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Physical Review A

Phase coherence of a Bose-Einstein condensate in an optical antidot lattice

Kazuya Yamashita, Kouhei Hanasaki, Akihiro Ando, Toshiya Kinoshita

Published Dec 5, 2019• 2 citations
Publisher

Abstract

We report on the experimental investigation of the phase coherence of a Bose-Einstein condensate in an optical antidot lattice (ADL). In the ADL, a series of potential hills are arranged on a two-dimensional (2D) square lattice and crisscrossing channels with zero ac Stark shift form a 2D mesh with multiple junctions. Due to these structural features, matter wave interference released from the ADL is clearly visible even at antidot heights of the 300 times the photon recoil energy. However, phase coherence is significantly reduced at extremely tall antidot heights and atom hopping is suppressed. We explain this loss of coherence by introducing a periodic effective potential felt by the atoms on the mesh lines, which is the result of the quantization of the faster atomic motion in the orthogonal direction. This effective potential localizes atoms at the junctions, forming a bundle of tubelike gases. Using the Bose-Hubbard model, we interpret the coherence properties in terms of a 2D Josephson junction array. We have also observed the emergence of vortexlike holes after merging the tubelike gases. We discuss the effect of transverse thermal phase fluctuations and interpret the appearance of the vortexlike holes as a possible signature of the Berezinskii-Kosterlitz-Thouless crossover in the 2D lattice plane.

DOI
10.1103/physreva.100.063611

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We report on the experimental investigation of the phase coherence of a Bose-Einstein condensate in an optical antidot lattice (ADL). In the ADL, a series of potential hills are arranged on a two-dimensional (2D) square lattice and crisscrossing channels with zero ac Stark shift form a 2D mesh with multiple junctions. Due to these structural features, matter wave interference released from the ADL is clearly visible even at antidot heights of the 300 times the photon recoil energy. However, phase coherence is significantly reduced at extremely tall antidot heights and atom hopping is suppressed. We explain this loss of coherence by introducing a periodic effective potential felt by the atoms on the mesh lines, which is the result of the quantization of the faster atomic motion in the orthogonal direction. This effective potential localizes atoms at the junctions, forming a bundle of tubelike gases. Using the Bose-Hubbard model, we interpret the coherence properties in terms of a 2D Josephson junction array. We have also observed the emergence of vortexlike holes after merging the tubelike gases. We discuss the effect of transverse thermal phase fluctuations and interpret the appearance of the vortexlike holes as a possible signature of the Berezinskii-Kosterlitz-Thouless crossover in the 2D lattice plane.
Bose-Einstein condensates of rubidium atoms are stored in a two-dimensional periodic dipole force potential, formed by a pair of standing wave laser fields. The resulting potential consists of a lattice of tightly confining tubes, each filled with a 1D quantum gas. Tunnel coupling between neighboring tubes is controlled by the intensity of the laser fields. By observing the interference pattern of atoms released from more than 3000 individual lattice tubes, the phase coherence of the coupled quantum gases is studied. The lifetime of the condensate in the lattice and the dependence of the interference pattern on the lattice configuration are investigated.
We investigate the possibility that Bose–Einstein condensates, loaded on a 2D optical lattice, undergo—at finite temperature—a Berezinskii–Kosterlitz–Thouless transition. We show that—in an experimentally attainable range of parameters—a planar lattice of Bose–Einstein condensates is described by the XY model at finite temperature. We demonstrate that the interference pattern of the expanding condensates provides the experimental signature of the Berezinskii–Kosterlitz–Thouless transition by showing that, near the critical temperature, the component of the momentum distribution and the central peak of the atomic density profile sharply decrease. The finite-temperature transition for a 3D optical lattice is also discussed in this paper, and analogies with superconducting Josephson junction networks are stressed throughout the text.
Phase coherence and localization of Bose-Einstein Condensates (BEC) in optical lattices is a notable property that is changing under the superfluid-Mott insulator phase transition. For a single-component BEC, long-range phase coherence across lattice wells is lost as the lattice height is sufficiently increased. Phase coherences of two-component overlapping mixture of BECs, however, are nontrivial because of the interspecies interaction between components, affecting localization of condensates. For such cases, the BECs form two interdependent mean-field lattices made of each component in addition to optical lattices. We prepare initial BEC clouds as a collection of small Bogoliubov quasiparticles added to classical mean-fields, and obtain the dynamics under phase space representations, where the density operators are projected onto phase space. Among various phase space representations, we focus on a Truncated Wigner Approximation (TWA) and a positive P representation, and we construct a hybrid model to combine them. Since a high volume of numerical integration is required for sufficient convergence from ensembles, we construct efficient numerical methods to reduce the sample variance. We demonstrate time evolution of phase coherence of one-component and two-component BECs in state-dependent optical lattices. For one-component BECs, we show that phase coherence loss depends on lattice heights. In the cycling process of lattice height changes, we investigate nonadiabatic effects depending on initial ramp-up speeds. The hybrid model compared with the TWA exhibits temporal fluctuations in coherence and sudden phase diffusion at the end of ramp-up of a lattice. For two-component BECs, we consider that the two wavefunctions are localized at periodic potential wells whose positions differ by a half-period between the two. Dependence on population imbalance between two components becomes another factor on coherence loss. We show that under gradual loading of an optical lattice effective only to first component, loss of phase coherence of first atoms is enhanced and that of second atoms is weakened as the fraction of second atoms is increased in the mixture. We also demonstrate effects of localizing mean-field lattices on coherence loss under various lattice heights.
We investigate the possibility that Bose-Einstein condensates (BECs), loaded on a 2D optical lattice, undergo- at finite temperature- a Berezinskii-Kosterlitz-Thouless (BKT) transition. We show that- in an experimentally attainable range of parameters- a planar lattice of BECs is described by the XY model at finite temperature. We demonstrate that the interference pattern of the expanding condensates provides the experimental signature of the BKT transition by showing that, near the critical temperature, the ⃗k = 0 component of the momentum distribution and the central peak of the atomic density profile sharply decrease. The finite-temperature transition for a 3D optical lattice is also discussed, and the analogies with superconducting Josephson junction networks are stressed through the text. 1 I.
We report on the direct observation of an oscillating atomic current in a one-dimensional array of Josephson junctions realized with an atomic Bose-Einstein condensate. The array is created by a laser standing wave, with the condensates trapped in the valleys of the periodic potential and weakly coupled by the interwell barriers. The coherence of multiple tunneling between adjacent wells is continuously probed by atomic interference. The square of the small-amplitude oscillation frequency is proportional to the microscopic tunneling rate of each condensate through the barriers and provides a direct measurement of the Josephson critical current as a function of the intermediate barrier heights. Our superfluid array may allow investigation of phenomena so far inaccessible to superconducting Josephson junctions and lays a bridge between the condensate dynamics and the physics of discrete nonlinear media.