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Delocalization effects, entanglement entropy and spectral collapse of boson mixtures in a double well

Fabio Lingua, Mazzarella, Giovanni, Vittorio Penna

Published Jan 1, 2016• 15 citations
OpenAlex

Abstract

We investigate the ground-state properties of a two-species condensate of interacting bosons in a double-well potential. Each atomic species is described by a two-space-mode Bose-Hubbard model. The coupling of the two species is controlled by the interspecies interaction W. To analyze the ground state when W is varied in both the repulsive ( W > 0 ) and the attractive ( W < 0 ) regime, we apply two different approaches. First we solve the problem numerically (i) to obtain an exact description of the ground-state structure and (ii) to characterize its correlation properties by studying (the appropriate extensions to the present case of) the quantum Fisher information, the coherence visibility and the entanglement entropy as functions of W. Then we approach analytically the description of the low-energy scenario by means of the Bogoliubov scheme. In this framework the ground-state transition from delocalized to localized species (with space separation for W > 0 , and mixing for W < 0 ) is well reproduced. These predictions are qualitatively corroborated by our numerical results. We show that such a transition features a spectral collapse reflecting the dramatic change of the dynamical algebra of the four-mode model Hamiltonian.

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Delocalization effects, entanglement entropy and spectral collapse of boson mixtures in a double well

Fabio Lingua, G Mazzarella, V Penna

Abstract We investigate the ground-state properties of a two-species condensate of interacting bosons in a double-well potential. Each atomic species is described by a two-space-mode Bose–Hubbard model. The coupling of the two species is controlled by the interspecies interaction W . To analyze the ground state when W is varied in both the repulsive ( W > 0 ) and the attractive ( W < 0 ) regime, we apply two different approaches. First we solve the problem numerically (i) to obtain an exact description of the ground-state structure and (ii) to characterize its correlation properties by studying (the appropriate extensions to the present case of) the quantum Fisher information, the coherence visibility and the entanglement entropy as functions of W . Then we approach analytically the description of the low-energy scenario by means of the Bogoliubov scheme. In this framework the ground-state transition from delocalized to localized species (with space separation for W > 0 , and mixing for W < 0 ) is well reproduced. These predictions are qualitatively corroborated by our numerical results. We show that such a transition features a spectral collapse reflecting the dramatic change of the dynamical algebra of the four-mode model Hamiltonian.

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Continuous-variable approach to the spectral properties and quantum states of the two-component Bose-Hubbard dimer

Fabio Lingua, Vittorio Penna

A bosonic gas formed by two interacting species trapped in a double-well potential features macroscopic localization effects when the interspecies interaction becomes sufficiently strong. A repulsive interaction spatially separates the species into different wells while an attractive interaction confines both species in the same well. We perform a fully analytic study of the transitions from the weak- to the strong-interaction regime by exploiting the semiclassical method in which boson populations are represented in terms of continuous variables. We find an explicit description of low-energy eigenstates and spectrum in terms of the model parameters which includes the neighborhood of the transition point. To test the effectiveness of the continuous-variable method we compare its predictions with the exact results found numerically. Numerical calculations confirm the spectral collapse evidenced by this method when the space localization takes place.

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Quantum properties of a binary bosonic mixture in a double well

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This work contains a detailed analysis of the properties of the ground state of a two-component two-site Bose-Hubbard model, which captures the physics of a binary mixture of Bose-Einstein condensates trapped in a double-well potential. The atom-atom interactions within each species and among the two species are taken as variable parameters, while the hopping terms are kept fixed. To characterize the ground state, we use observables such as the imbalance of population and its quantum uncertainty. The quantum many-body correlations present in the system are further quantified by studying the degree of condensation of each species, the entanglement between the two sites, and the entanglement between the two species. The latter is measured by means of the Schmidt gap, the von Neumann entropy, or the purity obtained after tracing out a part of the system. A number of relevant states are identified, e.g., Schr\"odinger catlike many-body states, in which the outcome of the population imbalance of both components is completely correlated, and other states with even larger von Neumann entropy which have a large spread in Fock space.

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Entanglement entropy and macroscopic quantum states with dipolar bosons in a triple-well potential

Luca Dell’Anna, G. Mazzarella, Vittorio Penna +1 more

We study interacting dipolar atomic bosons in a triple-well potential within a ring geometry. This system is shown to be equivalent to a three-site Bose-Hubbard model. We analyze the ground state of dipolar bosons by varying the effective on-site interaction. This analysis is performed both numerically and analytically by using suitable coherent-state representations of the ground state. The latter exhibits a variety of forms ranging from the SU(3) coherent state in the delocalization regime to a macroscopic catlike state with fully localized populations, passing for a coexistence regime where the ground state displays a mixed character. We characterize the quantum correlations of the ground state from the bipartition perspective. We calculate both numerically and analytically (within the previous coherent-state representation) the single-site entanglement entropy which, among various interesting properties, exhibits a maximum value in correspondence to the transition from the catlike to the coexistence regime. In the latter case, we show that the ground-state mixed form corresponds, semiclassically, to an energy exhibiting two almost-degenerate minima.

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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.

