Mobility edges in bichromatic optical lattices

Boers, Dave; Goedeke, Benjamin; Hinrichs, Dennis; Holthaus, Martin

doi:10.1103/physreva.75.063404

Cited by 145 publications

(148 citation statements)

References 23 publications

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“…h 0 is a constant which vanishes in the limit V 0 → 0 and grows with the lattice depth V 0 . For shallow and deep lattices it can be calculated analytically [109] and the result reads [112] h 0 a π…”

Section: Wannier Functionsmentioning

confidence: 99%

Ultracold bosons with short-range interaction in regular optical lattices

2016

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During the last decade, many exciting phenomena have been experimentally observed and theoretically predicted for ultracold atoms in optical lattices. This paper reviews these rapid developments concentrating mainly on the theory. Different types of the bosonic systems in homogeneous lattices of different dimensions as well as in the presence of harmonic traps are considered. An overview of the theoretical methods used for these investigations as well as of the obtained results is given. Available experimental techniques are presented and discussed in connection with theoretical considerations. Eigenstates of the interacting bosons in homogeneous lattices and in the presence of harmonic confinement are analyzed. Their knowledge is essential for understanding of quantum phase transitions at zero and finite temperature.

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Section: Wannier Functionsmentioning

confidence: 99%

Ultracold bosons with short-range interaction in regular optical lattices

2016

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“…The second lattice is weaker (s 2 ≪ s 1 ) and introduces a "deterministic" disorder, or quasi-disorder [2,20,21]. For a noninteracting gas in such a potential, the evolution of the system is described by the AubryAndrè model [4], which is obtained from the Schrödinger equation by expanding the single-particle wavefunction ψ(x) over a set of Wannier states, maximally localized at the minima of the primary lattice in the lowest Bloch band, |ψ = j ψ j |w j [18,22]. In the presence of interactions between the atoms, one can instead start from the Gross-Pitaevskii (GP) equation [23,24] and use the same procedure in order to get a generalized AubryAndrè model which includes an additional nonlinear term that represents the mean-field interaction.…”

Section: The Modelmentioning

confidence: 99%

Effects of interaction on the diffusion of atomic matter waves in one-dimensional quasiperiodic potentials

2009

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We study the behaviour of an ultracold atomic gas of bosons in a bichromatic lattice, where the weaker lattice is used as a source of disorder. We numerically solve a discretized mean-field equation, which generalizes the one-dimensional Aubry-Andrè model for particles in a quasi-periodic potential by including the interaction between atoms. We compare the results for commensurate and incommensurate lattices. We investigate the role of the initial shape of the wavepacket as well as the interplay between two competing effects of the interaction, namely self-trapping and delocalization. Our calculations show that, if the condensate initially occupies a single lattice site, the dynamics of the interacting gas is dominated by self-trapping in a wide range of parameters, even for weak interaction. Conversely, if the diffusion starts from a Gaussian wavepacket, self-trapping is significantly suppressed and the destruction of localization by interaction is more easily observable.

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“…Away from this regime multi-band processes come into play, and the effect of the independent tuning of the OL intensity and the interaction strength can be captured only via multi-band or continuous-space models. Recent theoretical and experimental studies have addressed the regime of shallow OLs and strong interactions, investigating intriguing phenomena such as Mott and pinning bosonic localization transitions [14][15][16][17][18], Anderson localization [19][20][21], Bose-Glass phases [22], and itinerant ferromagnetism [23,24].…”

mentioning

confidence: 99%

One-dimensional repulsive Fermi gas in a tunable periodic potential

Pilati

Barbiero²,

Fazio

et al. 2017

Phys. Rev. A

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By using unbiased continuos-space quantum Monte Carlo simulations, we investigate the ground state properties of a one-dimensional repulsive Fermi gas subjected to a commensurate periodic optical lattice (OL) of arbitrary intensity. The equation of state and the magnetic structure factor are determined as a function of the interaction strength and of the OL intensity. In the weak OL limit, Yang's theory for the energy of a homogeneous Fermi gas is recovered. In the opposite limit (deep OL), we analyze the convergence to the Lieb-Wu theory for the Hubbard model, comparing two approaches to map the continuous-space to the discrete-lattice model: the first is based on (noninteracting) Wannier functions, the second effectively takes into account strong-interaction effects within a parabolic approximation of the OL wells. We find that strong antiferromagnetic correlations emerge in deep OLs, and also in very shallow OLs if the interaction strength approaches the TonksGirardeau limit. In deep OLs we find quantitative agreement with density matrix renormalization group calculations for the Hubbard model. The spatial decay of the antiferromagnetic correlations is consistent with quasi long-range order even in shallow OLs, in agreement with previous theories for the half-filled Hubbard model.Making unbiased predictions for the properties of strongly correlated Fermi systems is one of the major challenges in quantum physics research. One dimensional systems play a central role in this context since, on the one hand, correlations effects are more pronounced in low dimensions and, on the other hand, exact results have been derived in a few relevant cases [1]. Two such cases are the homogeneous Fermi gas, whose exact ground-state energy was first determined by Yang [2] via the Bethe Anstatz technique, and the single-band Hubbard model, whose solution was provided by Lieb and Wu [3]. These two paradigmatic models describe two opposite limits of realistic physical systems, which in general are neither perfectly homogeneous nor devoid of interband couplings. In the absence of exact analytical theories for the more realistic intermediate regime, developing unbiased computational techniques is of outmost importance. The experiments performed with ultracold atoms trapped in optical lattices (OLs) have emerged as the ideal playground to investigate quantum many-body phenomena in periodic potentials [4]. The intensity of the external periodic field can be easily varied by tuning a laser power, and also the interaction strength can by tuned exploiting Feshbach resonances [5]. This has recently allowed the remarkable observation of antiferromagnetic correlations in a controlled experimental setup, both in two and in one dimension [6][7][8][9][10][11][12]. The bulk of early research activity on OL systems focussed on deep OLs and weak interactions, where single-band tight-binding models are adequate [13]. Away from this regime multi-band processes come into play, and the effect of the independent tuning of the OL intensity and the in...

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Mobility edges in bichromatic optical lattices

Cited by 145 publications

References 23 publications

Ultracold bosons with short-range interaction in regular optical lattices

Ultracold bosons with short-range interaction in regular optical lattices

Effects of interaction on the diffusion of atomic matter waves in one-dimensional quasiperiodic potentials

One-dimensional repulsive Fermi gas in a tunable periodic potential

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