Scattering and binding of different atomic species in a one-dimensional optical lattice

Piil, Rune; Nygaard, Nicolai; Mølmer, Klaus

doi:10.1103/physreva.78.033611

Cited by 20 publications

(27 citation statements)

References 10 publications

(18 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(4) is equivalent to the findings in [14,17]. At this point it is convenient to introduce an adimensional Hamiltonian by dividing it by the collective tunneling, which is equivalent to setting J (K) ≡ 1 (energies become dimensionless) in Eq.…”

Section: General Separation Of the Two-body Problemmentioning

confidence: 99%

See 1 more Smart Citation

Lattice two-body problem with arbitrary finite-range interactions

Valiente

2010

Phys. Rev. A

View full text Add to dashboard Cite

We study the exact solution of the two-body problem on a tight-binding one-dimensional lattice, with pairwise interaction potentials which have an arbitrary but finite range. We show how to obtain the full spectrum, the bound and scattering states, and the "low-energy" solutions by very efficient and easy-to-implement numerical means. All bound states are proven to be characterized by roots of a polynomial whose degree depends linearly on the range of the potential, and we discuss the connections between the number of bound states and the scattering lengths. "Low-energy" resonances can be located with great precision with the methods we introduce. Further generalizations to include more exotic interactions are also discussed.

show abstract

Section: General Separation Of the Two-body Problemmentioning

confidence: 99%

“…In another spectacular experiment [7], repulsively bound pairs of atoms have been produced, and their main properties have been measured. This experiment has stimulated renewed interest in the study of few-body effects in discrete lattices [8][9][10][11][12][13][14], which had been studied almost only by Mattis [15] about 20 years ago.…”

Section: Introductionmentioning

confidence: 99%

Lattice two-body problem with arbitrary finite-range interactions

Valiente

2010

Phys. Rev. A

View full text Add to dashboard Cite

show abstract

“…In fact, (35) is valid for both signs of D. For positive detuning and repulsive interaction, a bound state can form in the gap between the LL-and LU-bands. This is an example of a pair bound by repulsive forces in gapped spectra [86][87][88]. Figure 7(a) shows E bP (K = 0) as a function of D/G at fixed δ = 0.5G, and figure 7(b) demonstrates typical wave functions for D = 0.5G -the in-gap analogs of figure 6(b).…”

Section: Gap Statesmentioning

confidence: 99%

Cavity polaritons with Rydberg blockade and long-range interactions

Litinskaya

Tignone

Pupillo

2016

J. Phys. B: At. Mol. Opt. Phys.

View full text Add to dashboard Cite

We study interactions between polaritons, arising when photons strongly couple to collective excitations in an array of two-level atoms trapped in an optical lattice inside a cavity. We consider two types of interactions between atoms: Dipolar forces and atomic saturability, which ranges from hard-core repulsion to Rydberg blockade. We show that, in spite of the underlying repulsion in the subsystem of atomic excitations, saturability induces a broadband bunching of photons for twopolariton scattering states. We interpret this bunching as a result of interference, and trace it back to the mismatch of the quantization volumes for atomic excitations and photons. We examine also bound bipolaritonic states: These include states created by dipolar forces, as well as a gap bipolariton, which forms solely due to saturability effects in the atomic transition. Both types of bound states exhibit strong bunching in the photonic component. We discuss the dependence of bunching on experimentally relevant parameters.

show abstract

“…In the absence of the external field (F = 0), the energy spectrum for the two-particle AHM can be determined analytically (see, for instance, [13,14]). The energy spectrum is continuous and comprises two bands.…”

Section: Ac-driven Asymmetric Hubbard Model: Basic Model and Two-mentioning

confidence: 99%

Low-energy doublons in the ac-driven two-species Hubbard model

Longhi

Valle

2013

Phys. Rev. A

View full text Add to dashboard Cite

The hopping dynamics of two fermionic species with different effectivemasses in the one-dimensionalHubbard model driven by an external field are theoretically investigated. A multiple-time-scale asymptotic analysis of the driven asymmetric Hubbard model shows that a high-frequency bichromatic external field can sustain a low-energy particle bound state (a doublon) in which two fermions of different species occupy nearest-neighbor sites and cotunnel along the lattice. The predictions of the asymptotic analysis are confirmed by direct numerical simulations of the two-particle Hubbard Hamiltonian

show abstract

Scattering and binding of different atomic species in a one-dimensional optical lattice

Cited by 20 publications

References 10 publications

Lattice two-body problem with arbitrary finite-range interactions

Lattice two-body problem with arbitrary finite-range interactions

Cavity polaritons with Rydberg blockade and long-range interactions

Low-energy doublons in the ac-driven two-species Hubbard model

Contact Info

Product

Resources

About