Ultracold bosons with short-range interaction in regular optical lattices

We study the superfluid response, the energetic and structural properties of a one-dimensional ultracold Bose gas in an optical lattice of arbitrary strength. We use the Bose-Fermi mapping in the limit of infinitely large repulsive interaction and the diffusion Monte Carlo method in the case of finite interaction. For slightly incommensurate fillings we find a superfluid behavior which is discussed in terms of vacancies and interstitials. It is shown that both the excitation spectrum and static structure factor are different for the cases of microscopic and macroscopic fractions of defects. This system provides a extremely well-controlled model for studying defect-induced superfluidity.

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“…The superfluid fraction N s /N of the Tonks-Girardeau gas in deep optical lattices for N ≤ L can be calculated analytically and is given by [47] …”

Section: Superfluid Fractionmentioning

confidence: 99%

Optical lattices as a tool to study defect-induced superfluidity

et al. 2017

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“…This formula accounts to leading-order for the splitting of the harmonic-oscillator energy-levels due to tunneling [38,39]. The comparison of Fig.…”

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confidence: 99%

“…Specifically, we compute via the DMRG method the spin-spin correlation function g(r 1 , r 2 ) = Ŝ z r1Ŝ z r2 , where the spin density operator isŜ z r =n r,↑ −n r,↓ [41]. The Hubbard model results can be compared with the continuous-space magnetic structure factor using the following transformation (valid in the tight-binding limit) [38]:…”

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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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“…On the one hand, bosonic ultracold atoms in optical lattices can approximately be described by the Bose-Hubbard Hamiltonian [5,[7][8][9]. The two-species Bose-Hubbard Hamiltonian is a special case of the general lattice Hamiltonian (1), describing the tunneling J and on-site repulsion U of bosons with no spin quantum number (i.e., index s omitted),Ĥ…”

Section: Bose-hubbard Modelmentioning

confidence: 99%

Dicke superradiance as nondestructive probe for the state of atoms in optical lattices

Brinke

Schützhold

2016

Eur. Phys. J. D

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Abstract. We present a proposal for a probing scheme utilizing Dicke superradiance to obtain information about ultracold atoms in optical lattices. A probe photon is absorbed collectively by an ensemble of lattice atoms generating a Dicke state. The lattice dynamics (e.g., tunneling) affects the coherence properties of that Dicke state and thus alters the superradiant emission characteristics -which in turn provides insight into the lattice (dynamics). Comparing the Bose-Hubbard and the Fermi-Hubbard model, we find similar superradiance in the strongly interacting Mott insulator regime, but crucial differences in the weakly interacting (superfluid or metallic) phase. Furthermore, we study the possibility to detect whether a quantum phase transition between the two regimes can be considered adiabatic or a quantum quench.

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Ultracold bosons with short-range interaction in regular optical lattices

Cited by 112 publications

References 487 publications

Optical lattices as a tool to study defect-induced superfluidity

Optical lattices as a tool to study defect-induced superfluidity

One-dimensional repulsive Fermi gas in a tunable periodic potential

Dicke superradiance as nondestructive probe for the state of atoms in optical lattices

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