Pathway toward the formation of supermixed states in ultracold boson mixtures loaded in ring lattices

Abstract

We investigate the mechanism of formation of supermixed soliton-like states in bosonic binary mixtures loaded in ring lattices. We evidence the presence of a common pathway which, irrespective of the number of lattice sites and upon variation of the interspecies attraction, leads the system from a mixed and delocalized phase to a supermixed and localized one, passing through an intermediate phase where the supermixed soliton progressively emerges. The degrees of mixing, localization and quantum correlation of the two condensed species, quantified by means of suitable indicators commonly used in Statistical Thermodynamics and Quantum Information Theory, allow one to reconstruct a bi-dimensional mixing-supermixing phase diagram featuring two characteristic critical lines. Our analysis is developed both within a semiclassical approach capable of capturing the essential features of the two-step mixing-demixing transition and with a fully-quantum approach. arXiv:1903.09212v2 [cond-mat.quant-gas]

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

“…As it is visible in Figure 9, where the expectation value ⟨∆n⟩ = ⟨ψ0 ∆n ψ0⟩ is plotted, when T Ua is small enough, a sequence of lobe-like domains is present, which corresponds to the sequence of values 15 (SM configuration), 13.5 (first superfluid-like lobe), 12 (first Mott-like lobe), 10.5, and so on. We conclude this Section by recalling that it is possible to find, either within the CV picture [21], or by means of the dynamical-algebra method [31], the region of the parameters space where the mixed configuration (the one sketched in the leftmost panel of Figure 1) is stable. It is given by inequality…”

“…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.…”

“…Going from left to right, the latter increase, a circumstance which favours boson delocalization and determines the blurring of the phase diagram illustrated in Figure 2 (see Ref. [21] for further details). Each plot includes more than 20k points [41], corresponding to as many numerical diagonalizations of Hamiltonian (1).…”

“…The analytic treatment developed in Ref. [21] was based on the Continuous Variable (CV) Picture [32,33,34,35,36], a rather versatile approximation scheme which, under the assumption that the number of particles loaded in the system, Na and N b , is large enough, allows one to turn the search for the ground state of Hamiltonian (1) into that for the global minimum of effective potential Figure 1: Pictorial representation of some states belonging to phases M, PL, and SM, respectively. Labels 1, 2, 3 correspond to site numbers, while the vertical axis corresponds to (normalized) boson populations x * ,j and y * ,j characterizing the ground-state configuration.…”

“…In particular, mixing-demixing transitions have been thoroughly described, in the case of small-size lattices, for repulsive [14,17,18,19,20] and attractive [21] interspecies couplings. These analyses have highlighted rather complex quantum phase diagrams where various phases, differing in the degree of mixing and localization of the two bosonic species, are recognizable.…”