State engineering of impurities in a lattice by coupling to a Bose gas

Abstract

We investigate the localization pattern of interacting impurities, which are trapped in a lattice potential and couple to a Bose gas. For small interspecies interaction strengths, the impurities populate the energetically lowest Bloch state or localize separately in different wells with one extra particle being delocalized over all the wells, depending on the lattice depth. In contrast, for large interspecies interaction strengths we find that due to the fractional filling of the lattice and the competition of the repulsive contact interaction between the impurities and the attractive interaction mediated by the Bose gas, the impurities localize either pairwise or completely in a single well. Tuning the lattice depth, the interspecies and intraspecies interaction strength correspondingly allows for a systematic control and engineering of the two localization patterns. The sharpness of the crossover between the two states as well as the broad region of their existence supports the robustness of the engineering. Moreover, we are able to manipulate the ground state's degeneracy in the form of triplets, doublets and singlets by implementing different boundary conditions, such as periodic and hard wall boundary conditions. where ĉ † is the field operator of the lattice A bosons, m A their mass, V 0 the lattice depth, g AA the intraspecies interaction strength, k the number of wells in the lattice and L is the length of the system. The B species is described by the Hamiltonian of the Lieb-Liniger model [63-65] for periodic boundary conditions New J. Phys. 20 (2018) 103042 K Keiler and P Schmelcher

Interaction-induced single-impurity tunneling in a binary mixture of trapped ultracold bosons

“…Hence, initially the subsystems are not entangled, thereby forming a single product state. We further note that the two species strongly avoid overlap in this ground state configuration (see [46]), reminiscent of the phase separation of two Bose gases [12]. The quench is performed by lowering the interspecies interaction strength.…”

Entanglement-assisted tunneling dynamics of impurities in a double well immersed in a bath of lattice trapped bosons

“…In the extreme case such systems consist of a single impurity immersed in a majority species. These setups have been studied theoretically [25][26][27][28][29][30][31][32] and experimentally [33][34][35][36], for a single impurity, serving as a simulator of polaron physics, as well as for many impurities [37][38][39][40][41][42] and are indeed a subject of ongoing research. While the ground state properties of a single impurity in a bath are to a certain extent well understood, less focus has been placed on the transport properties and the emergent collisions of the impurity through the bath [43][44][45][46].…”

One-dimensional mixtures of several ultracold atoms: a review

“…[189]). Finally, we note that this problem has attracted recently a lot of interest, also in other external trapping potentials, such as double wells or optical lattices [190,191] as well as in the case of attractive impurity [192]. In general, when the mass imbalance is present and for any number of particles, certain arrangements of unequal masses make the problem solvable for limits in unsolvable in the equal mass case [193].…”