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arXiv:cond-mat/0509560 · Physical Review Letters

Phase Coherence, Visibility, and the Superfluid–Mott-Insulator Transition on One-Dimensional Optical Lattices

Pinaki Sengupta, Marcos Rigol, G. G. Batrouni, P. J. H. Denteneer, Richard T. Scalettar

Published Nov 22, 2005• 28 citations
arXivHTMLPDF

Abstract

We study the phase coherence and visibility of trapped atomic condensates on one-dimensional optical lattices, by means of quantum Monte Carlo simulations. We obtain structures in the visibility similar to the kinks recently observed experimentally by Gerbier et al. [Phys. Rev. Lett. 95, 050404 (2005); 10.1103/PhysRevLett.95.050404cond-mat/0507087]. We examine these features in detail and offer a connection to the evolution of the density profiles as the depth of the lattice is increased. Our simulations reveal that, as the interaction strength U is increased, the evolution of superfluid and Mott-insulating domains stall for finite intervals of U. The density profiles do not change with increasing U. We show here that in one dimension the visibility provides unequivocal signatures of the melting of Mott domains with densities larger than 1.

DOI
10.1103/physrevlett.95.220402

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We study the phase coherence and visibility of trapped atomic condensates on one-dimensional optical lattices, by means of quantum Monte Carlo simulations. We obtain structures in the visibility similar to the kinks recently observed experimentally by Gerbier et al. [Phys. Rev. Lett. 95, 050404 (2005); 10.1103/PhysRevLett.95.050404cond-mat/0507087]. We examine these features in detail and offer a connection to the evolution of the density profiles as the depth of the lattice is increased. Our simulations reveal that, as the interaction strength U is increased, the evolution of superfluid and Mott-insulating domains stall for finite intervals of U. The density profiles do not change with increasing U. We show here that in one dimension the visibility provides unequivocal signatures of the melting of Mott domains with densities larger than 1.
The study of ultracold optically trapped atoms has opened new vistas in the physics of correlated quantum systems. Much attention has now turned to mixtures of bosonic and fermionic atoms. A central puzzle is the disagreement between the experimental observation of a reduced bosonic visibility Vb{\mathcal{V}}_{b}Vb​, and quantum Monte Carlo (QMC) calculations which show Vb{\mathcal{V}}_{b}Vb​ increasing. In this paper, we present QMC simulations which evaluate the density profiles and Vb{\mathcal{V}}_{b}Vb​ of mixtures of bosons and fermions in one-dimensional optical lattices. We resolve the discrepancy between theory and experiment by identifying parameter regimes where Vb{\mathcal{V}}_{b}Vb​ is reduced, and where it is increased. We present a simple qualitative picture of the different response to the fermion admixture in terms of the superfluid and Mott-insulating domains before and after the fermions are included. Finally, we show that Vb{\mathcal{V}}_{b}Vb​ exhibits kinks which are tied to the domain evolution present in the pure case, and also additional structure arising from the formation of boson-fermion molecules, a prediction for future experiments.
We study the superfluid-Mott-insulator transition of ultracold bosonic atoms in a one-dimensional optical lattice with a double-well confining trap using the density-matrix renormalization group method. At low density, the system behaves similarly as two separated ones inside each well. At high density, however, interesting features appear resulting from the quantum tunnelling between the two wells and the competition between the ``superfluid'' and Mott regions. These interesting features are characterized by a rich step-plateau structure in the visibility and the satellite peaks in the momentum distribution function, with an oscillating pattern as a function of the on-site repulsion. These properties shed light on the understanding of the quantum phase coherence between two coupled condensates.
We investigate the phase coherence properties of ultracold Bose gases in optical lattices, with special emphasis on the Mott insulating phase. We show that phase coherence on short length scales persists even deep in the insulating phase, preserving a finite visibility of the interference pattern observed after free expansion. This behavior can be attributed to a coherent admixture of particle-hole pairs to the perfect Mott state for small but finite tunneling. In addition, small but reproducible kinks are seen in the visibility, in a broad range of atom numbers. We interpret them as signatures for density redistribution in the shell structure of the trapped Mott insulator.
The Bose-Hubbard model describes the physics of a system of bosonic ultracold atoms in an optical lattice, in which a phase transition is present between a superfluid phase and a Mott insulator one. \nThe exact solution of this Hamiltonian is only feasible to find the ground-state of small systems, while other techniques (as mean-field schemes or quantum Monte Carlo) are necessary to study systems of larger size. \n \nAs a first application, we study the trapped model - relevant for the comparison with current experiments - through an inhomogeneous mean-field scheme. We describe some signatures of the phase crossover between superfluid and Mott insulator. In particular, the visibility of the quasimomentum distribution shows some kinks as a function of the lattice depth; we describe these features and we link them with the ones observed in other works in the literature. \n \nAs a second application, we use quantum Monte Carlo techniques to study the one-dimensional Bose-Hubbard model with long-range interactions and we focus on the appearance of the Haldane insulating phase, distinguishable from the Mott one through the presence of non-local hidden order. \nNon-local correlation functions are also used to describe the difference between the superfluid phase and the Mott insulator one.
Over the last several years, the boson‐Hubbard Hamiltonian has been widely used as an effective model of the physics of ultra‐cold optically trapped atoms. In this paper we will review its equilibrium properties, in one dimension, both in the absence and in the presence of an external potential. Then we will describe some new results for the visibility V of the interference pattern obtained after the free expansion of a gas. We will show that the evolution of V exhibits kinks with increasing interaction strength U/t, replicating phenomena seen experimentally. The behavior of the density profiles ni correlates well with the features in V. These profiles reveal an unexpected ‘freezing’ — a range of interaction strengths in which they remain unchanged. Finally, we show that V exhibits an increase with U/t signaling when a central ni = 2 Mott region melts and coherence develops between two superfluid regions with local densities 1 < ni < 2.
Bose–Einstein condensates (BEC) of sodium atoms are transferred into one-dimensional (1D) optical lattice potentials, formed by two laser beams with a wavelength of 1064 nm, in a shallow optical trap. The phase coherence of the condensate in the lattice potential is studied by changing the lattice depth. A qualitative change in behavior of the BEC is observed at a lattice depth of ∼ 13.7 E r, where the quantum gas undergoes a transition from a superfluid state to a state that lacks well-to-well phase coherence.