Monodromy and chaos for condensed bosons in optical lattices

Abstract

We introduce a theory for the stability of a condensate in an optical lattice. We show that the understanding of the stability-to-ergodicity transition involves the fusion of monodromy and chaos theory. Specifically, the condensate can decay if a connected chaotic pathway to depletion is formed, which requires swap of seperatrices in phase-space. arXiv:1810.06019v2 [cond-mat.quant-gas]

Quasistatic transfer protocols for atomtronic superfluid circuits

“…Initially all the particles are condensed in k=0. Following [35] we define a depletion coordinate n and an imbalance coordinate M , such that the occupations of the orbitals are n 0 = N −2n, and n ± = n±M . The model Hamiltonian can be written in terms of (n, M ), and the conjugate phases (ϕ, φ).…”

“…It is the smallest ring that possibly can be exploited as a SQUID-type Qubit device [29][30][31][32]. The first requirement is to have the possibility to witness a stable superflow [33][34][35]. The second requirement is to have the possibility to witness coherent operation.…”

“…The hope is that coherent operation might be feasible for BHH configuration with few sites, as already established for protocols that involve two sites (BJJ). The most promising configuration is naturally the 3 site trimer [33][34][35][36]. For the analysis of such circuit one has to confront the handling of a quantum system that has an underlying mixed phase space [33,34,37].…”

“…Striking forms of irreversibility can be observed in hysteresis experiments with ultracold atoms, both is double well geometry [38] and in ring geometry [39,40]. In the context of Bose-Hubbard circuits the implications of mixed phase-space have been explored for some related themes: the stability of superflow [33][34][35]; the efficiency of a nonlinear stimulated Raman adiabatic passage [11]; and the Hamiltonian hysteresis that follows the reversal of the driving scheme [12].…”

Stochastic modeling of spreading and dissipation in mixed-chaotic systems that are driven quasistatically

“…Rather their phasespace is mixed, resulting in the failure of the adiabatic picture [9][10][11][12][13], and of linear-response theory. Namely, the phasespace structure varies with the control parameter: tori are destroyed; chaotic corridors are opened allowing migration between different regions in phasespace [14,15]; stochastic regions merge into chaos; sticky regions are formed [16][17][18][19]; sets of tori re-appear or emerge. Some of those issues can be regarded as a higher-dimensional version of non-linear scenarios that are relate to bifurcations of fixed points, notably swallow-tail loops [20][21][22][23][24], or as a higher-dimensional version of the well-studied separatrix crossing [25][26][27][28][29][30][31][32][33][34][35][36], where the Kruskal-Neishtadt-Henrard theorem is followed.…”