Repulsively interacting particles in a periodic potential can form bound composite objects, whose dissociation is suppressed by a band gap. Nearly pure samples of such repulsively bound pairs of cold atoms---``dimers''---have recently been prepared by Winkler et al. [Nature (London) 441, 853 (2006)]. We here derive an effective Hamiltonian for a lattice loaded with dimers only and discuss its implications for the many-body dynamics of the system. We find that the dimer-dimer interaction includes strong on-site repulsion and nearest-neighbor attraction which always dominates over the dimer kinetic energy at low temperatures. The dimers then form incompressible, minimal-surface ``droplets'' of a quantum lattice liquid. For low lattice filling, the effective Hamiltonian can be mapped onto the spin- $1∕2$ $XXZ$ model with fixed total magnetization which exhibits a first-order phase transition from the droplet to a gas phase. This opens the door to studying first-order phase transitions using highly controllable ultracold atoms.Repulsively interacting particles in a periodic potential can form bound composite objects, whose dissociation is suppressed by a band gap. Nearly pure samples of such repulsively bound pairs of cold atoms---``dimers''---have recently been prepared by Winkler et al. [Nature (London) 441, 853 (2006)]. We here derive an effective Hamiltonian for a lattice loaded with dimers only and discuss its implications for the many-body dynamics of the system. We find that the dimer-dimer interaction includes strong on-site repulsion and nearest-neighbor attraction which always dominates over the dimer kinetic energy at low temperatures. The dimers then form incompressible, minimal-surface ``droplets'' of a quantum lattice liquid. For low lattice filling, the effective Hamiltonian can be mapped onto the spin-$1∕2$ $XXZ$ model with fixed total magnetization which exhibits a first-order phase transition from the droplet to a gas phase. This opens the door to studying first-order phase transitions using highly controllable ultracold atoms.

arXiv:cond-mat/0610198Physical Review ASep 12, 200790 citations

Repulsive bound-atom pairs in an optical lattice with two-body interaction of nearest neighbors

Y.-M. Wang, J.-Q. Liang

Repulsively interacting particles in a periodic potential can form bound composite objects with long lifetimes, as has been observed experimentally [Winkler et al., Nature (London) 441, 853 (2006)]. In this paper, a complete two-particle solution of one-dimensional periodical potential was derived in a strong interaction regime, where the on-site approximation of a two-body interaction in the Bose-Hubbard model (BHM) is extended to include the interaction of nearest neighbors, which results in atom-pair hopping. The energy spectrum of the bound pair is drastically reshaped due to the pair-hopping term, and complex eigenenergy corresponding to metastable states is also found that has not been discovered in the usual BHM. When the absolute value of a center-of-mass quasimomentum wave vector is greater than a critical value ( $|K|>{K}_{c}$ ), two bound-pair solutions are found. Furthermore, the spatial and momentum distributions of the bound pair displays a crossover from dark to bright soliton-like solutions in the extended BHM. Our results reduce to that of the usual BHM in the weak interaction case.Repulsively interacting particles in a periodic potential can form bound composite objects with long lifetimes, as has been observed experimentally [Winkler et al., Nature (London) 441, 853 (2006)]. In this paper, a complete two-particle solution of one-dimensional periodical potential was derived in a strong interaction regime, where the on-site approximation of a two-body interaction in the Bose-Hubbard model (BHM) is extended to include the interaction of nearest neighbors, which results in atom-pair hopping. The energy spectrum of the bound pair is drastically reshaped due to the pair-hopping term, and complex eigenenergy corresponding to metastable states is also found that has not been discovered in the usual BHM. When the absolute value of a center-of-mass quasimomentum wave vector is greater than a critical value ($|K|>{K}_{c}$), two bound-pair solutions are found. Furthermore, the spatial and momentum distributions of the bound pair displays a crossover from dark to bright soliton-like solutions in the extended BHM. Our results reduce to that of the usual BHM in the weak interaction case.

