Two-species boson mixture on a ring: A group-theoretic approach to the quantum dynamics of low-energy excitations

Abstract

We investigate the weak excitations of a system made up of two condensates trapped in a BoseHubbard ring and coupled by an interspecies repulsive interaction. Our approach, based on the Bogoliubov approximation scheme, shows that one can reduce the problem Hamiltonian to the sum of sub-HamiltoniansĤ k , each one associated to momentum modes ±k. EachĤ k is then recognized to be an element of a dynamical algebra. This uncommon and remarkable property allows us to present a straightforward diagonalization scheme, to find constants of motion, to highlight the significant microscopic processes, and to compute their time evolution. The proposed solution scheme is applied to a simple but non trivial closed circuit, the trimer. The dynamics of lowenergy excitations, corresponding to weakly-populated vortices, is investigated considering different choices of the initial conditions, and the angular-momentum transfer between the two condensates is evidenced. Finally, the condition for which the spectral collapse and dynamical instability are observed is derived analytically.

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…”

“…in fact, can capture the ultra-quantum effects originating from the interplay between the spatial fragmentation of the two condensates and the competition among tunnelling (Ta and T b ), intra-(Ua and U b ) and inter-(W ) species couplings [31,17,18,19,20,21]. Operator Aj (A † j ) destroys (creates) a species-a boson in the j-th site.…”

Phase separation can be stronger than chaos

“…Engineering of experimental setups capable of trapping boson mixtures [8][9][10] in optical lattices [11][12][13] has stimulated the interest of the theoretical community for the understanding of demixing effect in the presence of spatial fragmentation. In this context, beyond phase separation [14][15][16], a rich variety of phenomena have been highlighted including (but not limited to) the formation of boson currents in ring lattices, [17], the appearance of novel phases exhibiting magnetic-like properties [18,19], quantum emulsions [20], the emergence of polaron excitations [21,22], the entanglement between the species [23,24], the collision of a condensate with impurities [25][26][27], the formation of immiscible solitons [28] and the modulation instability in the phase separation [29]. Systems consisting of two bosonic species and optical lattices with ring geometry are within the reach of current experimental setups.…”

Quantum phase transitions and the degree of nonidentity in the system with two different species of vector bosons

“…The typical example is the system of vector bosons. This case corresponds to Bose-Hubbard model that is absent in the standard solid state theory and is the topic of intensive research last time [22][23][24][25][26][27][28][29][30][31][32][33][34], and [35][36][37] for review. Numerous striking effects, in particular, induced by the multispecie nature of boson system have been found recently including quantum phase transitions, many-body localization, and topological order, as well as the superfluidity and supersolidity of ultracold atomic systems [35][36][37].…”