Tunneling couplings in discrete lattices, single-particle band structure, and eigenstates of interacting atom pairs

Piil, Rune; Mølmer, Klaus

doi:10.1103/physreva.76.023607

Cited by 45 publications

(85 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Research on two-particle bound states includes experimental realizations [49] and theoretical investigations [35,[50][51][52][53][54][55]. The creation of the two-particle NOON-state…”

Section: Two-particle Solitons: Interference Patterns For High-anmentioning

confidence: 99%

Bright-soliton quantum superpositions: Signatures of high- and low-fidelity states

Gertjerenken

2013

Phys. Rev. A

View full text Add to dashboard Cite

Scattering quantum bright solitons off barriers has been predicted to lead to nonlocal quantum superpositions, in particular the NOON-state. The focus of this paper lies on signatures of both highand low-fidelity quantum superposition states. We numerically demonstrate that a one-dimensional geometry with the barrier potential situated in the middle of an additional -experimentally typical -harmonic confinement gives rise to particularly well-observable signatures. In the elastic scattering regime we investigate signatures of NOON-states on the N -particle level within an effective potential approach. We show that removing the barrier potential and subsequently recombining both parts of the quantum superposition leads to a high-contrast interference pattern in the center-of-mass coordinate for narrow and broad potential barriers. We demonstrate that the presented signatures can be used to clearly distinguish quantum superpositions states from statistical mixtures and are sufficiently robust against experimentally relevant excitations of the center-of-mass wave function to higher lying oscillator states. For two-particle solitons we extend these considerations to lowfidelity superposition states: even for strong deviations from the two-particle NOON-state we find interference patterns with high contrast.

show abstract

“…Research on two-particle bound states includes experimental realizations [49] and theoretical investigations [35,[50][51][52][53][54][55]. The creation of the two-particle NOON-state…”

Section: Two-particle Solitons: Interference Patterns For High-anmentioning

confidence: 99%

Bright-soliton quantum superpositions: Signatures of high- and low-fidelity states

Gertjerenken

2013

Phys. Rev. A

View full text Add to dashboard Cite

show abstract

“…The binding energies E B K are defined with respect to the edges of the scattering band (9). Note that in the case of repulsive interaction, U > 0 (α K < 0), the sign of the wave function (15) alternates between the neighboring sites j r .…”

Section: B Bound Statesmentioning

confidence: 99%

“…is the collective hopping rate [11,15], which in the case of identical particles, J A = J B = J, reduces to the standard [8,9,12,14] expression J K = 2J cos(K/2). Equation (8) admits two kinds of solutions, corresponding to the scattering states of asymptotically free particles and to the two-particle bound, or dimer, states.…”

Section: Two Particles In a Latticementioning

confidence: 99%

“…[8]. This seminal achievement has led to several theoretical studies of the properties of interaction-bound atom pairs-"dimers"-in periodic potentials [9][10][11][12][13][14][15][16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

“…In a one-dimensional (1D) tight-binding lattice, two bosons can form a bound dimer [8][9][10][11][12][13] for any finite strength of the on-site interaction, be it an attraction or a repulsion. Next level of complexity corresponds to three bosons, which obviously can form a strongly-bound "trimer" with all three particles occupying the same lattice site.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Exotic Few-Body Bound States in a Lattice

Petrosyan

Valiente

2010

Modern Optics and Photonics

View full text Add to dashboard Cite

Strongly-interacting ultra-cold atoms in tight-binding optical lattice potentials provide an ideal platform to realize the fundamental Hubbard model. Here, after outlining the elementary single particle solution, we review and expand our recent work on complete characterization of the bound and scattering states of two and three bosonic atoms in a one-dimensional optical lattice. In the case of two atoms, there is a family of interaction-bound "dimer" states of co-localized particles that exists invariantly for either attractive or repulsive on-site interaction, with the energy below or above the two-particle scattering continuum, respectively. Adding then the third particle-"monomer"-we find that, apart from the simple strongly-bound "trimer" corresponding to all three particles occupying the same lattice site, there are two peculiar families of weakly-bound trimers with energies below and above the monomer-dimer scattering continuum, the corresponding binding mechanism being an effective particle exchange interaction.

show abstract

Ultracold bosons with short-range interaction in regular optical lattices

2016

View full text Add to dashboard Cite

During the last decade, many exciting phenomena have been experimentally observed and theoretically predicted for ultracold atoms in optical lattices. This paper reviews these rapid developments concentrating mainly on the theory. Different types of the bosonic systems in homogeneous lattices of different dimensions as well as in the presence of harmonic traps are considered. An overview of the theoretical methods used for these investigations as well as of the obtained results is given. Available experimental techniques are presented and discussed in connection with theoretical considerations. Eigenstates of the interacting bosons in homogeneous lattices and in the presence of harmonic confinement are analyzed. Their knowledge is essential for understanding of quantum phase transitions at zero and finite temperature.

show abstract

Tunneling couplings in discrete lattices, single-particle band structure, and eigenstates of interacting atom pairs

Cited by 45 publications

References 23 publications

Bright-soliton quantum superpositions: Signatures of high- and low-fidelity states

Bright-soliton quantum superpositions: Signatures of high- and low-fidelity states

Exotic Few-Body Bound States in a Lattice

Ultracold bosons with short-range interaction in regular optical lattices

Contact Info

Product

Resources

About