Ultracold bosons in zig-zag optical lattices

Greschner, Sebastian; Santos, Luís; Vekua, T.

doi:10.1103/physreva.87.033609

Cited by 51 publications

(72 citation statements)

References 48 publications

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“…4. Explicit expressions of nonlocal parity [27] and string orders can be borrowed from the corresponding orders of S = 1 spin chain [28] For shallow lattices, as depicted in Fig. 1, a dimer state wins, consistent with weak-coupling bosonization analysis.…”

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confidence: 53%

Band-to-Mott-insulator transformations in four-component alkali-metal fermions at half-filling

2013

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Under the influence of an external magnetic field and spin-changing collisions, the band insulator state of one-dimensional s-wave repulsively interacting four-component fermions at half-filling transforms into Mott insulator states with a spontaneously doubled unit cell: a dimerized state for shallow lattices and a Néel state for deep lattices via an intermediate topological state. These Mott insulator phases could be of special interest for experiments as they can be reached starting from band insulator state and changing magnetic field adiabatically. [3,4]. At sufficiently low temperatures the MI phase should acquire a magnetic Néel (antiferromagnetic) ordering. Still it has not been resolved [5]; the main obstacle is the absence of efficient cooling methods in the presence of an optical lattice [6].By increasing the number of components above two, an interesting possibility of hosting exotic ground states like 2D spin liquids [7,8] or 1D topological states [9,10] emerges. A novel ingredient in multicomponent alkali-metal gases, different from the two-component case, is the presence of spin-changing collisions: two interacting atoms cannot only exchange their initial internal hyperfine states, but they can also change them to new values. The spin-changing collisions open a fascinating prospect to arrive at unconventional MI ground states of multicomponent Fermi gases starting from the band insulator (BI) state made of only two components having vanishing entropy per particle. For fermions due to the Pauli principle the minimal number of components required for BI to MI transformation is four.In this work we present the ground-state phases of fourcomponent alkali-metal fermions at half-filling obtained by nonperturbative analytical and numerical tools, particularly tailored for studying 1D systems. We identify various MI phases: Dimer and Néel states spontaneously break discrete lattice translational symmetry and are characterized by doubly degenerate ground state in thermodynamic limit and local order parameters; whereas singlet and a topological Haldane phase do not break any microscopic symmetry and are characterized by unique ground state and nonlocal parity and string orders, respectively. Even though these different MI phases are manifested below the ultralow temperatures, typical to the superexchange scale, the fact that one can start from the BI state and by adiabatically changing the magnetic field enter into these nontrivial states, makes the system of half-filled four-component alkali-metal fermions a particularly attractive candidate to resolve ground-state spin order in experiments on ultracold lattice gases. Note that the spin-changing collision processes, crucial for BI to MI transformations, are maximally pronounced at half-filling.Our main result, the ground-state phase diagram of four components of 40 K atoms, is presented in Fig. 1. Most importantly all states can be explored just by changing the lattice depth and strength of the external magnetic field without the need to modify the natura...

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confidence: 53%

Band-to-Mott-insulator transformations in four-component alkali-metal fermions at half-filling

2013

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“…Indeed in onedimensional (1D) systems, SPT phases are the only realizable class of topological quantum states, a prominent example being the so-called Haldane phase of odd-integer spin chains [33,34]. Generalizations of the Haldane phase have been theoretically studied in the context of ultracold gases [35][36][37][38][39][40].Real or synthetic ladder-like lattices have recently constituted the focus of major efforts [41][42][43] in the context of the realization of static gauge fields in ultra-cold atomic systems. We show below that although in 1D spin-1/2 U(1) QLMs are topologically trivial, when implemented in ladder-like lattices these models present an intriguing ground-state phase diagram, which interestingly includes an SPT phase that we characterize using a generalized topological order parameter and the entanglement spectrum.…”

