Bloch and Josephson Oscillations in a Ring of an Ideal Bose Gas

TL;DR

This paper demonstrates that an ideal Bose gas in a thin ring exhibits quantum oscillations analogous to Bloch and Josephson effects, with periodic angular momentum and time-dependent oscillations, inherent to quantum regimes of such systems.

Contribution

It reveals that Bose gases in rings naturally show Bloch and Josephson oscillations, extending these phenomena beyond Fermi gases and including interacting particles.

Findings

Angular momentum is periodic in angular velocity with quantum period.

Angular momentum oscillates periodically in time under constant torque.

Oscillations are intrinsic to quantum regimes of ring systems, regardless of interactions.

Abstract

We show that an Ideal Bose gas that is contained within a very thin ring exhibits phenomena analogous to the Bloch and Josephson oscillations of a charged Ideal Fermi gas in a thin ring. If the walls of the ring are constrained to have an angular velocity $\omega$, the angular momentum has an anomalous component that is periodic in $\omega$, with a period equal to the quantum of angular velocity $\omega_{0}\equiv \hbar /mR^{2}$. If a constant applied torque is applied to the walls, there will be component of the angular momentum of the gas that is periodic in time, with a 'Josephson frequency' given by $f_{J} =\tau/N \hbar$. Finally, we show that the oscillations are an automatic feature of the quantum regime of any ring of an ensemble of identical particles, even with particle interactions.