Wannier functions for one-dimensional<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>s</mml:mi><mml:mo>−</mml:mo><mml:mi>p</mml:mi></mml:math>optical superlattices

Ganczarek, Wojciech; Modugno, Michèle; Pettini, Giulio; Zakrzewski, Jakub

doi:10.1103/physreva.90.033621

Cited by 6 publications

(12 citation statements)

References 49 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…They present a monotonic decrease for increasing , as a consequence of the deepening of the potential wells. Notice that the degeneracy between J s and J p takes place below the resonance, at = 1.5 [45]. This figure also shows the behavior of the tunneling coefficients J s and J p obtained from the single band approach (thin lines), for comparison.…”

Section: "S-p" Resonancementioning

confidence: 81%

“…This can be realized e.g. with θ 0 = 0 and V 0 = 32E R , for which the s − p resonance occurs at = 2 [45]. This configuration is also relevant for the realization of an effective Dirac dynamics [44,61,62], that will be considered in the following section.…”

Section: "S-p" Resonancementioning

confidence: 92%

“…Another interesting situation emerges when the first two excited bands become resonant, a situation that occurs when the p-like orbital in the deepest well and the s-like orbital in the other one are almost degenerate [45,60]. This can be realized e.g.…”

Section: "S-p" Resonancementioning

confidence: 99%

“…It is also interesting to note that, at resonance, almost optimally localized states can be built from a simple analytic approach that captures the essential features of the system and leads to simple analytic expressions for the tunneling coefficients, see Ref. [45]. Tunneling coefficients.…”

Section: "S-p" Resonancementioning

confidence: 99%

“…Here we shall review these concepts, following the lines of Refs. [41][42][43][44][45][46][47]. First, in sect.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Tight-binding models for ultracold atoms in optical lattices: general formulation and applications

Modugno

Ibañez-Azpiroz

Pettini

2016

Sci. China Phys. Mech. Astron.

Self Cite

View full text Add to dashboard Cite

Tight-binding models for ultracold atoms in optical lattices can be properly defined by using the concept of maximally localized Wannier functions for composite bands. The basic principles of this approach are reviewed here, along with different applications to lattice potentials with two minima per unit cell, in one and two spatial dimensions. Two independent methods for computing the tight-binding coefficients -one ab initio, based on the maximally localized Wannier functions, the other through analytic expressions in terms of the energy spectrum -are considered. In the one dimensional case, where the tight-binding coefficients can be obtained by designing a specific gauge transformation, we consider both the case of quasi resonance between the two lowest bands, and that between s and p orbitals. In the latter case, the role of the Wannier functions in the derivation of an effective Dirac equation is also reviewed. Then, we consider the case of a two dimensional honeycomb potential, with particular emphasis on the Haldane model, its phase diagram, and the breakdown of the Peierls substitution. Tunable honeycomb lattices, characterized by movable Dirac points, are also considered. Finally, general considerations for dealing with the interaction terms are presented.

show abstract

Section: "S-p" Resonancementioning

confidence: 81%

Section: "S-p" Resonancementioning

confidence: 92%

Section: "S-p" Resonancementioning

confidence: 99%

Section: "S-p" Resonancementioning

confidence: 99%

“…Here we shall review these concepts, following the lines of Refs. [41][42][43][44][45][46][47]. First, in sect.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Tight-binding models for ultracold atoms in optical lattices: general formulation and applications

Modugno

Ibañez-Azpiroz

Pettini

2016

Sci. China Phys. Mech. Astron.

Self Cite

View full text Add to dashboard Cite

show abstract

Entanglement in Spatial Adiabatic Processes for Interacting Atoms

2018

View full text Add to dashboard Cite

We study the dynamics of the non-classical correlations for few atom systems in the presence of strong interactions for a number of recently developed adiabatic state preparation protocols. We show that entanglement can be created in a controlled fashion and can be attributed to two distinct sources, the atom-atom interaction and the distribution of atoms among different traps.Keywords Entanglement · Spatial adiabatic passage 1 IntroductionCorrelations between quantum particles are responsible for many properties of advanced solid state systems which cannot be derived from single particle behaviour [1]. Recently these correlations were also recognised as a resource in quantum information and metrology, where they have to be deliberately created and engineered [2]. However, quantum correlations are known to be fragile, and preparing entangled states with high fidelity is often a difficult task [3,4].The Hilbert space of interacting few or many particle systems becomes more complex and crowded, and preparing quantum states in such systems has an additional degree of complexity. However, over the last two decades, systems of ultracold atoms have been developed where control over almost all internal and external degrees of freedom is possible. By today, ground state systems of a handful of particles can be deterministically prepared in laboratories [5], and dynamical control of their center-of-mass degree of freedom is possible using time-dependent electromagnetic fields [6] . The interaction between these ultracold atoms is usually short-range and for many species so-called Feshbach resonances exist, that can be used to adjust the interaction strength [7].One possible strategy for controlling interacting few atom systems is to generalise know single particle protocols. Out of these, one class that allows for high fidelities are adiabatic techniques, where the evolution follows one specific eigenstate at all times. For the control of the centre-of-mass of single particles, these are know as spatial adiabatic passage

show abstract

Physics of higher orbital bands in optical lattices: a review

Li¹,

Liu²

2016

Rep. Prog. Phys.

130

102

View full text Add to dashboard Cite

The orbital degree of freedom plays a fundamental role in understanding the unconventional properties in solid state materials. Experimental progress in quantum atomic gases has demonstrated that high orbitals in optical lattices can be used to construct quantum emulators of exotic models beyond natural crystals, where novel many-body states such as complex Bose-Einstein condensates and topological semimetals emerge. A brief introduction of orbital degrees of freedom in optical lattices is given and a summary of exotic orbital models and resulting many-body phases is provided. Experimental consequences of the novel phases are also discussed.

show abstract

Wannier functions for one-dimensionals−poptical superlattices

Cited by 6 publications

References 49 publications

Tight-binding models for ultracold atoms in optical lattices: general formulation and applications

Tight-binding models for ultracold atoms in optical lattices: general formulation and applications

Entanglement in Spatial Adiabatic Processes for Interacting Atoms

Physics of higher orbital bands in optical lattices: a review

Contact Info

Product

Resources

About