Necessary and sufficient condition for quantum adiabaticity in a driven one-dimensional impurity-fluid system

We study under what conditions the quantum adiabaticity is maintained in a closed many-body system consisting of a one-dimensional fluid and an impurity particle dragged through the latter by an external force. We employ an effective theory describing the low-energy sector of the system to derive the time dependence of the adiabaticity figure of merit: the adiabatic fidelity. We find that in order to maintain adiabaticity in a large system the external force FN should vanish with the system size N as 1/N or faster. This improves the necessary adiabatic condition FN=O(1/lnN) obtained for this system previously [O. Lychkovskiy et al., in Fourth International Conference on Quantum Technologies (ICQT-2017), AIP Conf. Proc. No. 1936 (AIP, New York, 2018), p. 020024]. The experimental implications of this result and its relation to the quasi-Bloch oscillations of the impurity are discussed.