Abstract
Phys. Rev. B 100, 064308 (2019) A classic example of a quantum quench concerns the release of a interacting
Bose gas from an optical lattice. The local properties of quenches such as this
have been extensively studied however the global properties of these
non-equilibrium quantum systems have received far less attention. Here we study
several aspects of global non-equilibrium behavior by calculating the amount of
work done by the quench as measured through the work distribution function.
Using Bethe Ansatz techniques we determine the Loschmidt amplitude and work
distribution function of the Lieb-Liniger gas after it is released from an
optical lattice. We find the average work and its universal edge exponents from
which we determine the long time decay of the Loshcmidt echo and highlight
striking differences caused by the the interactions as well as changes in the
geometry of the system. We extend our calculation to the attractive regime of
the model and show that the system exhibits properties similar to the super
Tonks-Girardaeu gas. Finally we examine the prominent role played by bound
states in the work distribution and show that, with low probability, they allow
for work to be extracted from the quench.