Physical Review AApr 15, 201028 citations

Universal Dimerized Quantum Droplets in a One-Dimensional Lattice

Ivan Morera, G. E. Astrakharchik, A. Polls +1 more

The ground-state properties of two-component bosonic mixtures in a one-dimensional optical lattice are studied both from few- and many-body perspectives. We rely directly on a microscopic Hamiltonian with attractive intercomponent and repulsive intracomponent interactions to demonstrate the formation of a quantum liquid. We reveal that its formation and stability can be interpreted in terms of finite-range interactions between dimers. We derive an effective model of composite bosons (dimers) which correctly captures both the few- and many-body properties and validate it against exact results obtained by the density matrix renormalization group method for the full Hamiltonian. The threshold for the formation of the liquid coincides with the appearance of a bound state in the dimer-dimer problem and possesses a universality in terms of the two-body parameters of the dimer-dimer interaction, namely, scattering length and effective range. For sufficiently strong effective dimer-dimer repulsion we observe fermionization of the dimers which form an effective Tonks-Girardeau state and identify conditions for the formation of a solitonic solution. Our predictions are relevant to experiments with dipolar atoms and two-component mixtures.The ground-state properties of two-component bosonic mixtures in a one-dimensional optical lattice are studied both from few- and many-body perspectives. We rely directly on a microscopic Hamiltonian with attractive intercomponent and repulsive intracomponent interactions to demonstrate the formation of a quantum liquid. We reveal that its formation and stability can be interpreted in terms of finite-range interactions between dimers. We derive an effective model of composite bosons (dimers) which correctly captures both the few- and many-body properties and validate it against exact results obtained by the density matrix renormalization group method for the full Hamiltonian. The threshold for the formation of the liquid coincides with the appearance of a bound state in the dimer-dimer problem and possesses a universality in terms of the two-body parameters of the dimer-dimer interaction, namely, scattering length and effective range. For sufficiently strong effective dimer-dimer repulsion we observe fermionization of the dimers which form an effective Tonks-Girardeau state and identify conditions for the formation of a solitonic solution. Our predictions are relevant to experiments with dipolar atoms and two-component mixtures.

arXiv:2007.01786Physical Review LettersJan 11, 202145 citations

Attractively bound pairs of atoms in the Bose-Hubbard model and antiferromagnetism

Bernd G Schmidt, Michael Bortz, Sebastian Eggert +2 more

We consider a periodic lattice loaded with pairs of bosonic atoms tightly bound to each other via strong attractive on-site interaction that exceeds the intersite tunneling rate. An ensemble of such lattice dimers is accurately described by an effective Hamiltonian of hard-core bosons with strong nearest-neighbor repulsion, which is equivalent to the $XXZ$ model with Ising-like anisotropy. We calculate the ground-state phase diagram for a one-dimensional system, which exhibits incompressible phases, corresponding to an empty and a fully filled lattice (ferromagnetic phases) and a half-filled alternating density crystal (antiferromagnetic phase), separated from each other by compressible phases. In a finite lattice the compressible phases show characteristic oscillatory modulations on top of the antiferromagnetic density profile and in density-density correlations. We derive a kink model that provides simple quantitative explanation of these features. To describe the long-range correlations of the system, we employ the Luttinger-liquid theory with the relevant Luttinger parameter $K$ obtained exactly using the Bethe-ansatz solution. We calculate the density-density as well as first-order correlations and find excellent agreement with numerical results obtained with density-matrix renormalization-group methods.We consider a periodic lattice loaded with pairs of bosonic atoms tightly bound to each other via strong attractive on-site interaction that exceeds the intersite tunneling rate. An ensemble of such lattice dimers is accurately described by an effective Hamiltonian of hard-core bosons with strong nearest-neighbor repulsion, which is equivalent to the $XXZ$ model with Ising-like anisotropy. We calculate the ground-state phase diagram for a one-dimensional system, which exhibits incompressible phases, corresponding to an empty and a fully filled lattice (ferromagnetic phases) and a half-filled alternating density crystal (antiferromagnetic phase), separated from each other by compressible phases. In a finite lattice the compressible phases show characteristic oscillatory modulations on top of the antiferromagnetic density profile and in density-density correlations. We derive a kink model that provides simple quantitative explanation of these features. To describe the long-range correlations of the system, we employ the Luttinger-liquid theory with the relevant Luttinger parameter $K$ obtained exactly using the Bethe-ansatz solution. We calculate the density-density as well as first-order correlations and find excellent agreement with numerical results obtained with density-matrix renormalization-group methods.

