SU(1,1) echoes for breathers in quantum gases

TL;DR

This paper introduces SU(1,1) echoes that can reverse quantum dynamics of breathers in interacting many-body systems governed by su(1,1) algebra, enabling state recovery without Hamiltonian sign change.

Contribution

It designs a novel echo protocol applicable to systems beyond su(2), specifically targeting breathers in quantum gases governed by su(1,1) algebra.

Findings

SU(1,1) echoes produce closed trajectories on Poincare disks.

They can recover initial states without changing Hamiltonian sign.

Revival times can exhibit period multiplication based on initial breather shape.

Abstract

Though the celebrated spin echoes have been widely used to reverse quantum dynamics, they are not applicable to systems whose constituents are beyond the control of the su(2) algebra. Here, we design echoes to reverse quantum dynamics of breathers in three-dimensional unitary fermions and two-dimensional bosons and fermions with contact interactions, which are governed by an underlying su(1,1) algebra. Geometrically, SU(1,1) echoes produce closed trajectories on a single or multiple Poincare disks and thus could recover any initial states without changing the sign of the Hamiltonian. In particular, the initial shape of a breather determines the superposition of trajectories on multiple Poincare disks and whether the revival time has period multiplication. Our work provides physicists with a recipe to tailor collective excitations of interacting many-body systems.