Variance as a sensitive probe of correlations

Klaiman, Shachar; Alon, Ofir E.

doi:10.1103/physreva.91.063613

Cited by 54 publications

(108 citation statements)

References 33 publications

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“…Finally, we note that although we only show examples with a few particles in this tutorial, the MCTDH-X is able to provide many-body states of systems with a much larger number of particles [101,102].…”

Section: Conclusion and Discussionmentioning

confidence: 99%

MCTDH-X: The multiconfigurational time-dependent Hartree method for indistinguishable particles software

Lin

Molignini

Papariello

et al. 2020

Quantum Sci. Technol.

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We introduce and describe the multiconfigurational time-depenent Hartree for indistinguishable particles (MCTDH-X) software, which is hosted, documented, and distributed at http://ultracold.org. This powerful tool allows the investigation of ground state properties with time-independent Hamiltonians, and dynamics of interacting quantum many-body systems in different spatial dimensions. The MCTDH-X software is a set of programs and scripts to compute, analyze, and visualize solutions for the time-dependent and time-independent many-body Schrödinger equation for indistinguishable quantum particles. As the MCTDH-X software represents a general solver for the Schrödinger equation, it is applicable to a wide range of problems in the fields of atomic, optical, molecular physics as well as condensed matter systems. In particular, it can be used to study light-matter interactions, correlated dynamics of electrons in solid states, as well as some aspects related to quantum information and computing. The MCTDH-X software solves a set of non-linear coupled working equations based on the application of the variational principle to the Schrödinger equation. These equations are obtained by using an ansatz for the many-body wavefunction that is a time-dependent expansion in a set of time-dependent, fully symmetrized bosonic (X=B) or fully anti-symmetrized fermionic (X=F) many-body basis states. It is the time-dependence of the basis set, that enables MCTDH-X to deal with quantum dynamics at a superior accuracy as compared to, for instance, exact diagonalization approaches with a static basis, where the number of basis states necessary to capture the dynamics of the wavefunction typically grows rapidly with time.Herein, we give an introduction to the MCTDH-X software via an easy-to-follow tutorial with a focus on accessibility.The illustrated exemplary problems are hosted at http://ultracold.org/tutorial and consider the physics of a few interacting bosons or fermions in a double-well potential. We explore computationally the position-space and momentum-space density, the one-body reduced density matrix, Glauber correlation functions, phases, (dynamical) phase transitions as well as the imaging of the quantum systems. Although a few particles in a double well potential represent a minimal model system, we are able to demonstrate a rich variety of phenomena with it. We use the double well to illustrate the fermionization of bosonic particles, the crystallization of fermionic particles, characteristics of the superfluid and Mott-insulator quantum phases in Hubbard models, and even dynamical phase transitions. We provide a complete set of input files and scripts to redo all computations in this paper at http://ultracold.org/data/tutorial_input_files.zip, accompanied by tutorial videos at https://www.youtube.com/playlist?list=PLJIFUqmSeGBKxmLcCuk6dpILnni_uIFGu. Our tutorial should guide the potential users to apply the MCTDH-X software also to more complex systems. arXiv:1911.00525v2 [cond-mat.quant-gas] 16 Jan 2020The time-dependen...

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Section: Conclusion and Discussionmentioning

confidence: 99%

MCTDH-X: The multiconfigurational time-dependent Hartree method for indistinguishable particles software

Lin

Molignini

Papariello

et al. 2020

Quantum Sci. Technol.