arXiv:0902.4442Physical Review AJun 30, 200922 citations

Quantum dynamics of one and two bosonic atoms in a combined tight-binding periodic and weak parabolic potential

Manuel Valiente, David Petrosyan

Strongly interacting bosonic particles in a tight-binding periodic potential superimposed by a weak parabolic trap is a paradigm for many cold atom experiments. Here, after revisiting the single-particle problem, we study interaction-bound dimers of bosonic atoms in the combined lattice and parabolic potential. We consider both repulsively and attractively bound dimers and find pronounced differences in their behaviour. We identify conditions under which attractive and repulsive dimers exhibit analogous dynamics. Our studies reveal that coherent transport and periodic oscillations of appropriately prepared one- and two-atom wave packets can be achieved, which may facilitate information transfer in optical-lattice–based quantum computation schemes.Strongly interacting bosonic particles in a tight-binding periodic potential superimposed by a weak parabolic trap is a paradigm for many cold atom experiments. Here, after revisiting the single-particle problem, we study interaction-bound dimers of bosonic atoms in the combined lattice and parabolic potential. We consider both repulsively and attractively bound dimers and find pronounced differences in their behaviour. We identify conditions under which attractive and repulsive dimers exhibit analogous dynamics. Our studies reveal that coherent transport and periodic oscillations of appropriately prepared one- and two-atom wave packets can be achieved, which may facilitate information transfer in optical-lattice–based quantum computation schemes.

arXiv:0803.0617Europhysics Letters (EPL)Jul 18, 200828 citations

Few-body bound states of two-dimensional bosons

G. Guijarro, G. E. Astrakharchik, Jordi Boronat +2 more

We study clusters of the type ${A}_{N}{B}_{M}$ with $N\ensuremath{\le}M\ensuremath{\le}3$ in a two-dimensional mixture of $A$ and $B$ bosons, with attractive $AB$ and equally repulsive $AA$ and $BB$ interactions. In order to check universal aspects of the problem, we choose two very different models: dipolar bosons in a bilayer geometry and particles interacting via separable Gaussian potentials. We find that all the considered clusters are bound and that their energies are universal functions of the scattering lengths ${a}_{AB}$ and ${a}_{AA}={a}_{BB}$ , for sufficiently large attraction-to-repulsion ratios ${a}_{AB}/{a}_{BB}$ . When ${a}_{AB}/{a}_{BB}$ decreases below $\ensuremath{\approx}10$, the dimer-dimer interaction changes from attractive to repulsive and the population-balanced $AABB$ and $AAABBB$ clusters break into $AB$ dimers. Calculating the $AAABBB$ hexamer energy just below this threshold, we find an effective three-dimer repulsion which may have important implications for the many-body problem, particularly for observing liquid and supersolid states of dipolar dimers in the bilayer geometry. The population-imbalanced $ABB$ trimer, $ABBB$ tetramer, and $AABBB$ pentamer remain bound beyond the dimer-dimer threshold. In the dipolar model, they break up at ${a}_{AB}\ensuremath{\approx}2{a}_{BB}$, where the atom-dimer interaction switches to repulsion.We study clusters of the type ${A}_{N}{B}_{M}$ with $N\ensuremath{\le}M\ensuremath{\le}3$ in a two-dimensional mixture of $A$ and $B$ bosons, with attractive $AB$ and equally repulsive $AA$ and $BB$ interactions. In order to check universal aspects of the problem, we choose two very different models: dipolar bosons in a bilayer geometry and particles interacting via separable Gaussian potentials. We find that all the considered clusters are bound and that their energies are universal functions of the scattering lengths ${a}_{AB}$ and ${a}_{AA}={a}_{BB}$, for sufficiently large attraction-to-repulsion ratios ${a}_{AB}/{a}_{BB}$. When ${a}_{AB}/{a}_{BB}$ decreases below $\ensuremath{\approx}10$, the dimer-dimer interaction changes from attractive to repulsive and the population-balanced $AABB$ and $AAABBB$ clusters break into $AB$ dimers. Calculating the $AAABBB$ hexamer energy just below this threshold, we find an effective three-dimer repulsion which may have important implications for the many-body problem, particularly for observing liquid and supersolid states of dipolar dimers in the bilayer geometry. The population-imbalanced $ABB$ trimer, $ABBB$ tetramer, and $AABBB$ pentamer remain bound beyond the dimer-dimer threshold. In the dipolar model, they break up at ${a}_{AB}\ensuremath{\approx}2{a}_{BB}$, where the atom-dimer interaction switches to repulsion.

