Dipolar Bose gas in a highly anharmonic trap

Ancilotto, Francesco; Toigo, Flavio

doi:10.1103/physreva.89.023617

Cited by 7 publications

(5 citation statements)

References 43 publications

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“…Moreover, low-lying excitations in such systems were addressed, for example in vortex lattices [26,193,194,195]. Furthermore, investigations were made on the decay of the counter-rotating quadrupole mode [196], on Tkachenko modes [197,198], on the twiston spectrum [199], or on excitations in anharmonic traps [200,201]. In the latter works, the mean-field excitations were calculated by utilizing the BdG theory.…”

Section: Rotating Bose-einstein Condensates In An Anharmonic Trapmentioning

confidence: 99%

Many-body effects in the excitations and dynamics of trapped Bose-Einstein condensates

Alon¹,

Beinke²,

Cederbaum³

2021

Preprint

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This review explores the dynamics and the low-energy excitation spectra of Bose-Einstein condensates (BECs) of interacting bosons in external potential traps putting particular emphasis on the emerging manybody effects beyond mean-field descriptions. To do so, methods have to be used that, in principle, can provide numerically exact results for both the dynamics and the excitation spectra in a systematic manner. Numerically exact results for the dynamics are presented employing the well-established multicongurational time-dependent Hartree for bosons (MCTDHB) method. The respective excitation spectra are calculated utilizing the more recently introduced linear-response theory atop it (LR-MCTDHB). The latter theory gives rise to an, in general, non-hermitian eigenvalue problem. The theory and its newly developed implementation are described in detail and benchmarked towards the exactly-solvable harmonic-interaction model. Several applications to BECs in one-and two-dimensional potential traps are discussed. With respect to dynamics, it is shown that both the out-of-equilibrium tunneling dynamics and the dynamics of trapped vortices are of many-body nature. Furthermore, many-body effects in the excitation spectra are presented for BECs in different trap geometries. It is demonstrated that even for essentially-condensed systems, the spectrum of the lowest-in-energy excitations computed at the many-body level can differ substantially from the standard mean-field description. In general, it is shown that bosons carrying angular momentum are more sensitive to many-body effects than bosons without. These effects are present in both the dynamics and the excitation spectrum.

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Section: Rotating Bose-einstein Condensates In An Anharmonic Trapmentioning

confidence: 99%

Many-body effects in the excitations and dynamics of trapped Bose-Einstein condensates

Alon¹,

Beinke²,

Cederbaum³

2021

Preprint

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“…This study also aims to reveal the role of the interplay between complex trapping geometry and DDIs (cf [23][24][25]) in defining the frequencies at which PRs occur. Although the effects of the trapping geometry, such as the influence of the trap aspect ratio on the oscillation frequencies [26], stability [27,28], and the density profiles as well as breathing mode oscillations of DBECs [29] have been investigated in previous studies, the relationship between complex geometry and the structure of trap energy levels in the presence of interactions has not been discovered.…”

Section: Introductionmentioning

confidence: 99%

Characterization of the energy level-structure of a trapped dipolar Bose gas via mean-field parametric resonances

Sakhel¹,

Sakhel²

2021

Phys. Scr.

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Analyzing the energy levels of a trapped Bose-Einstein condensate (BEC) can be difficult when dipoledipole interactions (DDIs) are present. To address this issue, this study focuses on the parametric resonances (PRs) in the mean-field dynamics of a one-dimensional dipolar BEC (DBEC) over widely varying trapping geometries, with the primary objective of characterizing the energy levels of this system via analytical methods. This is achieved by matching the PR energies to the energy levels of the confining trap using perturbative methods. Further, this research reveals the role of the interplay between DDIs and the trapping geometry in defining the energies and amplitudes of the PRs. The PRs are induced by a negative Gaussian potential with a depth that oscillates with respect to time; DDIs also play a role in this induction. The dynamics of this system are modeled using the time-dependent Gross-Pitaevskii equation (TDGPE), which is numerically solved via the Crank-Nicolson method. The PRs are discussed based on analytical methods. First, we show that PRs similar to the ones obtained from the TDGPE can be reproduced via the Lagrangian variational method. Second, the energies at which the PRs occur are closely matched with the energy levels of the corresponding trap, calculated using the time-independent perturbation theory. Third, the most probable transitions between the trap energy levels yielding PRs are determined based on the time-dependent perturbation theory. The primary contribution of this research is that the energy levels of a DBEC within a complex trapping potential could be characterized.

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“…[20,[33][34][35]) in defining the frequencies at which PRs occur. Effects of trapping geometry have already been studied earlier such as the influence of the trap aspect ratio on the oscillation frequencies [36] and stability of a DBEC [37,38], except that it hasn't been related to the structure of the trap energy levels.…”

Section: Introductionmentioning

confidence: 99%

Characterization of the energy level-structure of a trapped dipolar Bose gas via mean-field parametric resonances

Sakhel,

Sakhel

2021

Preprint

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We report parametric resonances (PRs) in the mean-field dynamics of a one-dimensional dipolar Bose-Einstein condensate (DBEC) in widely varying trapping geometries. The chief goal is to characterize the energy levels of this system by analytical methods and the significance of this study arises from the commonly known fact that in the presence of interactions the energy levels of a trapped BEC are hard to calculate analytically. The latter characterization is achieved by a matching of the PR energies to energy levels of the confining trap using perturbative methods. Further, this work reveals the role of the interplay between dipole-dipole interactions (DDI) and trapping geometry in defining the energies and amplitudes of the PRs. The PRs are induced by a negative Gaussian potential whose depth oscillates with time. Moreover, the DDI play a role in this induction. The dynamics of this system is modeled by the time-dependent Gross-Pitaevskii equation (TDGPE) that is numerically solved by the Crank-Nicolson method. The PRs are discussed basing on analytical methods: first, it is shown that it is possible to reproduce PRs by the Lagrangian variational method that are similar to the ones obtained from TDGPE. Second, the energies at which the PRs arise are closely matched with the energy levels of the corresponding trap calculated by time-independent perturbation theory. Third, the most probable transitions between the trap energy levels yielding PRs are determined by time-dependent perturbation theory. The most significant result of this work is that we have been able to characterize the above mentioned energy levels of a DBEC in a complex trapping potential.

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Dipolar Bose gas in a highly anharmonic trap

Cited by 7 publications

References 43 publications

Many-body effects in the excitations and dynamics of trapped Bose-Einstein condensates

Many-body effects in the excitations and dynamics of trapped Bose-Einstein condensates

Characterization of the energy level-structure of a trapped dipolar Bose gas via mean-field parametric resonances

Characterization of the energy level-structure of a trapped dipolar Bose gas via mean-field parametric resonances

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