Phase separation can be stronger than chaos

Abstract

We investigate several dynamical regimes characterizing a bosonic binary mixture loaded in a ring trimer, with particular reference to the persistence of demixing. The degree of phase separation is evaluated by means of the 'entropy of mixing', an indicator borrowed from statistical thermodynamics. Three classes of demixed stationary configurations are identified and their energetic and linear stability carefully analyzed. An extended set of trajectories originating in the vicinity of fixed points are explicitly simulated and chaos is shown to arise according to three different mechanisms. In many dynamical regimes, we show that chaos is not able to disrupt the order imposed by phase separation, i.e. boson populations, despite evolving in a chaotic fashion, do not mix. This circumstance can be explained either with energetic considerations or in terms of dynamical restrictions.

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

“…The different width of the lobes for N2 = N3 and of those for N2 ≠ N3 will be explained in Section 4.2 (by means of a simple analytical model), while their different height can be explained by means of an analogy with the superfluid-Mott insulator transition. Note that, also, these two kinds of lobes visible in the right panel of Figure 8 alternately take the values S ≈ log 6 and S ≈ log 3, in that the number of macroscopic components present in the non-degenerate Schrödinger-cat-like states of the type (16) and (17) bears memory of the degeneracy D(E0) of the ground state if the tunnelling T was suppressed.…”

“…More interestingly, for −2.4 < α < −1, it takes the sequence of values 14, 13, 12, 11, 10, 9. Accordingly, the system ground state alternately takes the form of state (16) and state (17). This sequence of 6 different ground states corresponds to that of the 6 green lobe-like domains in the bottom part of the left panel of Figure 8 and to that of the blue lobe-like domains in the bottom part of the right panel of Figure 8.…”

“…Notice that there is a profound difference between states (17) and states (16). Concerning the effective two-well potential resulting from the exclusion of the macroscopically occupied site (which plays the role of particle reservoir), the former are marked by a commensurate filling, while the second feature an incommensurate filling.…”

“…In fact, states (16) are forcefully superfluid, even for T → 0 + , because of the extra boson expelled by the supermixed soliton and injected into the effective twowell potential. Nevertheless, the superfluid character of state (16) is strongly dammed by the fact that it includes just 6 Fock states (actually 2, if one neglects the possible ways to permute the position of the particle reservoir) and therefore it is far from being of the type…”

“…The behaviour of the latter is ruled by the competition among tunnelling processes (resulting from the spatial fragmentation of the condensates into separated wells), intra-and the inter-species couplings. Such interplay among different contributions in the overall energy balance of the system results, among the rest, in a rich scenario of mixing-demixing quantum phase transitions [5,6,7,8,9], in the emergence of novel quantum phases [10,11,12], in the possibility of entangling [13,14] the two bosonic species, and in that of triggering peculiar dynamical regimes [15,16].…”