Quantum breathing dynamics of ultracold bosons in one-dimensional harmonic traps: Unraveling the pathway from few- to many-body systems

Schmitz, Rüdiger; Krönke, Sven; Cao, Lushuai; Schmelcher, Peter

doi:10.1103/physreva.88.043601

Cited by 63 publications

(72 citation statements)

References 41 publications

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“…While this way of testing convergence is reliable and has produced the correct answer, varying M from 1 to 10 modes is a luxury that can only be afforded for small particle numbers N . In simulations with hundreds to thousands of particles (e.g., [21,23,45]), the options for choosing M are severely limited due to the unfavorable scaling of numerical effort when both N and M are large.…”

Section: Convergence Of Mctdhb Results With Increasing Mmentioning

confidence: 99%

Center-of-mass motion as a sensitive convergence test for variational multimode quantum dynamics

2016

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Publisher's copyright statement:Reprinted with permission from the American Physical Society: Physical Review A 94, 043603 c (2016) by the American Physical Society. Readers may view, browse, and/or download material for temporary copying purposes only, provided these uses are for noncommercial personal purposes. Except as provided by law, this material may not be further reproduced, distributed, transmitted, modi ed, adapted, performed, displayed, published, or sold in whole or part, without prior written permission from the American Physical Society.Additional information: Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-pro t purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. Multimode expansions in computational quantum dynamics promise convergence toward exact results upon increasing the number of modes. Convergence is difficult to ascertain in practice due to the unfavorable scaling of required resources for many-particle problems and therefore a simplified criterion based on a threshold value for the least occupied mode function is often used. Here we show how the separable quantum motion of the center of mass can be used to sensitively detect unconverged numerical multiparticle dynamics in harmonic potentials. Based on an experimentally relevant example of attractively interacting bosons in one dimension, we demonstrate that the simplified convergence criterion fails to assure qualitatively correct results. Furthermore, the numerical evidence for the creation of two-hump fragmented bright soliton-like states presented by A. I. Streltsov et al. [Phys. Rev. Lett. 100, 130401 (2008)] is shown to be inconsistent with exact results. Implications for understanding dynamical fragmentation in attractive boson systems are briefly discussed.

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Section: Convergence Of Mctdhb Results With Increasing Mmentioning

confidence: 99%

Center-of-mass motion as a sensitive convergence test for variational multimode quantum dynamics

2016

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“…7 starts with a comprehensive study of the time-dependent behavior and its peculiarities. Besides, recent works on the breathing mode from different authors [37,40] confirm the relevance of time-dependent methods in current research.…”

Section: Calculation Of the Breathing Frequenciesmentioning

confidence: 52%

“…Here, possible approaches include multiconfiguration Hartree-Fock and restricted active space methods, e.g. [40,83,130,131], nonequilibrium Green functions [82,132], diffusion Monte Carlo [133] or path integral Monte Carlo in configuration space [134].…”

Section: Discussionmentioning

confidence: 99%

“…While there exists a complete analytical solution for the dipole mode [38,39], the breathing mode demands a numerical approach in the general case. Particularly, due to the increasing success of time-dependent numerical methods, the quantum mechanical behavior of the breathing mode (BM) has been subject of several very recent investigations [37,[40][41][42][43]. In these works, the time-dependent response of the system to a monopole-type perturbation has been studied for finite numbers of various trapped interacting fermions and bosons with Coulomb or dipole interaction.…”

Section: Examples Of Trapped Systems and Common Physical Propertiesmentioning

confidence: 99%

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Quantum Breathing Mode of Trapped Particles: From Nanoplasmas to Ultracold Gases

Abraham

Bönitz

2014

Contrib. Plasma Phys.

