Tunneling of a few strongly repulsive hard-sphere bosons in an optical lattice with tight external harmonic confinement: A quantum Monte Carlo investigation in continuous space

Sakhel, Asaad R.; Dubois, Jonathan; Sakhel, Roger R.

doi:10.1103/physreva.81.043603

Cited by 2 publications

(23 citation statements)

References 52 publications

(172 reference statements)

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“…The discrete BHM is derived from a continuous space model that, due to its complexity, has only been addressed recently [13][14][15][16][17][18]. In this Rapid Communication, we use the exact diffusion quantum Monte Carlo method [13,15,[19][20][21] and investigate one-dimensional Bose gas in optical lattices using a continuous Hamiltonian in real space.…”

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confidence: 99%

One-dimensional Bose gas in optical lattices of arbitrary strength

et al. 2016

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One-dimensional Bose gas with contact interaction in optical lattices at zero temperature is investigated by means of the exact diffusion Monte Carlo algorithm. The results obtained from the fundamental continuous model are compared with those obtained from the lattice (discrete) Bose-Hubbard model, using exact diagonalization, and from the quantum sine-Gordon model. We map out the complete phase diagram of the continuous model and determine the regions of applicability of the Bose-Hubbard model. Various physical quantities characterizing the systems are calculated, and it is demonstrated that the sine-Gordon model used for shallow lattices is inaccurate. DOI: 10.1103/PhysRevA.93.021605 The Bose-Hubbard model (BHM) was introduced in 1963 [1,2]. While the original motivation was to describe a crystalline solid, for which the model failed, the BHM became one of the fundamental quantum many-body problems. It has found clear-cut realization with ultracold atoms in deep optical lattices. This led to the seminal observation [3] of the superfluidMott-insulator quantum phase transition [4] following the proposal of Ref. [5]. In many aspects the experiments surpass the theory as shallow optical lattices can be easily realized, while an exact quantum many-body description of such systems is lacking. Even the case of deep optical lattices is controversial, as the scattered discussions demonstrate [6][7][8][9][10][11], indicating the necessity to go beyond the standard BHM (for a review, see Ref. [12]). Nevertheless, the BHM is commonly used for lattice systems in different dimensions and it frequently works very well. Still, there arise natural and important questions that have motivated the present work: When can it be used with confidence? What is the regime of validity of the BHM?The discrete BHM is derived from a continuous space model that, due to its complexity, has only been addressed recently [13][14][15][16][17][18]. In this Rapid Communication, we use the exact diffusion quantum Monte Carlo method [13,15,[19][20][21] and investigate one-dimensional Bose gas in optical lattices using a continuous Hamiltonian in real space. We compare the results with those obtained from the BHM and determine its regions of validity. Furthermore, a whole new generation of clean experiments on one-dimensional Bose gases loaded in optical lattices [22,23] have appeared, while the comparison of theory with experiment is not perfect [24,25]. We also analyze the sine-Gordon (SG) model, commonly used for shallow lattices [9,26,27], and show that it cannot be straightforwardly used to predict the position of the phase transition and the value of the gap [24]. We calculate the static structure factor, the one-body density matrix, the energy gap, and the Luttinger parameter and its dependence on the interaction and lattice strengths. Finally, we compare our results with the experiments of Ref.[24]-surprisingly, our theory, which is in principle superior to all approximate ones, does not always provide a better description.The first quant...

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One-dimensional Bose gas in optical lattices of arbitrary strength

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“…The variational path integral Monte Carlo (VPI) method [42,43] was used to evaluate the SFF of the systems treated in Ref. [39]. We used quantum variational Monte Carlo (VMC) to compute the spatial configurations of the particles in the current systems from which the OBDMs are obtained.…”

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“…For further details refer to Ref. [39]. The interparticle interactions are given by the hard sphere (HS) potential…”

Section: A Hamiltonianmentioning

confidence: 99%

“…(4) above, and β, γ, and σ of Eq. (7) below] as outlined previously [39]. By using the Wannier-like function defined by…”

Section: A Hamiltonianmentioning

confidence: 99%

“…The current paper comes as a continuation to the investigation of the properties of HC bosons in a CHOCL by Sakhel et al [39], in continuous space and for a fewbody system. This is in an attempt to provide further manifestation of the condensate properties inside an OL.…”

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Global and local condensate and superfluid fractions of a few hard core bosons in a combined harmonic optical cubic lattice in continuous space

Sakhel

2012

Eur. Phys. J. D

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We explore the global and local condensate and superfluid (SF) fractions in a system of a few hard core (HC) bosons (N = 8 and N = 40) trapped inside a combined harmonic optical cubic lattice (CHOCL) at T = 0 K. The condensate fraction (CF) is computed for individual lattice wells by separating the one-body density matrix (OBDM) of the whole system into components at the various lattice sites. Then each "lattice-site" component is diagonalized to find its eigenvalues. The eigenvalues are obtained by a method presented earlier [Dubois and Glyde, Phys. Rev. A 63, 023602 (2001)]. The effects of interference between the condensates in the lattice wells on the CF in one well is also investigated. The SF fraction (SFF) is calculated for N = 40 by using the diffusion formula of Pollock and Ceperley [Pollock and Ceperley, Phys. Rev. B 36, 8343 (1987)]. Our chief result is an opposing behavior of the global CF and SFF with increasing lattice wave vector k. In addition, the CF in a lattice well is enhanced by the interference with its neighbor wells beyond the result when the interference is neglected. The global SF is depleted with a rise of the repulsion between the bosons, yet at very strong interaction superfluidity is still present. The global CF remains almost constant with increasing HC repulsion. A reduction in the lattice dimension, i.e. an increase in the lattice wave vector, increases the local CF in each lattice well, but reduces the corresponding local SFF. At large HC repulsion, a coexisting SF-(vacuum)MI phase is established.

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Tunneling of a few strongly repulsive hard-sphere bosons in an optical lattice with tight external harmonic confinement: A quantum Monte Carlo investigation in continuous space

Cited by 2 publications

References 52 publications

One-dimensional Bose gas in optical lattices of arbitrary strength

One-dimensional Bose gas in optical lattices of arbitrary strength

Global and local condensate and superfluid fractions of a few hard core bosons in a combined harmonic optical cubic lattice in continuous space

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