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Physica Scripta

Phase transitions in ultracold Bose gases confined in optical lattices

Santiago F. Caballero-Benítez, R. Paredes

Published May 13, 2015• 4 citations
Publisher

Abstract

We address the study of quantum Bose fluids confined in optical lattices subject to the influence of a time varying disordered external potential. The aim is to elucidate the interplay among lattice structure, interparticle interactions and the influence of structural disorder on dynamical and stationary ground state properties. The analysis in quasi one-dimension systems is done combining both mean field and Bose–Hubbard schemes to capture the essence of the quantum many body problem. Our predictions include the manifestation of superfluid, Mott and Anderson-like phases. We also present a natural extension of our technique to investigate two-dimensions systems. A general panorama of the current studies in bosonic systems is also given.

DOI
10.1088/0031-8949/90/6/068009

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We address the study of quantum Bose fluids confined in optical lattices subject to the influence of a time varying disordered external potential. The aim is to elucidate the interplay among lattice structure, interparticle interactions and the influence of structural disorder on dynamical and stationary ground state properties. The analysis in quasi one-dimension systems is done combining both mean field and Bose–Hubbard schemes to capture the essence of the quantum many body problem. Our predictions include the manifestation of superfluid, Mott and Anderson-like phases. We also present a natural extension of our technique to investigate two-dimensions systems. A general panorama of the current studies in bosonic systems is also given.
The dynamic response of ultracold Bose gases in one-dimensional optical lattices and superlattices is investigated based on exact numerical time evolutions in the framework of the Bose–Hubbard model. The system is excited by a temporal amplitude modulation of the lattice potential, as it was done in recent experiments. For regular lattice potentials, the dynamic signatures of the superfluid to Mott-insulator transition are studied and the position and the fine-structure of the resonances is explained by a linear response analysis. Using direct simulations and the perturbative analysis it is shown that in the presence of a two-colour superlattice the excitation spectrum changes significantly when going from the homogeneous Mott-insulator to the quasi-Bose-glass phase. A characteristic and experimentally accessible signature for the quasi-Bose-glass is the appearance of low-lying resonances and a suppression of the dominant resonance of the Mott-insulator phase.
An ultracold atomic Bose gas in an optical lattice is shown to provide an ideal system for the controlled analysis of disordered Bose lattice gases. This goal may be easily achieved under the current experimental conditions by introducing a pseudorandom potential created by a second additional lattice or, alternatively, by placing a speckle pattern on the main lattice. We show that, for a noncommensurable filling factor, in the strong-interaction limit, a controlled growing of the disorder drives a dynamical transition from superfluid to Bose-glass phase. Similarly, in the weak interaction limit, a dynamical transition from superfluid to Anderson-glass phase may be observed. In both regimes, we show that even very low-intensity disorder-inducing lasers cause large modifications of the superfluid fraction of the system.
We investigate the dynamic structure factor of atomic Bose and Fermi gases in one-dimensional optical lattices at zero temperature. The focus is on the generic behaviour of S ( k , ω) as a function of filling and interaction strength with the aim of identifying possible experimental signatures for the different quantum phase transitions. We employ the Hubbard or Bose–Hubbard model and solve the eigenvalue problem of the Hamiltonian exactly for moderate lattice sizes. This allows us to determine the dynamic structure factor and other observables directly in the phase transition regime, where approximation schemes are generally not applicable. We discuss the characteristic signatures of the various quantum phases appearing in the dynamic structure factor and illustrate that the centroid of the strength distribution can be used to estimate the relevant excitation gaps. Employing sum rules, these quantities can be evaluated using ground-state expectation values only. Important differences between bosonic and fermionic systems are observed, e.g., regarding the origin of the excitation gap in the Mott-insulator phase.
Abstract. The dynamic response of ultracold Bose gases in one-dimensional optical lattices and superlattices is investigated based on exact numerical time evolutions in the framework of the Bose-Hubbard model. The system is excited by a temporal amplitude modulation of the lattice potential, as it was done in recent experiments. For regular lattice potentials, the dynamic signatures of the superfluid to Mott-insulator transition are studied and the position and the fine-structure of the resonances is explained by a linear response analysis. Using direct simulations and the perturbative analysis it is shown that in the presence of a two-colour superlattice the excitation spectrum changes significantly when going from the homogeneous Mott-insulator the quasi Bose-glass phase. A characteristic and experimentally accessible signature for the quasi Bose-glass is the appearance of low-lying resonances and a suppression of the dominant resonance of the Mott-insulator phase.
Disorder is ubiquitous in condensed matter systems, but a thorough understanding of these systems is hindered by poor control over the nature of disorder and competing interactions. Ultracold gases trapped in optical lattices, on the other hand, offer an unprecedented level of control over interactions and disorder, and are ideal candidates to test theoretical predictions and study fascinating phenomena resulting from the interplay between disorder, interaction, and quantum degeneracy. In this dissertation, I present my research on strongly correlated many-body lattice bosons in the presence of disordered potentials. My results are based on quantum Monte Carlo simulations by the Worm algorithm. Experimentally, lattice bosons can be realized by ultracold gases in optical lattices. I studied the ground state phase diagram of the above systems in the presence of diagonal (quasi-periodic disordered potential or random disordered potential) and off-diagonal disorder (in the form of site dilution). First, I will discuss the ground state phase diagram of two-dimensional bosons in quasi-periodic lattices. Then, I will discuss the phase diagram as well as finite temperature thermodynamic properties of two-dimensional dipolar lattice bosons in the presence of random diagonal disordered potentials. Finally, I will discuss the phase diagram of two-dimensional hard-core lattice bosons system in the presence of long-range hopping and long-range two-body interactions both in the absence of disorder and in the presence of site dilution (equivalent to off-diagonal disorder). This system is equivalent to the long-range XXZ model as realized by polar molecules trapped in a deep optical lattice. These results provide theoretical guidance for experimentalists to find quantum phase transitions as well as exotic quantum phases in strongly correlated bosonic lattice systems.
Abstract. In the present paper we describe the properties induced by disorder on an ultracold gas of Bosonic atoms loaded into a two-dimensional optical lattice with global confinement ensured by a parabolic potential. Our analysis is centered on the spatial distribution of the various phases, focusing particularly on the superfluid properties of the system as a function of external parameters and disorder amplitude. In particular, it is shown how disorder can suppress superfluidity, while partially preserving the system coherence.