Depinning of the charged Bose glass: origin of the critical voltage in nanostructured Josephson-junction chains
The low-temperature states of bosonic condensates exhibit fundamental quantum effects at the macroscopic scale. The combined effects of interaction and disorder in these can have drastic consequences, leading to the Mott insulator and Bose-Anderson glass. The latter is thought to describe helium-4 in porous media, cold atoms in disordered optical potentials, disordered magnetic insulators, and thin superconducting films. The prototypical Bose-Hubbard model without disorder predicts a Beresinskii-Kosterlitz-Thouless quantum phase transition between superfluid and Mott insulator. Experimental implementation using arrays of Josephson junctions has been explored, however, the possibility of the insulating glass has not been considered. The ubiquity of such a phase in Josephson-junction arrays would have important implications for their proposed use as a fundamental current standard. Unlike the Mott insulator, the insulating glass is compressible, therefore AC synchronisation of charge may not be possible. We have measured critical voltages for a large number of simple chains of sub-micron Josephson junctions with significantly varying energy scales. We observe universal scaling of critical voltage with single-junction Bloch bandwidth. Our measurements reveal a localisation length exponent that steepens with Luttinger parameter, arising from precursor fluctuations as one approaches the Bose glass-superfluid quantum phase transition. This contrasts with the fixed exponent found for classical pinning of charge density waves, vortex lattices, and disordered spin systems, and is in excellent agreement with the quantum theory of one-dimensional disordered bosonic insulators. We thereby demonstrate a unique signature of the charged Bose glass in insulating Josephson-junction chains.