Mean-field phase diagram of the 1-D Bose gas in a disorder potential

Abstract

We study the quantum phase transition of the 1D weakly interacting Bose gas in the presence of disorder. We characterize the phase transition as a function of disorder and interaction strengths, by inspecting the long-range behavior of the one-body density matrix as well as the drop in the superfluid fraction. We focus on the properties of the low-energy Bogoliubov excitations that drive the phase transition, and find that the transition to the insulator state is marked by a diverging density of states and a localization length that diverges as a power-law with power 1. We draw the phase diagram and we observe that the boundary between the superfluid and the Bose glass phase is characterized by two different algebraic relations. These can be explained analytically by considering the limiting cases of zero and infinite disorder correlation length.

10 pages, 10 figures

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• Anderson localization of a non-interacting Bose-Einstein condensate
• Direct observation of Anderson localization of matter-waves in a controlled disorder
• Extension of Bogoliubov theory to quasi-condensates
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Cited by in corpus (21)

• Localization of Bogoliubov quasiparticles in interacting Bose gases with correlated disorder
• Condensate deformation and quantum depletion of Bose-Einstein condensates in external potentials
• Correlation function of weakly interacting bosons in a disordered lattice
• Bragg spectroscopy of clean and disordered lattice bosons in one dimension: a spectral fingerprint of the Bose glass
• The superfluid insulator transition of ultra-cold bosons in disordered 1d traps
• Density of states in an optical speckle potential
• Cavity-induced switching between localized and extended states in a non-interacting Bose-Einstein condensate
• Propagation of collective pair excitations in disordered Bose superfluids
• Phase diagram of quasi-two-dimensional bosons in laser speckle potential
• Fragmentation and the Bose-glass phase transition of the disordered 1D Bose gas
• Superfluid-insulator transition of two-dimensional disordered Bose gases
• Normal and superfluid fractions of inhomogeneous nonequilibrium quantum fluids
• Instanton theory for bosons in disordered speckle potential
• Light scattering from ultracold gases in disordered optical lattices
• Anderson localization of excitations in disordered Gross-Pitaevskii lattices
• Anderson localization of Bogoliubov excitations on quasi-1D strips
• Full distribution of the superfluid fraction and extreme value statistics in a one dimensional disordered Bose gas
• Superfluid-insulator transition in weakly interacting disordered Bose gases: a kernel polynomial approach
• Disorder Effects on Exciton-Polariton Condensates
• Equilibrium and Non-equilibrium Gross-Pitaevskii Lattice Dynamics: Interactions, Disorder, and Thermalization
• Bogoliubov Theory for a Superfluid Bose Gas Flowing in a Random Potential: Stability and Critical Velocity