Recurrence time in the quantum dynamics of the 1D Bose gas

TL;DR

This paper investigates the recurrence times in the quantum dynamics of a 1D Bose gas, revealing how they depend on interaction strength and system size, with implications for cold atom experiments.

Contribution

It provides new estimates of recurrence times for various initial states in the 1D Bose gas, including rigorous calculations in free regimes and analysis across different coupling strengths.

Findings

Recurrence times are proportional to powers of system size in certain regimes.

Recurrence times are significantly longer than in free particles, up to 100 times.

Estimated recurrence time in experiments is around ten milliseconds.

Abstract

Recurrence time is evaluated for some initial quantum states in the one-dimensional Bose gas with repulsive short-range interactions. In the relatively strong and weak coupling cases some different types of initial states show almost complete recurrence and the estimates of recurrence time are proportional to some powers of the system size at least in some range of the system size. They are much longer than in the case of free particles such as 100 times. In the free-bosonic and free-fermionic regimes we evaluate the recurrence time rigorously, which is proportional to the square of the system size. The estimate of recurrence time is given by the order of ten milliseconds in the corresponding experimental systems of cold atoms trapped in one dimension of ten micrometers in length. It is much shorter than the estimate in a generic quantum many-body system, which may be as long as the age of the universe.