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“…where á ñ x i denotes the mean position of the ith species and á ¢ ñ x x i j refers to the two-body spatial moment of the position of particles of species i and j respectively [79,80].…”

Section: Appendix B Remarks On Convergencementioning

confidence: 99%

Dark–bright soliton dynamics beyond the mean-field approximation

et al. 2017

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The dynamics of dark-bright (DB) solitons beyond the mean-field approximation is investigated. We first examine the case of a single DB soliton and its oscillations within a parabolic trap. Subsequently, we move to the setting of collisions, comparing the mean-field approximation to that involving multiple orbitals in both the dark and the bright component. Fragmentation is present and significantly affects the dynamics, especially in the case of slower solitons and in that of lower atom numbers. It is shown that the presence of fragmentation allows for bipartite entanglement between the distinguishable species. Most importantly the interplay between fragmentation and entanglement leads to the splitting of each of the parent mean-field DB solitons, placed off-center within the parabolic trap, into a fast and a slow daughter solitary wave. The latter process is in direct contrast to the predictions of the mean-field approximation. A variety of excitations including DB solitons in multiple (concurrently populated) orbitals is observed. Dark-antidark states and domain-wall-bright soliton complexes can also be observed to arise spontaneously in the beyond mean-field dynamics. that slower solitons and smaller atom numbers result in significant deviations from the mean-field, Gross-Pitaevskii (GP) limit.However, to the best of our knowledge, such studies have not been performed in a systematic fashion in multi-component settings and for associated solitary wave structures. In that light, herein we explore the case of DB solitons and their dynamics, as well as collisions both at and beyond the mean-field limit. To incorporate the quantum fluctuations stemming from the correlations in the DB soliton dynamics, we employ the multi-layer multi-configuration time-dependent Hartree method for bosons (ML-MCTDHB) [47,48] designed for simulating the quantum dynamics of bosonic mixtures. We consider both the oscillation of a single DB solitary wave in a trap, as well as the interaction of two symmetric solitary waves inside a parabolic trap. We compare and contrast the findings of the mean-field case (where a single orbital is effectively used in the dark-and brightcomponents) with cases where multiple orbitals are used. In all cases it is found that the initial mean-field DB solitons split into daughter DB solitary waves, in contrast to the well-known mean-field predictions. The robustness of the presented results is ensured by exploring settings that involve a higher number of orbitals thereby supporting the validity of our approximation and of the observed beyond mean-field excitations (see also appendix B). Within the employed multi-orbital approximation bipartite entanglement (see [49,50] and references therein) between the distinguishable species resulting from the spontaneous fragmentation of the DBs is generally present. More importantly it is the interplay between fragmentation and the resulting entanglement which gives rise to the observed dynamical structures.The dynamics of a single DB soliton being initialized off-ce...

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“…To investigate the frequency spectrum of the breathing mode we employ σ [46][47][48]. For a single interaction quench, it has been shown [14] that σ 2 M (ω) possesses two distinct frequency branches, shown in Fig.…”

Section: B Dominant Intrawell Excitations: the Cradle And The Breathmentioning

confidence: 99%

Quantum dynamical response of ultracold few-boson ensembles in finite optical lattices to multiple interaction quenches

2017

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The correlated non-equilibrium quantum dynamics following a multiple interaction quench protocol for few-bosonic ensembles confined in finite optical lattices is investigated. The quenches give rise to an interwell tunneling and excite the cradle and a breathing mode. Several tunneling pathways open during the time interval of increased interactions, while only a few occur when the system is quenched back to its original interaction strength. The cradle mode, however, persists during and in between the quenches, while the breathing mode possesses dinstinct frequencies. The occupation of excited bands is explored in detail revealing a monotonic behavior with increasing quench amplitude and a non-linear dependence on the duration of the application of the quenched interaction strength. Finally, a periodic population transfer between momenta for quenches of increasing interaction is observed, with a power-law frequency dependence on the quench amplitude. Our results open the possibility to dynamically manipulate various excited modes of the bosonic system.

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Variance as a sensitive probe of correlations

Cited by 54 publications

References 33 publications

MCTDH-X: The multiconfigurational time-dependent Hartree method for indistinguishable particles software

MCTDH-X: The multiconfigurational time-dependent Hartree method for indistinguishable particles software

Dark–bright soliton dynamics beyond the mean-field approximation

Quantum dynamical response of ultracold few-boson ensembles in finite optical lattices to multiple interaction quenches

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