Condensate states in Fermi and Bose-Hubbard ladders

Ji-Guo wang, Dong-Dong Pu, Ya-Fei Song +4 more

Ji-Guo wang, Dong-Dong Pu, Ya-Fei Song +4 more

Dong-Dong Pu, Ji-Guo Wang, Ya-Fei Song +4 more

F. X. Liu, E. S. Ma, Z. Song

Although neither hardcore bosons nor fermions can occupy the same single-site state, they still obey different statistics, resulting in distinct many-particle quantum states, such as condensate states versus Fermi-liquid states. However, when only pair states are considered, the two can take the same form, since a local hardcore Bose pair and a Fermi pair obey the same statistics. In this work we demonstrate this by studying both Fermi and Bose extended Hubbard ladders, which can be realized experimentally in synthetic atomic ladders. A set of exact condensate-pair eigenstates for the Fermi ladder is constructed under SU(2) symmetry and can then be obtained by the spectrum generating algebra. The corresponding hardcore boson counterpart can be simply obtained by replacing fermionic operators with hardcore bosonic ones. Nevertheless, the boson-pair eigenstates are associated not with symmetry but with the restricted spectrum generating algebra. We also investigate the effect of next-nearest-neighbor hopping on the condensate states through numerical simulations of the dynamic response. The conclusions can be extended to a two-layer system. Our result reveals not only the resemblance of fermions to hardcore bosons, but also a possible mechanism of Hilbert-space fragmentation.

Ai‐Xia Zhang, Li-Xia Cai, Siqi He +4 more

We investigate the localization of a Bose-Einstein condensate trapped in a two-leg ladder in the presence of an artificial magnetic field via Bose-Hubbard model and discuss its abundant localized phenomena using variational approximation and direct numerical simulation. A two-leg bosonic ladder provides an ideal platform to study the complex dynamics of Bose-Einstein condensates in an optical lattice subject to an artificial magnetic field. As a main result, the system displays rich interesting localized states including self-trapping, soliton and breather. The coupling of the repulsive atomic interaction, artificial magnetic field, the rung-to-leg coupling ratio of the ladder, and the initial population difference of atoms between the two legs of the ladder results in the transitions between the localized states. The critical conditions for the transitions between the localized states are given analytically and are intuitively demonstrated in the phase diagram. Particularly, when the rung-to-leg coupling radio of the ladder satisfies a critical condition, we have the localized states with no local atomic currents between the two legs, otherwise, we observe the localized states with local atomic currents between the two legs. Finally, the results obtained via variational method are confirmed by the numerical simulations of the full discrete nonlinear Schrödinger equation describing the system.

Murray T. Batchelor, Angela Foerster

Abstract The Yang–Baxter equation has long been recognised as the masterkey to integrability, providing the basis for exactly solved models which capture the fundamental physics of a number of realistic classical and quantum systems. In this article we provide an introductory survey of the impact of Yang–Baxter integrable models on experiments in condensed matter physics and ultracold atoms. A number of prominent examples are covered, including the hard-hexagon model, the Heisenberg spin chain, the transverse quantum Ising chain, a spin ladder model, the Lieb–Liniger Bose gas, the Gaudin–Yang Fermi gas and the two-site Bose–Hubbard model. The review concludes by pointing to some other recent developments with promise for further progress.