical analysis of the coupling between the two orthogonal oscillation modes of a dc-SQUID, revealing conditions for strong interaction and potential quantum information applications.

Contribution

It demonstrates that the transverse mode energy can be comparable to the longitudinal mode, enabling strong coupling and complex quantum effects in existing dc-SQUID devices.

Findings

Strong coupling between modes observed at typical device parameters

Hamiltonian describing conditional quantum operations and entanglement

Atomic-like structure with V-like scheme for two-mode states

Abstract

We make a detailed theoretical description of the two-dimensional nature of a dc-SQUID, analyzing the coupling between its two orthogonal phase oscillation modes. While it has been shown that the mode defined as "longitudinal" can be initialized, manipulated and measured, so as to encode a quantum bit of information, the mode defined as "transverse" is usually repelled at high frequency and does not interfere in the dynamics. We show that, using typical parameters of existing devices, the transverse mode energy can be made of the order of the longitudinal one. In this regime, we can observe a strong coupling between these modes, described by an Hamiltonian providing a wide range of interesting effects, such as conditional quantum operations and entanglement. This coupling also creates an atomic-like structure for the combined two mode states, with a V-like scheme.