Critical temperature of trapped interacting bosons from large-N based theories

Ultracold atoms provide clues to an important many-body problem regarding the dependence of Bose-Einstein condensation (BEC) transition temperature $T_c$ on interactions. However, cold atoms are trapped in harmonic potentials and theoretical evaluations of the $T_c$ shift of trapped interacting Bose gases are challenging. While previous predictions of the leading-order shift have been confirmed, more recent experiments exhibit higher-order corrections beyond available mean-field theories. By implementing two large-N based theories with the local density approximation (LDA), we extract next-order corrections of the $T_c$ shift. The leading-order large-N theory produces results quantitatively different from the latest experimental data. The leading-order auxiliary field (LOAF) theory containing both normal and anomalous density fields captures the $T_c$ shift accurately in the weak interaction regime. However, the LOAF theory shows incompatible behavior with the LDA and forcing the LDA leads to density discontinuities in the trap profiles. We present a phenomenological model based on the LOAF theory, which repairs the incompatibility and provides a prediction of the $T_c$ shift in stronger interaction regime.Comment: 11 pages, 3 figure

Dynamical crossover between the infinite-volume and empty-lattice limits of ultra-cold fermions in 1D optical lattices

Unlike typical condensed-matter systems, ultra-cold atoms loaded into optical lattices allow separate control of both the particle number and system size. As a consequence, there are two distinct "thermodynamic" limits that can be defined for these systems: i) "infinite-volume limit" at constant finite density, and ii) "empty-lattice limit" at constant particle number. To probe the difference between these two limits and their crossover, we consider a partially occupied lattice and study the transport of non-interacting fermions and fermions interacting at the mean-field level into the unoccupied region. In the infinite-volume limit, a finite steady-state current emerges. On the other hand, in the empty-lattice limit there is no finite steady-state current. By changing the initial filling, we find a smooth crossover between the two limits. Our predictions may be verified using available experimental tools and demonstrate a fundamental difference between isolated small systems such as ultra-cold atoms and conventional condensed-matter systems.Comment: 6 pages, 5 figure

Site-wise manipulations and Mott insulator-superfluid transition of interacting photons using superconducting circuit simulators

The Bose Hubbard model (BHM) of interacting bosons in a lattice has been a paradigm in many-body physics, and it exhibits a Mott insulator (MI)-superfluid (SF) transition at integer filling. Here a quantum simulator of the BHM using a superconducting circuit is proposed. Specifically, a superconducting transmission line resonator supporting microwave photons is coupled to a charge qubit to form one site of the BHM, and adjacent sites are connected by a tunable coupler. To obtain a mapping from the superconducting circuit to the BHM, we focus on the dispersive regime where the excitations remain photon-like. Standard perturbation theory is implemented to locate the parameter range where the MI-SF transition may be simulated. This simulator allows single-site manipulations and we illustrate this feature by considering two scenarios where a single-site manipulation can drive a MI-SF transition. The transition can be analyzed by mean-field analyses, and the exact diagonalization was implemented to provide accurate results. The variance of the photon density and the fidelity metric clearly show signatures of the transition. Experimental realizations and other possible applications of this simulator are also discussed.Comment: 13 pages, 9 figure