Café com Física



21 de outubro de 2015

Axel Pelster
Technical University Kaiserslautern, Germany

Bosons in Optical Lattices

Spinless bosons in optical lattices reveal a generic quantum phase transition once the depth of the potential wells is tuned. When the on-site interaction energy is small compared to the hopping energy, the ground state is superfluid, as the bosons are delocalized and phase coherent over the whole lattice. In the opposite limit, where the on-site interaction energy dominates over the hopping energy, the ground state is a Mott insulator, as each boson is trapped in one of the respective potential minima.

In order to describe both thermodynamic and dynamic properties of this quantum phase transition we developed a Ginzburg-Landau theory [1,2]. To this end we started from the microscopic Bose-Hubbard model, applied diagrammatic techniques within a systematic strong-coupling expansion, and calculated the underlying effective action. Already the first beyond mean-field order exhibits for the boundary of the quantum phase transition in a three-dimensional cubic lattice a relative error of less than 3% when compared with most recent Quantum Monte Carlo simulations [1]. Higher orders turn out to be so accurate that they even allow for the calculation of critical exponents [3]. Furthermore, the Ginzburg-Landau theory yields excitation spectra both in the Mott and the superfluid phase, which agree qualitatively with recent experiments [4].

Finally, we discuss three intriguing examples how the quantum phase transition of bosons in optical lattices can be tuned. In the first example we consider a spinor Bose gas loaded into a three-dimensional cubic optical lattice, where the different superfluid phases of spin-1 bosons are tunable due to the presence of an external magnetic field [5]. Then we deal with interacting bosons in an optical lattice with a periodic modulation of the s-wave scattering length, so the location of the quantum phase boundary turns out to depend quite sensitively on both driving amplitude and frequency [6]. Afterwards, we study the Bose-Hubbard model for the optical Kagome superlattice, where the delicate interplay between onsite repulsion and artificial symmetry breaking yields an anisotropic superfluid density, whose directional dependence is tunable by several system parameters [7,8].

[1] F.E.A. dos Santos and A. Pelster, Phys. Rev. A 79, 013614 (2009) [2] B. Bradlyn, F.E.A. dos Santos, and A. Pelster, Phys. Rev. A 79, 01361 (2009) [3] D. Hinrichs, A. Pelster, and M. Holthaus, Applied Physics B 113, 57 (2013) [4] T.D. Grass, F.E.A. dos Santos, and A. Pelster, Phys. Rev. A 84, 013613 (2011) [5] M. Mobarak and A. Pelster, Laser Phys. Lett. 10, 115501 (2013) [6] T. Wang, X.-F. Zhang, F.E.A. dos Santos, S. Eggert, and A. Pelster, Phys. Rev. A 90, 013633 (2014) [7] T. Wang, X.-F. Zhang, S. Eggert, and A. Pelster, Phys. Rev. A 87, 063615 (2013) [8] X.-F. Zhang, T. Wang, S. Eggert, and A. Pelster, Phys. Rev. B 92, 014512 (2015)