Excitations of the One Dimensional Bose-Einstein Condensates in a Random Potential

Abstract

We examine bosons hopping on a one-dimensional lattice in the presence of a random potential at zero temperature. Bogoliubov excitations of the Bose-Einstein condensate formed under such conditions are localized, with the localization length diverging at low frequency as $\ell (\omega )\sim 1/{\omega }^{\alpha }$. We show that the well known result $\alpha =2$ applies only for sufficiently weak random potential. As the random potential is increased beyond a certain strength, $\alpha$ starts decreasing. At a critical strength of the potential, when the system of bosons is at the transition from a superfluid to an insulator, $\alpha =1$. This result is relevant for understanding the behavior of the atomic Bose-Einstein condensates in the presence of random potential, and of the disordered Josephson junction arrays.

References in corpus (13)

• Quantum Phase Slips in Superconducting Nanowires
• A widely tunable parametric amplifier based on a SQUID array resonator
• Anderson Localization of Expanding Bose-Einstein Condensates in Random Potentials
• Bosonic Excitations in Random Media
• Experimental observation of the Bogoliubov transformation for a Bose-Einstein condensed gas
• Phase transition of one dimensional bosons with strong disorder
• Anderson Localization of Bogolyubov Quasiparticles in Interacting Bose-Einstein Condensates
• Effects of dissipation on a quantum critical point with disorder
• Onset of Superfluidity in 4He Films Adsorbed on Disordered Substrates
• Effect of interactions on the localization of a Bose-Einstein condensate in a quasi-periodic lattice
• Anderson localization of elementary excitations in a one dimensional Bose-Einstein condensate
• The insulating phases and superfluid-insulator transition of disordered boson chains
• Universal transport in 2D granular superconductors

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