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arXiv:1602.01339 · Physical Review A

Quantum properties of a binary bosonic mixture in a double well

Pere Mujal, Bruno Juliá-Díaz, A. Polls

Published Apr 21, 2016• 17 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.93.043619

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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.
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.
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.
In a double-well potential, a Bose-Einstein condensate exhibits Josephson oscillations or self-trapping, depending on its initial preparation and on the ratio of interparticle interaction to interwell tunneling. Here, we elucidate the role of the exchange symmetry for the dynamics with a mixture of two distinguishable species with identical physical properties, that is, which are governed by an isospecific interaction and external potential. In the mean-field limit, the spatial population imbalance of the mixture can be described by the dynamics of a single species in an effective potential with modified properties or, equivalently, with an effective total particle number. The oscillation behavior can be tuned by populating the second species while maintaining the spatial population imbalance and all other parameters constant. In the corresponding many-body approach, the single-species description approximates the full counting statistics well also outside the realm of spin-coherent states. The method is extended to general Bose-Hubbard systems and to their classical mean-field limits, which suggests an effective single-species description of multicomponent Bose gases with weakly an-isospecific interactions.
Abstract The time evolution of probability density, the ground-state fidelity and the entanglement of a Bose-Fermi mixture in a 1D double well potential, are studied through the two-mode approximation. We found that the behavior of the quantum return probability shows three distinct regions. The first region is characterized by a complete miscibility, and correlated tunneling of bosons and fermion. The second region is characterized by correlated sequential tunneling and in the last region we found an increase in the tunneling frequency of the two species. Through the Von Neumann entropy, we found that the boson-fermion coupling allows a maximum entanglement of quantum correlations of bosons and fermions in the same value. Finally, Considering variations in the interaction between pairs of fermions λ FF , pairs of bosons λ BB , and variations in the interaction between particles of different species λ BF , we calculated the fidelity in the λ FF − λ BF and λ BB − λ BF planes and we found that the drop of the two fidelities becomes deeper and deeper as the boson-fermion interaction decreases.
We investigate an integrable Hamiltonian modeling a heterotriatomic molecular Bose-Einstein condensate. This model describes a mixture of two species of atoms in different proportions, which can combine to form a triatomic molecule. Beginning with a classical analysis, we determine the fixed points of the system. Bifurcations of these points separate the parameter space into different regions. Three distinct scenarios are found, varying with the atomic population imbalance. This result suggests the ground-state properties of the quantum model exhibit a sensitivity on the atomic population imbalance, which is confirmed by a quantum analysis using different approaches, such as the ground-state expectation values, the behavior of the quantum dynamics, the energy gap, and the ground-state fidelity.
We study the interpolation from occupation number Fock states to Schr\"odinger cat states on systems modeled by a two-mode Bose-Hubbard Hamiltonian, like, for instance, bosons in a double well or superconducting Cooper pair boxes. In the repulsive interaction regime, by a simplified single particle description, we calculate analytically energy, number fluctuations, stability under coupling to a heat bath, entanglement entropy, and Fisher information, all in terms of hypergeometric polynomials of the single particle overlap parameter. Our approach allows us to find how those quantities scale with the number of bosons. In the attractive interaction regime we calculate the same physical quantities in terms of the imbalance parameter, and find that the spontaneous symmetry breaking, occurring at interaction Uc{U}_{c}Uc​, predicted by a semiclassical approximation, is valid only in the limit of infinite number of bosons. For a large but finite number we determine a characteristic strength of interaction Uc∗{U}_{c}^{*}Uc∗​, which can be promoted as the crossover point from coherent to incoherent regimes and can be identified as the threshold of fragility of the cat state. Moreover, we find that the Fisher information is always in direct ratio to the variance of on-site number of bosons, for both positive and negative interactions. We finally show that the entanglement entropy is maximum close to Uc∗{U}_{c}^{*}Uc∗​ and exceeds its coherent value within the whole range of interaction between 2Uc2{U}_{c}2Uc​ and zero.