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Particles spatially confined in trapping potentials have attracted increasing interest over the recent decade. Of particular importance are systems of charged particles, such as non-neutral plasmas, nanoplasmas, electrons in metal clusters, electrons in quantum-confined semiconductor structures ("artificial atoms"), electrons on the surface of liquid helium, ions in traps or highly charged particles (grains) in dusty plasmas. A second example of recent interest are systems with other kinds of pair interactions, including dipole interaction, which is important for excitons in quantum wells or ultracold Fermi and Bose gases in traps and optical lattices.Trapped systems are fundamentally different from macroscopic systems since they are dominated by strong spatial inhomogeneity and finite size effects (the properties depend on the exact particle number). Furthermore, by changing the strength of the confinement potential, the many-particle state of the system can be externally controlled-from weak coupling (gas-like) to strong coupling (crystal-like). While trapped classical particles are meanwhile well understood and accessible to first-principle computer simulations, their quantum counterparts still pose big challenges, both for experiment and theory. Therefore, collective properties that can be easily measured or computed and allow to diagnose the many-particle state of the system are of prime importance. It has been found that the quantum breathing mode (monopole oscillation) is one of the most important such properties. In recent years a number of theoretical studies has demonstrated that the quantum breathing mode is ideally suited to measure the coupling strength (the degree of nonideality) of a trapped system, its kinetic and interaction energy and other key observables. This give rise to a novel kind of "spectroscopy" of trapped systems.In this review these developments are summarized. The quantum breathing mode is studied for trapped fermions and bosons with Coulomb and dipole interaction, respectively. A systematic description of collective oscillations and especially the breathing mode is provided. Making use of time-dependent perturbation theory, it is shown how the corresponding breathing frequencies are connected to the properties of the initial equilibrium system. This gives rise to the application of the quantum mechanical sum rules. It is demonstrated how an improved version of the conventional sum rule formulas is suitable for an accurate description of the breathing mode in small systems. Finally, the dependence of the breathing mode on the particle number N is analyzed and the limit of large N is studied for one-dimensional and two-dimensional systems.

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“…In general, the breathing mode then refers to a uniform expansion and contraction of the local wavepacket. For a recent study concerning the dependence of the breathing mode frequency on the particle number as well as on the interaction strength see [54], while for further related and recent investigations we refer the reader to Refs [55]- [58]. As we shall discuss briefly here, this local breathing mode can also be triggered by a quench of the interaction strength in a harmonic trap.…”

Section: Density-wave Tunneling and Breathing Modementioning

confidence: 99%

Interaction quench induced multimode dynamics of finite atomic ensembles

Mistakidis

Cao

Schmelcher

2014

J. Phys. B: At. Mol. Opt. Phys.

101

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The correlated non-equilibrium dynamics of few-boson systems in one-dimensional finite lattices is investigated. Starting from weak interactions we perform a sudden interaction quench and employ the numerically exact Multi-Layer Multi-Configuration time-dependent Hartree method for bosons to obtain the resulting quantum dynamics. Focusing on the low-lying modes of the finite lattice we observe the emergence of density-wave tunneling, breathing and cradle-like processes. In particular, the tunneling induced by the quench leads to a "global" density-wave oscillation. The resulting breathing and cradle modes are inherent to the local intrawell dynamics and connected to excited-band states. Moreover, the interaction quenches couple the density-wave and the cradle modes allowing for resonance phenomena.These are associated with an avoided-crossing in the respective frequency spectrum and lead to a beating dynamics for the cradle. Finally, complementing the numerical studies, an effective Hamiltonian in terms of the relevant Fock states is derived for the description of the spectral properties and the related resonant dynamics.

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Quantum breathing dynamics of ultracold bosons in one-dimensional harmonic traps: Unraveling the pathway from few- to many-body systems

Cited by 63 publications

References 41 publications

Center-of-mass motion as a sensitive convergence test for variational multimode quantum dynamics

Center-of-mass motion as a sensitive convergence test for variational multimode quantum dynamics

Quantum Breathing Mode of Trapped Particles: From Nanoplasmas to Ultracold Gases

Interaction quench induced multimode dynamics of finite atomic ensembles

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