One-Dimensional Mott Insulator Formed by Quantum Vortices in Josephson Junction Arrays.

Abstract

Low-dimensional systems of strongly interacting bosons reveal a broad spectrum of quantum phase transitions. For bosons with repulsive interactions in a periodic potential, a phase transition occurs from a superfluid to a Mott insulator when the boson density changes from incommensurate to commensurate with the periodic lattice [1]. This phase transition is driven by the competition between the hopping of bosons and the repulsive interactions between the bosons. In two dimensions, the transition has been studied in experimental systems such as 4 He on graphite [2] and flux lines in superconductors with artificial pinning centers [3]. The phase diagram of one-dimensional bosons on a lattice has been theoretically studied with analytical [4] and quantum Monte Carlo methods [5]. The theoretical studies focus mainly on interacting bosons with short-range interactions. Experimentally, Josephson junction arrays can be used to study interacting bosons in one dimension. We do not know of any other experimental one-dimensional boson system. A voltage across a Josephson junction array is connected with the motion of vortices. Vortices in Josephson junction arrays behave as mass-carrying particles in a periodic potential landscape caused by the junction lattice. Traveling from cell to cell the vortex has to overcome an energy barrier, which is proportional to the Josephson coupling energy EJ . The vortex mass is inversely proportional to the charging energy EC [6]. In the limit of high barriers and large vortex mass (EJ ? EC) the vortices behave as classical particles. For smaller mass and lower barrier height (EJ EC) the vortices exhibit quantum mechanical properties [6,7]. These quantum vortices behave as bosons. They repel each other over a long range with a force proportional to EJ . Because of the quantum mechanical nature of the vortices and the periodic lattice potential, bands will form. The bandwidth is proportional to EC. Josephson junction arrays have the advantage that EJ and EC are experimentally well controllable and can be varied over a wide range. Is this Letter, we report the observation of a onedimensional Mott insulator formed by quantum vortices in a very long and narrow array of Josephson junctions. Around one-dimensional commensurate densities the mobility of the vortices vanishes for a finite window of the magnetic field. By varying EJyEC the stability of the Mott insulator can be changed. In this way the lobelike shape of the Mott insulating phase of interacting bosons in a one-dimensional periodic potential has been determined experimentally for the first time. The samples consist of an array of Josephson junctions. Each island is coupled to four neighboring islands (square cell) with small Josephson junctions. The length L of the array (L › 1000 cells) is much larger than the width W of the array (W › 7 cells). Along the length of the array the islands at both edges are connected by a narrow superconducting strip (busbar). These busbars repel the vortices and confine the vortex motion to one dimension. The current is injected in the middle and the voltage probes are situated at one end of the busbar. The sample layout is schematically sketched in Fig. 1. The area of a cell S is 2 mm 2 . Samples were fabricated using electron beam lithography and a shadow evaporation technique. They consist of high quality Al-Al2O3-Al tunnel junctions. We present the results of three different samples, which are indicated by A, B, and C. The capacitances C, estimated from the FIG. 1. Layout of the sample. The transport properties are determined by a four-terminal measurement. The current is injected in the middle of the sample and the resulting voltage is measured at one end of the sample. The Josephson junctions are denoted by crosses.