<i>Colloquium</i>
: Multiconfigurational time-dependent Hartree approaches for indistinguishable particles

Lode, Axel U. J.; Lévêque, Camille; Madsen, Lars Bojer; Streltsov, Alexej I.; Alon, Ofir E.

doi:10.1103/revmodphys.92.011001

Cited by 119 publications

(106 citation statements)

References 225 publications

(317 reference statements)

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“…To compute the time-dependent many-boson wavefunction we use the multiconfigurational time-dependent Hartree for bosons (MCTDHB) method [67][68][69]. MCTDHB represents the wavefunction as a variationally-optimal ansatz which is a linear-combination of all time-dependent permanents generated by distributing the N bosons over M time-adaptive orbitals.…”

Section: Bosons In An Annulus Subject To a Tiltmentioning

confidence: 99%

Analysis of a Trapped Bose–Einstein Condensate in Terms of Position, Momentum, and Angular-Momentum Variance

Alon

2019

Symmetry

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We analyze, analytically and numerically, the position, momentum, and in particular the angularmomentum variance of a Bose-Einstein condensate (BEC) trapped in a two-dimensional anisotropic trap for static and dynamic scenarios. The differences between the variances at the mean-field level, which are attributed to the shape of the BEC, and the variances at the many-body level, which incorporate depletion, are used to characterize position, momentum, and angular-momentum correlations in the BEC for finite systems and at the limit of an infinite number of particles where the bosons are 100% condensed. Finally, we also explore inter-connections between the variances.

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Section: Bosons In An Annulus Subject To a Tiltmentioning

confidence: 99%

Analysis of a Trapped Bose–Einstein Condensate in Terms of Position, Momentum, and Angular-Momentum Variance

Alon

2019

Symmetry

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“…The time-dependent many-boson Schrödinger equation has been solved by an in-principle numerically exact many-body method, called the multi-configurational time-dependent Hartree method for bosons (MCTDHB), [74][75][76] which has been developed by our group and benchmarked with an exactly-solvable model [77,78]. This method has already been extensively used in the literature [47,50,70,[79][80][81][82][83][84][85][86][87][88].…”

Section: Theoretical Frameworkmentioning

confidence: 99%

Many-body quantum dynamics of an asymmetric bosonic Josephson junction

Haldar

Alon

2019

New J. Phys.

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The out-of-equilibrium quantum dynamics of an interacting Bose gas trapped in a one-dimensional asymmetric double-well potential is studied by solving the many-body Schrödinger equation numerically accurately. We examine how the gradual loss of symmetry of the confining trap affects the macroscopic quantum tunneling dynamics of the system between the two wells. In an asymmetric double well, the two wells are not equivalent anymore, say, the left well is deeper than the right one. Accordingly, we analyze the dynamics by initially preparing the condensate in both the left and the right wells. The dynamics of the system is characterized by the time evolution of a few physical quantities of increasing many-body complexity, namely, the survival probability, depletion and fragmentation, and the many-particle position and momentum variances. In particular, we have examined the frequencies and amplitudes of the oscillations of the survival probabilities, the time scale for the development of fragmentation and its degree, and the growth and oscillatory behavior of the many-particle position and momentum variances. There is an overall suppression of the oscillations of the survival probabilities in an asymmetric double well, except for resonant values of asymmetry for which the one-body ground state energy in the right well matches with one of the one-body excited states in the left well, thereby resulting in resonantly enhanced tunneling from the right well ground state. Overall, depending on whether the condensate is initially prepared in the left or right well, the repulsive inter-atomic interactions affect the survival probabilities differently. For a sufficiently strong repulsive interaction, the system is found to become fragmented. The degree of fragmentation depends both on the asymmetry of the trap and the initial well in which the condensate is prepared in a non-trivial manner. Furthermore, we show that the phenomenon of resonantly enhanced tunneling can be accompanied by a large degree of fragmentation (depletion) for the strong (weak) interaction. The many-particle position and momentum variances follow the density oscillations of the system in the asymmetric double well and bears prominent signatures of the degree of depletion or fragmentation, depending on the strength of the interactions. These quantities further exhibit a fine structure signifying a breathing-mode oscillation. Finally, a universality of fragmentation for systems made of different numbers of particles but the same interaction parameter is also found and its dependence on the asymmetry is investigated. The phenomenon is robust despite the asymmetry of the junction and admits a macroscopically-large fragmented condensate characterized by a diverging many-particle position variance. This is as far as one can get from the dynamics of the density in the junction.recently. This has opened a whole new research field of strongly correlated systems with potential applications in quantum technology and quantum simulation of condensed-matter problems [...

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“…using the MCTDHB approach [20,21], open-source software available at http://ultracold.org. The MCTDHB and MCTDHB-based approximations [22][23][24][25] were successfully applied to study the out-of-equilibrium dynamics of bosonic systems [26][27][28][29][30][31][32][33][34][35][36], see Reference [37] for a review and Reference [38] for a direct comparison of MCTDHB with experimental data using so-called single-shot simulations [39][40][41][42][43][44]. In this work, we use the MCTDHB method as implemented in the MCTDH-X package [45][46][47].…”

Section: Numerical Approachmentioning

confidence: 99%

Fidelity and Entropy Production in Quench Dynamics of Interacting Bosons in an Optical Lattice

et al. 2019

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We investigate the dynamics of a few bosons in an optical lattice induced by a quantum quench of a parameter of the many-body Hamiltonian. The evolution of the many-body wave function is obtained by solving the time-dependent many-body Schrödinger equation numerically, using the multiconfigurational time-dependent Hartree method for bosons (MCTDHB). We report the time evolution of three key quantities, namely, the occupations of the natural orbitals, that is, the eigenvalues of the one-body reduced density matrix, the many-body Shannon information entropy, and the quantum fidelity for a wide range of interactions. Our key motivation is to characterize relaxation processes where various observables of an isolated and interacting quantum many-body system dynamically converge to equilibrium values via the quantum fidelity and via the production of many-body entropy. The interaction, as a parameter, can induce a phase transition in the ground state of the system from a superfluid (SF) state to a Mott-insulator (MI) state. We show that, for a quench to a weak interaction, the fidelity remains close to unity and the entropy exhibits oscillations. Whereas for a quench to strong interactions (SF to MI transition), the relaxation process is characterized by the first collapse of the quantum fidelity and entropy saturation to an equilibrium value. The dip and the non-analytic nature of quantum fidelity is a hallmark of dynamical quantum phase transitions. We quantify the characteristic time at which the quantum fidelity collapses and the entropy saturates.

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Colloquium : Multiconfigurational time-dependent Hartree approaches for indistinguishable particles

Cited by 119 publications

References 225 publications

Analysis of a Trapped Bose–Einstein Condensate in Terms of Position, Momentum, and Angular-Momentum Variance

Analysis of a Trapped Bose–Einstein Condensate in Terms of Position, Momentum, and Angular-Momentum Variance

Many-body quantum dynamics of an asymmetric bosonic Josephson junction

Fidelity and Entropy Production in Quench Dynamics of Interacting Bosons in an Optical Lattice

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