Bosons in a two-dimensional bichromatic quasiperiodic potential: Analysis of the disorder in the Bose-Hubbard parameters and phase diagrams

Niederle, Astrid Elisa; Rieger, Heiko

doi:10.1103/physreva.91.043632

Cited by 12 publications

(17 citation statements)

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“…In the incommensurate case, for λ = λ 0 (1 − ) with 1 our LMF calculation combined with a SF cluster analysis [29,35] reveals a much richer phase diagram than predicted by conventional mean-field theory [18]: In addition to MI, SF z , and SF phases, we could identify also an isotropic and striped superglass (SG) phase, which is characterised by an aperiodic (glassy) density modulation and isotropic or striped superfluid (off-diagonal) order. The striped SG regions are characterized by superfluid stripes in z direction, implying off-diagonal order (i.e., phase coherence) along these stripes.…”

Section: Discussionmentioning

confidence: 99%

“…We analyze the phase diagram emerging from the Hamiltonian (1) using local mean field (LMF) theory [34] combined with a superfluid cluster analysis [29,35]. Within this framework, we define the so-called local SF parameter by equation ψ i = Ø[i]a , which has to be determined self-consistently, being the expectation value of operator Ø[i]a taken over the ground state of the LMF Hamiltonian ĤMF…”

Section: B Local Mean Field With Superfluid Cluster Analysismentioning

confidence: 99%

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Ultracold bosons with cavity-mediated long-range interactions: A local mean-field analysis of the phase diagram

2016

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Ultracold bosonic atoms in optical lattices self-organize into a variety of structural and quantum phases when placed into a single-mode cavity and pumped by a laser. Cavity optomechanical effects induce an atom density modulation at the cavity-mode wave length that competes with the optical lattice arrangement. Simultaneously short-range interactions via particle hopping promote superfluid order, such that a variety of structural and quantum coherent phases can occur. We analyze the emerging phase diagram in two dimensions by means of an extended Bose-Hubbard model using a local mean field approach combined with a superfluid cluster analysis. For commensurate ratios of the cavity and external lattice wave lengths the Mott insulator-superfluid transition is modified by the appearance of charge density wave and supersolid phases, at which the atomic density supports the buildup of a cavity field. For incommensurate ratios, the optomechanical forces induce the formation of Bose-glass and superglass phases, namely non-superfluid and superfluid phases, respectively, displaying quasi-periodic density modulations, which in addition can exhibit structural and superfluid stripe formation. The onset of such structures is constrained by the onsite interaction and is favourable at fractional densities. Experimental observables are identified and discussed.

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Section: Discussionmentioning

confidence: 99%

Section: B Local Mean Field With Superfluid Cluster Analysismentioning

confidence: 99%

Ultracold bosons with cavity-mediated long-range interactions: A local mean-field analysis of the phase diagram

2016

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“…Link configuration of distinct vertexes in Penrose lattice. Listed are index α determined in the present work, the total number of paths using k links, M k (k = 1, 2, 3), the number of vertexes having l links, to which one can access using k links, m 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 0 0 0 m (5) 1 3 3 3 1 1 1 2 2 2 2 2 2 2 2 0 0 0 1 1 1 1 0 0 0 5 3 1 m (6) 1 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 m (7) 1 0 0 0 0 1 1 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 M2 15 15 15 15 16 16 16 17 17 17 17 16 16 16 15 15 15 17 17 17 17 18 19 21 25 24 23 m (3) 2 11 10 9 9 12 12 11 15 14 14 13 6 5 4 0 0 0 0 0 0 0 3 5 10 20 10 2 m note that this self-consistent procedure gives moderately accurate results as compared with quantum Monte Carlo simulations and gives equivalent results with variational Gutzwiller method [44][45][46][47][48][49][50][51][52].…”

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confidence: 91%

Mean-field study of the Bose-Hubbard model in Penrose lattice

Ghadimi,

Sugimoto,

Tohyama

2020

Preprint

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We examine the Bose-Hubbard model in the Penrose lattice based on inhomogeneous mean-field theory. Since averaged coordination number in the Penrose lattice is four, mean-field phase diagram consisting of the Mott insulator (MI) and superfluid (SF) phase is similar to that of the square lattice. However, the spatial distribution of Bose condensate in the SF phase is significantly different from uniform distribution in the square lattice. We find a fractal structure in its distribution near the MI-SF phase boundary. The emergence of the fractal structure is a consequence of cooperative effect between quasiperiodicity in the Penrose lattice and criticality at the phase transition.

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“…This behavior is analogous to the potential generated by the superposition of two incommensurate optical lattices [85] which has been used for generating controllable disordered potential, allowing the observation of Anderson localization and new quantum phases (Bose glass) in ultracold gases [86,87]. Here, we move a step further and we create synthetic random interactions between the atoms, generalizing the Anderson model where disorder affects only the local potential and/or the tunneling amplitude [88,89].…”

Section: A One Probe and One Cavitymentioning

confidence: 99%

Quantum simulators based on the global collective light-matter interaction

Caballero-Benítez¹,

Mazzucchi²,

Mekhov³

2016

Phys. Rev. A

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We show that coupling ultracold atoms in optical lattices to quantized modes of an optical cavity leads to quantum phases of matter, which at the same time posses properties of systems with both short-and long-range interactions. This opens perspectives for novel quantum simulators of finiterange interacting systems, even though the light-induced interaction is global (i.e. infinitely long range). This is achieved by spatial structuring of the global light-matter coupling at a microscopic scale. Such simulators can directly benefit from the collective enhancement of the global lightmatter interaction and constitute an alternative to standard approaches using Rydberg atoms or polar molecules. The system in the steady state of light induces effective many-body interactions that change the landscape of the phase diagram of the typical Bose-Hubbard model. Therefore, the system can support non-trivial superfluid states, bosonic dimer, trimers, etc. states and supersolid phases depending on the choice of the wavelength and pattern of the light with respect to the classical optical lattice potential. We find that by carefully choosing the system parameters one can investigate diverse strongly correlated physics with the same setup, i.e., modifying the geometry of light beams. In particular, we present the interplay between the density and bond (or matter-wave coherence) interactions. We show how to tune the effective interaction length in such a hybrid system with both short-range and global interactions. arXiv:1602.08424v3 [cond-mat.quant-gas] 1 Jul 2016 † câc and the lightatom interaction is [25]: H ab = c,p g * pâcF † pc + g pâ † cFpc(2) withF pc =D pc +B pc .D pc = j J pc jjn j is the density coupling of light to the atoms,B pc = i,j J pc ij (b † ibj + h.c.) is due to the inter-site densities reflecting matterfield interference, or bonds [26,40]. The sums go over

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Bosons in a two-dimensional bichromatic quasiperiodic potential: Analysis of the disorder in the Bose-Hubbard parameters and phase diagrams

Cited by 12 publications

References 50 publications

Ultracold bosons with cavity-mediated long-range interactions: A local mean-field analysis of the phase diagram

Ultracold bosons with cavity-mediated long-range interactions: A local mean-field analysis of the phase diagram

Mean-field study of the Bose-Hubbard model in Penrose lattice

Quantum simulators based on the global collective light-matter interaction

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