Fermionic Properties of Two Interacting Bosons in a Two-Dimensional Harmonic Trap

Mujal, Pere; Polls, A.; Juliá-Dı́az, B.

doi:10.3390/condmat3010009

Cited by 9 publications

(10 citation statements)

References 37 publications

(47 reference statements)

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“…This is an indicator that the system becomes correlated in the proper way in order to reduce the total energy by avoiding the atom-atom interaction. This kind of behavior was found previously in a harmonically trapped system of interacting bosons in two dimensions [38,39].…”

Section: B Ground-state Energy and Degeneracysupporting

confidence: 83%

Spin-orbit-coupled bosons interacting in a two-dimensional harmonic trap

2020

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A system of bosons in a two-dimensional harmonic trap with the presence of Rashba-type spinorbit coupling is investigated. An analytic treatment of the ground state of a single atom in the weak-coupling regime is presented and used as a basis for a perturbation theory in the interacting two-boson system. The numerical diagonalization of both the single-particle and the two-boson Hamiltonian matrices allows us to go beyond those approximations and obtain not only the ground state, but also the low-energy spectra and the different energy contributions separately. We show that the expectation value of the spin-orbit term is related to the expectation value ofσzLz for the eigenstates of the system, regardless of the trapping potential. The ground state of the repulsively interacting two-boson system is characterized. With the presence of a sufficiently strong interaction and spin-orbit coupling strength, there is an energy-level crossing in the ground state of the system that changes its structure. This is reflected in a discontinuity in the different energy terms and it is signaled in the spatial density of the system.

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Section: B Ground-state Energy and Degeneracysupporting

confidence: 83%

Spin-orbit-coupled bosons interacting in a two-dimensional harmonic trap

2020

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“…For the case of neutral bosons the Wignermolecule regime corresponds to a process of 2D fermionization, when the strong repulsion keeps the particles away from each other overtaking the propensity of bosons to bunch together due to statistics. This fermionization behavior is well known for strongly repelling strictly 1D bosons (Girardeau, 1960); in two dimensions, it has also been recently further verified via exact numerical calculations for two interacting bosons (Mujal et al, 2018).…”

Section: J Trapped Ultracold Ions and Neutral Atomic Gasessupporting

confidence: 53%

Symmetry restoration in mean-field approaches

Sheikh,

Dobaczewski,

Ring

et al. 2019

Preprint

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The mean-field approximation based on effective interactions or density functionals plays a pivotal role in the description of finite quantum many-body systems that are too large to be treated by ab initio methods. Examples are strongly interacting atomic nuclei and mesoscopic condensed matter systems. In this approach, the linear Schrodinger equation for the exact many-body wave function is mapped onto a non-linear density-dependent one-body potential problem. This approximation, not only provides computationally very simple solutions even for systems with many particles, but due to the non-linearity, it also allows for obtaining solutions that break essential symmetries of the system, often connected with phase transitions. However, mean-field approach suffers from the drawback that the corresponding wave functions do not have sharp quantum numbers and, therefore, many results cannot be compared directly with experimental data. In this article, we discuss general group theoretical techniques to restore the broken symmetries, and provide detailed expressions on the restoration of translational, rotational, spin, isospin, parity and gauge symmetries, where the latter corresponds to the restoration of the particle number. In order to avoid the numerical complexity of exact projection techniques, various approximation methods available in the literature are examined. We present applications of the projection methods to simple nuclear models, realistic calculations in relatively small configuration spaces, nuclear energy density functional theory, as well as in other mesoscopic systems. We also discuss applications of projection techniques to quantum statistics in order to treat the averaging over restricted ensembles with fixed quantum numbers. Further, unresolved problems in the application of the symmetry restoration methods to the energy density functional theories are highlighted. CONTENTSL. Other electronic systems 60 M. Other emerging directions 60 VIII. Projected statistics 61 A. Symmetry restoration at finite temperature 62 B. Thermo-field dynamics 63 IX. Summary, conclusions, and perspectives 63 X. Acknowledgments 64 A. Overlaps and matrix elements between HFB states: the generalized Wick's theorem 65

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“…Accordingly, novel in situ [1][2][3][4][5] and time-of-flight (TOF) [6][7][8][9][10][11][12] experimental techniques and protocols that measure key quantities such as second-and higher-order many-body correlations of interacting particles in real (space coordinates) and momentum space, respectively, are being developed. In addition, the importance of such quantities has been reflected in a growing number of theoretical studies [13][14][15][16][17] which have mainly analyzed space correlations. In this sense it is notable that two recent theoretical publications [18,19] have focused, with the use of exact diagonalization and the Hubbard model, on secondorder momentum correlations for trapped, interacting ultracold atoms beyond earlier studies of first-order momentum correlations [20,21].…”

Section: Introductionmentioning

confidence: 99%

Interference, spectral momentum correlations, entanglement, and Bell inequality for a trapped interacting ultracold atomic dimer: Analogies with biphoton interferometry

2019

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Aiming at elucidating similarities and differences between quantum-optics biphoton interference phenomena and the quantum physics of quasi-one-dimensional double-well optically-trapped ultracold neutral bosonic or fermionic atoms, we show that the analog of the optical biphoton jointcoincidence spectral correlations, studied with massless non-interacting biphotons emanating from EPR-Bell-Bohm single-occupancy sources, corresponds to a distinct contribution in the total secondorder momentum correlations of the massive, interacting, and time-evolving ultracold atoms. This single-occupancy contribution can be extracted from the total second-order momentum correlation function measured in time-of-flight experiments, which for the trapped atomic system contains, in general, a double-occupancy, NOON, component. The dynamics of the two-particle system are modeled by a Hubbard Hamiltonian. The general form of this partial coincidence spectrum is a cosine-square quantum beating dependent on the difference of the momenta of the two particles, while the corresponding coincidence probability proper, familiar from its role in describing the Hong-Ou-Mandel coincidence dip of overlapping photons, results from an integration over the particle momenta. Because the second-order momentum correlations are mirrored in the time-of-flight spectra in space, our theoretical findings provide impetus for time-of-flight experimental protocols for emulating with (massive) ultracold atoms venerable optical interferometries that use two space-time separated and entangled (massless) photons or double-slit optical sources. The implementation of such developments will facilitate testing of fundamental aspects and enable applications of quantum physics with trapped massive ultracold atoms, that is, investigations of nonlocality and violation of Bell inequalities, entanglement, and quantum information science. arXiv:1812.05977v2 [cond-mat.quant-gas]

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Fermionic Properties of Two Interacting Bosons in a Two-Dimensional Harmonic Trap

Cited by 9 publications

References 37 publications

Spin-orbit-coupled bosons interacting in a two-dimensional harmonic trap

Spin-orbit-coupled bosons interacting in a two-dimensional harmonic trap

Symmetry restoration in mean-field approaches

Interference, spectral momentum correlations, entanglement, and Bell inequality for a trapped interacting ultracold atomic dimer: Analogies with biphoton interferometry

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