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Quantum phase diagram of an interacting ultracold Bose gas in a 1D random potential

Laurent Sanchez-Palencia

Published Jan 1, 2007• 0 citations
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Superfluid-insulator transition in an ultracold Fermi gas in the external disorder potential of the amplitude V 0 is studied as a function of its concentration n and the magnetic field B in the presence of the Feshbach resonance. We find the zero temperature phase diagrams in the plane (B, n) at a given V 0 and in the plane (V 0, n) at a given B. We study the transition between cases of classical and quantum random potentials which can be implemented by tuning intensity of speckles. Our results for the Bose-Einstein condensation side of the diagram are also valid for a Bose gas.
The zero temperature phase diagram for ultracold bosons in a random 1D potential is obtained through a site decoupling mean-field scheme performed over a Bose-Hubbard (BH) Hamiltonian, whose hopping term is considered as a random variable. As for the model with random on-site potential, the presence of disorder leads to the appearance of a Bose glass phase. The different phases—i.e., Mott insulator, superfluid, and Bose glass—are characterized in terms of condensate fraction and superfluid fraction. Furthermore, the boundary of the Mott lobes is related to an off-diagonal Anderson model featuring the same disorder distribution as the original BH Hamiltonian.
We study the thermodynamic properties of a 2D array of coupled one-dimensional Bose gases. The system is realized with ultracold bosonic atoms loaded in the potential tubes of a two-dimensional optical lattice. For negligible coupling strength, each tube is an independent weakly interacting 1D Bose gas featuring Tomonaga Luttinger liquid behavior. By decreasing the lattice depth, we increase the coupling strength between the 1D gases and allow for the phase transition into a 3D condensate. We extract the phase diagram for such a system and compare our results with theoretical predictions. Because of the high effective mass across the periodic potential and the increased 1D interaction strength, the phase transition is shifted to large positive values of the chemical potential. Our results are prototypical to a variety of low-dimensional systems, where the coupling between the subsystems is realized in a higher spatial dimension such as coupled spin chains in magnetic insulators.