Rotating Bose-Einstein condensates: Closing the gap between exact and mean-field solutions

Cremon, Jonas; Jackson, A.D.; Karabulut, Elife; Kavoulakis, G. M.; Mottelson, Ben R.; Reimann, S. M.

doi:10.1103/physreva.91.033623

Cited by 14 publications

(8 citation statements)

References 55 publications

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“…In References [ 62 , 68 , 69 , 85 , 87 , 88 , 93 , 94 , 95 , 96 , 97 ], an intricate connection of angular momentum content and the presence of correlations or the fragmentation of many-boson states has been pointed out. This motivates us to analyze the time-evolution of the eigenvalues of the reduced one-body density matrix as a precursor of correlations and the departure of the analyzed state from a mean-field description; we, thus, underpin the limitations of a mean-field description, see Figure 4 for a plot of

as a function of time and strength B of the AMF.…”

Section: Resultsmentioning

confidence: 99%

Dynamics of Ultracold Bosons in Artificial Gauge Fields—Angular Momentum, Fragmentation, and the Variance of Entropy

Lode

Dutta

Lévêque

2021

Entropy

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We consider the dynamics of two-dimensional interacting ultracold bosons triggered by suddenly switching on an artificial gauge field. The system is initialized in the ground state of a harmonic trapping potential. As a function of the strength of the applied artificial gauge field, we analyze the emergent dynamics by monitoring the angular momentum, the fragmentation as well as the entropy and variance of the entropy of absorption or single-shot images. We solve the underlying time-dependent many-boson Schrödinger equation using the multiconfigurational time-dependent Hartree method for indistinguishable particles (MCTDH-X). We find that the artificial gauge field implants angular momentum in the system. Fragmentation—multiple macroscopic eigenvalues of the reduced one-body density matrix—emerges in sync with the dynamics of angular momentum: the bosons in the many-body state develop non-trivial correlations. Fragmentation and angular momentum are experimentally difficult to assess; here, we demonstrate that they can be probed by statistically analyzing the variance of the image entropy of single-shot images that are the standard projective measurement of the state of ultracold atomic systems.

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as a function of time and strength B of the AMF.…”

Section: Resultsmentioning

confidence: 99%

Dynamics of Ultracold Bosons in Artificial Gauge Fields—Angular Momentum, Fragmentation, and the Variance of Entropy

Lode

Dutta

Lévêque

2021

Entropy

View full text Add to dashboard Cite

show abstract

“…In Refs. [58,65,66,81,83,84,[88][89][90][91][92], an intricate connection of angular momentum content and the presence of correlations or the fragmentation of many-boson states has been pointed out. This motivates us to analyze the time-evolution of the eigenvalues of the reduced one-body density matrix as a precursor of correlations and the departure of the analyzed state from a mean-field description; we, thus, underpin the limitations of a mean-field description, see Fig.…”

Section: Resultsmentioning

confidence: 99%

Dynamics of Ultracold Bosons in Artificial Gauge Fields: Angular Momentum, Fragmentation, and the Variance of Entropy

Lode,

Dutta,

Lévêque

2020

Preprint

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We consider the dynamics of two-dimensional interacting ultracold bosons triggered by suddenly switching on an artificial gauge field. The system is initialized in the ground state of a harmonic trapping potential. As a function of the strength of the applied artificial gauge, we analyze the emergent dynamics by monitoring the angular momentum, the fragmentation as well the entropy and variance of the entropy of absorption or single-shot images. We solve the underlying time-dependent many-boson Schrödinger equation using the multiconfigurational time-dependent Hartree method for indistinguishable particles (MCTDH-X). We find that the artificial gauge field implants angular momentum in the system. Fragmentation -multiple macroscopic eigenvalues of the reduced one-body density matrix -emerges in sync with the dynamics of angular momentum: the bosons in the many-body state develop non-trivial correlations. Fragmentation and angular momentum are experimentally difficult to assess; here, we demonstrate that they can be probed by statistically analyzing the variance of the image entropy of single-shot images that are the standard projective measurement of the state of ultracold atomic systems.

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“…Computations employing a many-body description arerather rare. An examples is the analysis of the yrast spectra in a harmonic confinement obtained by exact diagonalization using the lowest Landau level approximation [203,204,202,205].…”

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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Rotating Bose-Einstein condensates: Closing the gap between exact and mean-field solutions

Cited by 14 publications

References 55 publications

Dynamics of Ultracold Bosons in Artificial Gauge Fields—Angular Momentum, Fragmentation, and the Variance of Entropy

Dynamics of Ultracold Bosons in Artificial Gauge Fields—Angular Momentum, Fragmentation, and the Variance of Entropy

Dynamics of Ultracold Bosons in Artificial Gauge Fields: Angular Momentum, Fragmentation, and the Variance of Entropy

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

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