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confidence: 99%

Hidden Order and Symmetry Protected Topological States in Quantum Link Ladders

2017

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We show that whereas spin-1/2 one-dimensional U(1) quantum-link models (QLMs) are topologically trivial, when implemented in ladder-like lattices these models may present an intriguing ground-state phase diagram, which includes a symmetry protected topological (SPT) phase that may be readily revealed by analyzing long-range string spin correlations along the ladder legs. We propose a simple scheme for the realization of spin-1/2 U(1) QLMs based on single-component fermions loaded in an optical lattice with s-and p-bands, showing that the SPT phase may be experimentally realized by adiabatic preparation.The realization of lattice gauge models using ultra cold gases has attracted a major theoretical attention in recent years [1][2][3][4]. Various ideas for creating dynamical gauge fields have been proposed [5][6][7][8][9][10][11][12][13][14][15][16][17]. Recently the Schwinger model has been simulated in ion chains [18]. Particular interest has been devoted to quantum-link models (QLMs) [19], which generalize lattice gauge theory [20] by realizing continuous gauge symmetries with discrete gauge variables (quantum links). QLMs are relevant in particle physics, and in particular QCD [21], and in condensed matter physics [22,23]. In U(1) QLMs, links are represented by quantum spins and fermions provide the matter field, making these QLMs particularly suitable for simulation with cold lattice gases.In this Letter we study the topological properties of spin-1/2 U(1) QLMs. Topological quantum systems have become one of the most active research areas during the past decades [24,25]. In particular the understanding of topological phases in strongly correlated quantum systems remains challenging. The study of symmetry protected topological (SPT) states has triggered a large progress in this field [26]. SPT phases have been classified by means of entanglement properties and group theoretical considerations [27][28][29][30][31][32]. Indeed in onedimensional (1D) systems, SPT phases are the only realizable class of topological quantum states, a prominent example being the so-called Haldane phase of odd-integer spin chains [33,34]. Generalizations of the Haldane phase have been theoretically studied in the context of ultracold gases [35][36][37][38][39][40].Real or synthetic ladder-like lattices have recently constituted the focus of major efforts [41][42][43] in the context of the realization of static gauge fields in ultra-cold atomic systems. We show below that although in 1D spin-1/2 U(1) QLMs are topologically trivial, when implemented in ladder-like lattices these models present an intriguing ground-state phase diagram, which interestingly includes an SPT phase that we characterize using a generalized topological order parameter and the entanglement spectrum. We show that the SPT phase may be revealed by analyzing string spin correlations along the ladder legs. Moreover, we propose a simple scheme for the realization of the QLM based on s-p lattices [44], showing that the SPT phase may be experimentally realized by adiab...

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“…The MI phase of a usual 1D Bose-Hubbard model is characterized by a finite hidden parity order due to bound particle-hole pairs that has been observed in experiments with single-site resolution [48]. A nonvanishing string order, but vanishing parity order, characterizes the Haldane insulator, predicted in polar lattice gases [50,51] and bosons in frustrated lattices [52]. The explicit expressions in the effective rung-state model may be borrowed from the corresponding orders of a spin S = 1 chain [51]: We define the rung-parity order O RPO ≡ lim |i−j |→∞ (−1) i<k<j δN k (with δN k =Ñ − N k ) and the rung-string order O RSO ≡ lim |i−j |→∞ δN i (−1) i<k<j δN k δN j .…”

Section: B Strong Rung-coupling Limitmentioning

confidence: 86%

Density-dependent synthetic magnetism for ultracold atoms in optical lattices

et al. 2015

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Raman-assisted hopping can allow for the creation of density-dependent synthetic magnetism for cold neutral gases in optical lattices. We show that the density-dependent fields lead to a nontrivial interplay between density modulations and chirality. This interplay results in a rich physics for atoms in two-leg ladders, characterized by a density-driven Meissner-superfluid to vortex-superfluid transition, and a nontrivial dependence of the density imbalance between the legs. Density-dependent fields also lead to intriguing physics in square lattices. In particular, it leads to a density-driven transition between a nonchiral and a chiral superfluid, both characterized by nontrivial charge density-wave amplitude. We finally show how the physics due to the density-dependent fields may be easily probed in experiments by monitoring the expansion of doublons and holes in a Mott insulator, which presents a remarkable dependence on quantum fluctuations.

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Ultracold bosons in zig-zag optical lattices

Cited by 51 publications

References 48 publications

Band-to-Mott-insulator transformations in four-component alkali-metal fermions at half-filling

Band-to-Mott-insulator transformations in four-component alkali-metal fermions at half-filling

Hidden Order and Symmetry Protected Topological States in Quantum Link Ladders

Density-dependent synthetic magnetism for ultracold atoms in optical lattices

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