Spectral Structure and Many-Body Dynamics of Ultracold Bosons in a Double-Well

Schäfer, Frank; Bastarrachea-Magnani, Miguel A.; Lode, Axel U. J.; Parny, Laurent de Forges de; Buchleitner, Andreas

doi:10.3390/e22040382

Cited by 5 publications

(2 citation statements)

References 90 publications

(185 reference statements)

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“…(ii) With a fast and non-adiabatic change of parameters in the Hamiltonian, excitations are inevitably triggered. Such a quench thus may result in a finite occupation of a large number of eigenstates of the final Hamiltonian [103]. To investigate these two scenarios, we now discuss two examples where the system contains N=5 or N=6 weakly-interacting bosons or fermions.…”

Section: Dynamical Behaviormentioning

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: Dynamical Behaviormentioning

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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show abstract

“…For illustration, we remark that the nodes can 'draw' whimsical patterns in the profile of the probability density |ψ j (x 1 , • • • , x N | 2 , see figures 5 and 6 in [42].…”

Section: Any Other Collection {N J } Does Not Correspond To the Ideal...mentioning

confidence: 99%

Exact crystalline solution for a one-dimensional few-boson system with point interaction

Tomchenko¹

2022

J. Phys. A: Math. Theor.

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We study the exact solutions for a one-dimensional system of $N=2; 3$ spinless point bosons for zero boundary conditions. In this case, we are based on M. Gaudin's formulae obtained with the help of Bethe ansatz. We find the density profile $\rho(x)$ and the nodal structure of a wave function for a set of the lowest states of the system for different values of the coupling constant $\gamma\geq 0$. The analysis shows that the ideal crystal corresponds to the quantum numbers (from Gaudin's equations) $n_{1}=\ldots =n_{N}=N$ and to the coupling constant $\gamma\lsim 1$. We also find that the ground state of the system ($n_{1}=\ldots =n_{N}=1$) corresponds to a liquid for any $\gamma$ and any $N\gg 1$. In this case, the wave function of the ground state is nodeless, and the wave function of the ideal crystal has nodes.

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MCTDH-X: The Multiconfigurational Time-Dependent Hartree Method for Indistinguishable Particles High-Performance Computation Project

Lode

Alon

Bastarrachea-Magnani

et al. 2021

High Performance Computing in Science and Engineering '20

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Spectral Structure and Many-Body Dynamics of Ultracold Bosons in a Double-Well

Cited by 5 publications

References 90 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

Exact crystalline solution for a one-dimensional few-boson system with point interaction

MCTDH-X: The Multiconfigurational Time-Dependent Hartree Method for Indistinguishable Particles High-Performance Computation Project

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