The quantum dynamics of one-dimensional bosonic Josephson junctions with attractive and repulsive interparticle interactions is studied by using the Bose-Hubbard model and by numerically exact computations of the full many-body Hamiltonian. A symmetry present in the Bose-Hubbard Hamiltonian dictates an equivalence between the evolution in time of the survival probability and the fragmentation of attractive and repulsive Josephson junctions with attractive and repulsive interactions of equal magnitude. The full many-body Hamiltonian does not possess this symmetry and, consequently, the dynamics of the attractive and repulsive junctions are different.The quantum dynamics of one-dimensional bosonic Josephson junctions with attractive and repulsive interparticle interactions is studied by using the Bose-Hubbard model and by numerically exact computations of the full many-body Hamiltonian. A symmetry present in the Bose-Hubbard Hamiltonian dictates an equivalence between the evolution in time of the survival probability and the fragmentation of attractive and repulsive Josephson junctions with attractive and repulsive interactions of equal magnitude. The full many-body Hamiltonian does not possess this symmetry and, consequently, the dynamics of the attractive and repulsive junctions are different.

arXiv:0911.4661Physical Review AJul 15, 201062 citations

Quantum dynamics of repulsively bound atom pairs in the Bose-Hubbard model

L. Wang, Yajiang Hao, S. Chen

arXiv:cond-mat/0701502The European Physical Journal DApr 17, 200830 citations

Quantum and thermal fluctuations in bosonic Josephson junctions

Bruno Juliá-Díaz, Alex D. Gottlieb, Joan Martorell +1 more

We use the Bose-Hubbard Hamiltonian to study quantum fluctuations in canonical equilibrium ensembles of bosonic Josephson junctions at relatively high temperatures, comparing the results for finite particle numbers $N$ to the classical limit that is attained as $N$ approaches infinity. We consider both attractive and repulsive atom-atom interactions, with special focus on the behavior near the $T=0$ quantum phase transition that occurs, for large enough $N$ , when attractive interactions surpass a critical level. Differences between Bose-Hubbard results for small $N$ and those of the classical limit are quite small even when $N\ensuremath{\sim}100$, with deviations from the limit diminishing as $1/N$ .We use the Bose-Hubbard Hamiltonian to study quantum fluctuations in canonical equilibrium ensembles of bosonic Josephson junctions at relatively high temperatures, comparing the results for finite particle numbers $N$ to the classical limit that is attained as $N$ approaches infinity. We consider both attractive and repulsive atom-atom interactions, with special focus on the behavior near the $T=0$ quantum phase transition that occurs, for large enough $N$, when attractive interactions surpass a critical level. Differences between Bose-Hubbard results for small $N$ and those of the classical limit are quite small even when $N\ensuremath{\sim}100$, with deviations from the limit diminishing as $1/N$.

arXiv:1307.4595Physical Review ASep 3, 201310 citations

Coherence and entanglement in the ground state of a bosonic Josephson junction: From macroscopic Schrödinger cat states to separable Fock states

G. Mazzarella, Luca Salasnich, Alberto Parola +1 more

We consider a bosonic Josephson junction made of $N$ ultracold and dilute atoms confined by a quasi-one-dimensional double-well potential within the two-site Bose-Hubbard model framework. The behavior of the system is investigated at zero temperature by varying the interatomic interaction from the strongly attractive regime to the repulsive one. We show that the ground state exhibits a crossover from a macroscopic Schr\"odinger-cat state to a separable Fock state through an atomic coherent regime. By diagonalizing the Bose-Hubbard Hamiltonian we characterize the emergence of the macroscopic cat states by calculating the Fisher information $F$ , the coherence by means of the visibility $\ensuremath{\alpha}$ of the interference fringes in the momentum distribution, and the quantum correlations by using the entanglement entropy $S$ . Both Fisher information and visibility are shown to be related to the ground-state energy by employing the Hellmann-Feynman theorem. This result, together with a perturbative calculation of the ground-state energy, allows simple analytical formulas for $F$ and $\ensuremath{\alpha}$ to be obtained over a range of interactions, in excellent agreement with the exact diagonalization of the Bose-Hubbard Hamiltonian. In the attractive regime the entanglement entropy attains values very close to its upper limit for a specific interaction strength lying in the region where coherence is lost and self-trapping sets in.We consider a bosonic Josephson junction made of $N$ ultracold and dilute atoms confined by a quasi-one-dimensional double-well potential within the two-site Bose-Hubbard model framework. The behavior of the system is investigated at zero temperature by varying the interatomic interaction from the strongly attractive regime to the repulsive one. We show that the ground state exhibits a crossover from a macroscopic Schr\"odinger-cat state to a separable Fock state through an atomic coherent regime. By diagonalizing the Bose-Hubbard Hamiltonian we characterize the emergence of the macroscopic cat states by calculating the Fisher information $F$, the coherence by means of the visibility $\ensuremath{\alpha}$ of the interference fringes in the momentum distribution, and the quantum correlations by using the entanglement entropy $S$. Both Fisher information and visibility are shown to be related to the ground-state energy by employing the Hellmann-Feynman theorem. This result, together with a perturbative calculation of the ground-state energy, allows simple analytical formulas for $F$ and $\ensuremath{\alpha}$ to be obtained over a range of interactions, in excellent agreement with the exact diagonalization of the Bose-Hubbard Hamiltonian. In the attractive regime the entanglement entropy attains values very close to its upper limit for a specific interaction strength lying in the region where coherence is lost and self-trapping sets in.

arXiv:1103.1976Physical Review AMay 5, 201160 citations

Dynamics of a bosonic Josephson junction with an impurity

Jan 1, 20160 citations

N

to the classical limit that is attained as

N

approaches infinity. We consider both attractive and repulsive atom-atom interactions, with special focus on the behavior near the

T=0

quantum phase transition that occurs, for large enough

N

, when attractive interactions surpass a critical level. Differences between Bose-Hubbard results for small

N

and those of the classical limit are quite small even when $N\ensuremath{\sim}100$, with deviations from the limit diminishing as

1/N

We consider a bosonic Josephson junction made of

N

ultracold and dilute atoms confined by a quasi-one-dimensional double-well potential within the two-site Bose-Hubbard model framework. The behavior of the system is investigated at zero temperature by varying the interatomic interaction from the strongly attractive regime to the repulsive one. We show that the ground state exhibits a crossover from a macroscopic Schr\"odinger-cat state to a separable Fock state through an atomic coherent regime. By diagonalizing the Bose-Hubbard Hamiltonian we characterize the emergence of the macroscopic cat states by calculating the Fisher information

F

, the coherence by means of the visibility $\ensuremath{\alpha}$ of the interference fringes in the momentum distribution, and the quantum correlations by using the entanglement entropy

S

. Both Fisher information and visibility are shown to be related to the ground-state energy by employing the Hellmann-Feynman theorem. This result, together with a perturbative calculation of the ground-state energy, allows simple analytical formulas for

F

and $\ensuremath{\alpha}$ to be obtained over a range of interactions, in excellent agreement with the exact diagonalization of the Bose-Hubbard Hamiltonian. In the attractive regime the entanglement entropy attains values very close to its upper limit for a specific interaction strength lying in the region where coherence is lost and self-trapping sets in.