Correlations between particles can lead to subtle and sometimes counterintuitive phenomena. We analyze one such case, occurring during the sudden expansion of fermions in a lattice when the initial state has a strong admixture of double occupancies. We promote the notion of quantum distillation: during the expansion and in the case of strongly repulsive interactions, doublons group together, forming a nearly ideal band insulator, which is metastable with low entropy. We propose that this effect could be used for cooling purposes in experiments with two-component Fermi gases.
We investigate the time evolution of the second-order R\'enyi entropy (RE) for bosons in a one-dimensional optical lattice following a sudden quench of the hopping amplitude
J. Specifically, we examine systems that are quenched into the strongly correlated Mott-insulating (MI) regime with $J/U\ensuremath{\ll}1$ (
U denotes the strength of the on-site repulsive interaction) from the MI limit with
J=0. In this regime, the low-energy excited states can be effectively described by fermionic quasiparticles known as doublons and holons. They are excited in entangled pairs through the quench dynamics. By developing an effective theory, we derive a direct relation between the RE and correlation functions associated with doublons and holons. This relation allows us to analytically calculate the RE and obtain a physical picture for the RE, both in the ground state and during time evolution through the quench dynamics, in terms of doublon-holon pairs. In particular, we show that the RE is proportional to the population of doublon-holon pairs that span the boundary of the subsystem. Our quasiparticle picture introduces some remarkable features that are absent in previous studies on the dynamics of entanglement entropy in free-fermion models. It provides with valuable insights into the dynamics of entanglement entropy in strongly-correlated systems.
At present, there is considerable interest in using atomic fermions in optical lattices to emulate the mathematical models that have been used to study strongly correlated electronic systems. Some of these models, such as the 2-dimensional fermion Hubbard model, are notoriously difficult to solve, and their key properties remain controversial despite decades of studies. It is hoped that the emulation experiments will shed light on some of these long-standing problems. A successful emulation, however, requires reaching temperatures as low as 10(-12) K and beyond, with entropy per particle far lower than what can be achieved today. Achieving such low-entropy states is an essential step and a grand challenge of the whole emulation enterprise. In this article, we point out a method to literally squeeze the entropy out from a Fermi gas into a surrounding Bose-Einstein condensed gas, which acts as a heat reservoir. This method allows one to reduce the entropy per particle of a lattice Fermi gas to a few percent of the lowest value obtainable today.