The phase-separation mechanism of a binary mixture in a ring trimer

Abstract

We show that, depending on the ratio between the inter- and the intra-species interactions, a binary mixture trapped in a three-well potential with periodic boundary conditions exhibits three macroscopic ground-state configurations which differ in the degree of mixing. Accordingly, the corresponding quantum states feature either delocalization or a Schrödinger cat-like structure. The two-step phase separation occurring in the system, which is smoothed by the activation of tunnelling processes, is confirmed by the analysis of the energy spectrum that collapses and rearranges at the two critical points. In such points, we show that also Entanglement Entropy, a quantity borrowed from quantum-information theory, features singularities, thus demonstrating its ability to witness the double mixining-demixing phase transition. The developed analysis, which is of interest to both the experimental and theoretical communities, opens the door to the study of the demixing mechanism in complex lattice geometries.

Quantum-Granularity Effect in the Formation of Supermixed Solitons in Ring Lattices

“…It is clear that, in the region of the (α, β) plane corresponding to phase PL, a staircase-like structure is present for sufficiently low values of T (see left and central columns of Figure 5). Conversely, this peculiar property is absent when tunnelling is large enough (see right column of Figure 5), a circumstance which can be explained in terms of the delocalizing effect of hopping processes, which tend to smooth down transitions and sharp features of the phase diagram [17,18,19,21]. The presence of this staircase-like structure in the central region of the (α, β) plane is due to the fact that, being the hopping amplitude small, the system responds to small variations of control parameters in a highly non-linear way.…”

“…Another effective indicator that can provide insight into the jerky transfers of bosons from/to the supermixed soliton is represented by D(E0), the degeneracy of the ground-state level when Ta = T b = 0. We recall, in this regard, that, as soon as the tunnelling is non-vanishing, the ground state of Hamiltonian (1) gets unique and not-degenerate [42], although it can take the form of a superposition of few macroscopically different configurations (a Schrödinger-cat state) [43,18]. As we shall discuss, such a superposition of different Fock states, although being not-degenerate, bears memory of the value of D(E0) that one would have if hopping processes were suppressed, since D(E0) at Ta = T b = 0 corresponds to the number of macroscopic configurations which constitute the non-degenerate Schrödinger-cat state at small but finite tunnellings.…”

“…With reference to definitions (4), in fact, we have verified that no additional phases emerge for α < −3, while the case of α > 0 has been thoroughly investigated in Refs. [18,19]. As regards M PL SM -3 -2 -1 0 0 0.5 1 Figure 2: Phase diagram of a (possibly asymmetric) two-species bosonic mixture confined in a 3-well potential and featuring repulsive intraspecies and attractive interspecies interactions.…”

“…Mixing-demixing and mixing-supermixing transitions in ultracold bosonic mixtures, which involve the localization of the condensed species in different sites of the lattice, have also been shown to be strongly associated to the presence of criticalities in a number of quantum indicators. The latter include, but are not limited to, the functional dependence of the ground state energy on model parameters, the energy fingerprint (constituted by the structure of the first excited energy levels), and the degree of entanglement between the bosonic species of the mixture [23,18,19,21,14].…”

Phase separation can be stronger than chaos

“…to saddle points of Hamiltonian (7). panel) exactly corresponds to one of the three kinds of ground states that were found and discussed in [38]. In fact, all FPs z *  in such region (depicted in green) are indeed global minima of function H .…”