arXiv:1911.01701Physical Review AApr 7, 202021 citations

1∕2

XXZ

model with fixed total magnetization which exhibits a first-order phase transition from the droplet to a gas phase. This opens the door to studying first-order phase transitions using highly controllable ultracold atoms.

|K|>{K}_{c}

), two bound-pair solutions are found. Furthermore, the spatial and momentum distributions of the bound pair displays a crossover from dark to bright soliton-like solutions in the extended BHM. Our results reduce to that of the usual BHM in the weak interaction case.

XXZ

model with Ising-like anisotropy. We calculate the ground-state phase diagram for a one-dimensional system, which exhibits incompressible phases, corresponding to an empty and a fully filled lattice (ferromagnetic phases) and a half-filled alternating density crystal (antiferromagnetic phase), separated from each other by compressible phases. In a finite lattice the compressible phases show characteristic oscillatory modulations on top of the antiferromagnetic density profile and in density-density correlations. We derive a kink model that provides simple quantitative explanation of these features. To describe the long-range correlations of the system, we employ the Luttinger-liquid theory with the relevant Luttinger parameter

K

obtained exactly using the Bethe-ansatz solution. We calculate the density-density as well as first-order correlations and find excellent agreement with numerical results obtained with density-matrix renormalization-group methods.

We study clusters of the type

{A}_{N}{B}_{M}

with $N\ensuremath{\le}M\ensuremath{\le}3$ in a two-dimensional mixture of

A

and

B

bosons, with attractive

AB

and equally repulsive

AA

and

BB

interactions. In order to check universal aspects of the problem, we choose two very different models: dipolar bosons in a bilayer geometry and particles interacting via separable Gaussian potentials. We find that all the considered clusters are bound and that their energies are universal functions of the scattering lengths

{a}_{AB}

and

{a}_{AA}={a}_{BB}

, for sufficiently large attraction-to-repulsion ratios

{a}_{AB}/{a}_{BB}

. When

{a}_{AB}/{a}_{BB}

decreases below $\ensuremath{\approx}10$, the dimer-dimer interaction changes from attractive to repulsive and the population-balanced

AABB

and

AAABBB

clusters break into

AB

dimers. Calculating the

AAABBB

hexamer energy just below this threshold, we find an effective three-dimer repulsion which may have important implications for the many-body problem, particularly for observing liquid and supersolid states of dipolar dimers in the bilayer geometry. The population-imbalanced

ABB

trimer,

ABBB

tetramer, and

AABBB

pentamer remain bound beyond the dimer-dimer threshold. In the dipolar model, they break up at ${a}_{AB}\ensuremath{\approx}2{a}_{BB}$, where the atom-dimer interaction switches to repulsion.