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Quantum phase transitions of atom-molecule Bose mixtures in a double-well potential

Armando Relaño, J. Dukelsky, P. Pérez-Fernández +1 more

The ground state and spectral properties of Bose gases in double-well potentials are studied in two different scenarios: (i) an interacting atomic Bose gas, and (ii) a mixture of an atomic gas interacting with diatomic molecules. A ground state second-order quantum phase transition is observed in both scenarios. For large attractive values of the atom-atom interaction, the ground state is degenerate. For repulsive and small attractive interaction, the ground state is not degenerate and is well approximated by a boson coherent state. Both systems depict an excited state quantum phase transition. In both cases, a critical energy separates a region in which all the energy levels are degenerate in pairs, from another region in which there are no degeneracies. For the atomic system, the critical point displays a singularity in the density of states, whereas this behavior is largely smoothed for the mixed atom-molecule system.

arXiv:1406.6833•Physical Review E•Oct 27, 2014•22 citations
We investigate the ground-state properties of a two-species condensate of interacting bosons in a double-well potential. Each atomic species is described by a two-space-mode Bose-Hubbard model. The coupling of the two species is controlled by the interspecies interaction W. To analyze the ground state when W is varied in both the repulsive ( W > 0 ) and the attractive ( W < 0 ) regime, we apply two different approaches. First we solve the problem numerically (i) to obtain an exact description of the ground-state structure and (ii) to characterize its correlation properties by studying (the appropriate extensions to the present case of) the quantum Fisher information, the coherence visibility and the entanglement entropy as functions of W. Then we approach analytically the description of the low-energy scenario by means of the Bogoliubov scheme. In this framework the ground-state transition from delocalized to localized species (with space separation for W > 0 , and mixing for W < 0 ) is well reproduced. These predictions are qualitatively corroborated by our numerical results. We show that such a transition features a spectral collapse reflecting the dramatic change of the dynamical algebra of the four-mode model Hamiltonian.
Abstract We investigate the ground-state properties of a two-species condensate of interacting bosons in a double-well potential. Each atomic species is described by a two-space-mode Bose–Hubbard model. The coupling of the two species is controlled by the interspecies interaction W . To analyze the ground state when W is varied in both the repulsive ( W > 0 ) and the attractive ( W < 0 ) regime, we apply two different approaches. First we solve the problem numerically (i) to obtain an exact description of the ground-state structure and (ii) to characterize its correlation properties by studying (the appropriate extensions to the present case of) the quantum Fisher information, the coherence visibility and the entanglement entropy as functions of W . Then we approach analytically the description of the low-energy scenario by means of the Bogoliubov scheme. In this framework the ground-state transition from delocalized to localized species (with space separation for W > 0 , and mixing for W < 0 ) is well reproduced. These predictions are qualitatively corroborated by our numerical results. We show that such a transition features a spectral collapse reflecting the dramatic change of the dynamical algebra of the four-mode model Hamiltonian.
A bosonic gas formed by two interacting species trapped in a double-well potential features macroscopic localization effects when the interspecies interaction becomes sufficiently strong. A repulsive interaction spatially separates the species into different wells while an attractive interaction confines both species in the same well. We perform a fully analytic study of the transitions from the weak- to the strong-interaction regime by exploiting the semiclassical method in which boson populations are represented in terms of continuous variables. We find an explicit description of low-energy eigenstates and spectrum in terms of the model parameters which includes the neighborhood of the transition point. To test the effectiveness of the continuous-variable method we compare its predictions with the exact results found numerically. Numerical calculations confirm the spectral collapse evidenced by this method when the space localization takes place.
This work contains a detailed analysis of the properties of the ground state of a two-component two-site Bose-Hubbard model, which captures the physics of a binary mixture of Bose-Einstein condensates trapped in a double-well potential. The atom-atom interactions within each species and among the two species are taken as variable parameters, while the hopping terms are kept fixed. To characterize the ground state, we use observables such as the imbalance of population and its quantum uncertainty. The quantum many-body correlations present in the system are further quantified by studying the degree of condensation of each species, the entanglement between the two sites, and the entanglement between the two species. The latter is measured by means of the Schmidt gap, the von Neumann entropy, or the purity obtained after tracing out a part of the system. A number of relevant states are identified, e.g., Schr\"odinger catlike many-body states, in which the outcome of the population imbalance of both components is completely correlated, and other states with even larger von Neumann entropy which have a large spread in Fock space.
We study interacting dipolar atomic bosons in a triple-well potential within a ring geometry. This system is shown to be equivalent to a three-site Bose-Hubbard model. We analyze the ground state of dipolar bosons by varying the effective on-site interaction. This analysis is performed both numerically and analytically by using suitable coherent-state representations of the ground state. The latter exhibits a variety of forms ranging from the SU(3) coherent state in the delocalization regime to a macroscopic catlike state with fully localized populations, passing for a coexistence regime where the ground state displays a mixed character. We characterize the quantum correlations of the ground state from the bipartition perspective. We calculate both numerically and analytically (within the previous coherent-state representation) the single-site entanglement entropy which, among various interesting properties, exhibits a maximum value in correspondence to the transition from the catlike to the coexistence regime. In the latter case, we show that the ground-state mixed form corresponds, semiclassically, to an energy exhibiting two almost-degenerate minima.
We consider a bosonic Josephson junction made of NNN 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 FFF, 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 SSS. 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 FFF 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.
The ground state and spectral properties of Bose gases in double-well potentials are studied in two different scenarios: (i) an interacting atomic Bose gas, and (ii) a mixture of an atomic gas interacting with diatomic molecules. A ground state second-order quantum phase transition is observed in both scenarios. For large attractive values of the atom-atom interaction, the ground state is degenerate. For repulsive and small attractive interaction, the ground state is not degenerate and is well approximated by a boson coherent state. Both systems depict an excited state quantum phase transition. In both cases, a critical energy separates a region in which all the energy levels are degenerate in pairs, from another region in which there are no degeneracies. For the atomic system, the critical point displays a singularity in the density of states, whereas this behavior is largely smoothed for the mixed atom-molecule system.