Matter-wave propagation in optical lattices: geometrical and flat-band effects

Metcalf, Mekena; Chern, Gia-Wei; Ventra, Massimiliano Di; Chien, Chih-Chun

doi:10.1088/0953-4075/49/7/075301

Cited by 15 publications

(10 citation statements)

References 54 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Effects of the second-neighbor hopping on nonlinear excitations [21,26,27], Bloch oscillations [28][29][30], wave localization [31], or the Mott insulator transition [32] have been investigated. Recently, several studies have explicitly addressed ultracold atoms in zigzag lattice geometries, both with interactions [33,34] and without [35]. Here, the zigzag geometry could be obtained experimentally by singling out a strip from an extended two-dimensional triangular optical lattice [36], or using recently demonstrated techniques for designing essentially arbitrary in-plane optical potentials [37,38].…”

Section: Introductionmentioning

confidence: 99%

Sub- and supercritical defect scattering in Schrödinger chains with higher-order hopping

Stockhofe

Schmelcher

2015

Phys. Rev. A

View full text Add to dashboard Cite

We theoretically analyze a discrete Schrödinger chain with hopping to the first and second neighbors, as can be realized with zigzag arrangements of optical waveguides or lattice sites for cold atoms. Already at moderate values, the second-neighbor hopping has a strong impact on the band structure, leading to the emergence of a new extremum located inside the band, accompanied by a van Hove singularity in the density of states. The energy band is then divided into a subcritical regime with the usual unique correspondence between wave number and energy of the travelling waves, and a supercritical regime, in which waves of different wave number are degenerate in energy. We study the consequences of these features in a scattering setup, introducing a defect that locally breaks the translational invariance. The notion of a local probability current is generalized beyond the nearest-neighbor approximation and bound states with energies outside the band are discussed. At subcritical energies inside the band, an evanescent mode coexists with the travelling plane wave, giving rise to resonance phenomena in scattering. At weak coupling to the defect, we identify a prototypical Fano-Feshbach resonance of tunable shape and provide analytical expressions for its profile parameters. At supercritical energies, we observe coupling of the degenerate travelling waves, leading to an intricate wave packet fragmentation dynamics. The corresponding branching ratios are analyzed.

show abstract

Section: Introductionmentioning

confidence: 99%

Sub- and supercritical defect scattering in Schrödinger chains with higher-order hopping

Stockhofe

Schmelcher

2015

Phys. Rev. A

View full text Add to dashboard Cite

show abstract

“…Different density distributions following different ramping times serve as direct evidence for memory effects, which are readily observable in fermionic systems at low temperatures and bosonic systems at intermediate temperatures. Since flat-bands can be found in a variety of lattice geometries, including saw-tooth 62 , cross stitch 63,64 , photonic rhombic lattice 65 , and the recently realized optical or photonic Lieb lattice [66][67][68] , geometry-induced memory effects may also be studied in those systems. On the other hand, photon-induced memory effects have been claimed in solid-state materials exhibiting structural transitions 69,70 , and the tunability of optical-lattice geometry can FIG.…”

Section: Discussionmentioning

confidence: 99%

Geometry-Induced Memory Effects in Isolated Quantum Systems: Cold-Atom Applications

Lai¹,

Chien²

2016

Phys. Rev. Applied

Self Cite

View full text Add to dashboard Cite

Memory effects can lead to history-dependent behavior of a system, and they are ubiquitous in our daily life and have broad applications. Here we explore possibilities of generating memory effects in simple isolated quantum systems. By utilizing geometrical effects from a class of lattices supporting flat-bands consisting of localized states, memory effects could be observed in ultracold atoms in optical lattices. As the optical lattice continuously transforms from a triangular lattice into a kagome lattice with a flat band, history-dependent density distributions manifest quantum memory effects even in noninteracting systems, including fermionic as well as bosonic systems in the proper ranges of temperatures. Rapid growth in ultracold technology predicts a bright future for quantum memory-effect systems, and here two prototypical applications of geometry-induced quantum memory effects are proposed: A cold-atom based accelerometer using an atomic differentiator to record the mechanical change rate of a coupled probe and an atomic quantum memory cell for storing information with write-in and read-out schemes.

show abstract

“…The zig-zag structure model has many applications and simulations in classical theory was formulated in [19]. The effects of the speed of matterwave propagation as a function of the lattice geometry was investigated in [20]. Indeed the zig-zag structure with the first-and second-neighbor interactions which may be referred to, as valence atoms lattice, sophisticate essentially the theory.…”

Section: Introductionmentioning

confidence: 99%

On continuum model analog to zig-zag optical lattice in quantum optics

Tantawy

Abdel‐Gawad

2021

Appl. Phys. B

View full text Add to dashboard Cite

A discrete model governing a system of cold bosonic atoms in zig-zag optical lattices in quantum optics was proposed in the literature. In an analog to this model, a continuum model is, here constructed. The resulting equation is a nonlinear Schrodinger equation NLSE with drift force and linear growth. Exact solutions of this equation are obtained. To this issue, a new transformation that allows to inspect the optical lattice due to soliton-periodic wave collision is introduced. Here, the colliding dynamics are inspected. A class of polynomial and rational solutions of the model equation constructed are obtained by using the unified and generalized unified methods. The solutions found reveal the propagation of local zigzagshaped pulses in optical lattices. Mixed smooth-sharp (shock-like) optical pulses are also observed. This leads to the issue that the collision is locally elastic (or inelastic). Furthermore, self-modulation zigzag-shaped pulses with compression, are remarked. We mention that the zigzag-shaped pulses, in an optical lattice, was not found in the literature. Thus, the results found in this work are original. It is found that the polarization of zig-zag optical lattice is self-focusing.

show abstract

Matter-wave propagation in optical lattices: geometrical and flat-band effects

Cited by 15 publications

References 54 publications

Sub- and supercritical defect scattering in Schrödinger chains with higher-order hopping

Sub- and supercritical defect scattering in Schrödinger chains with higher-order hopping

Geometry-Induced Memory Effects in Isolated Quantum Systems: Cold-Atom Applications

On continuum model analog to zig-zag optical lattice in quantum optics

Contact Info

Product

Resources

About