Role of Excited States in the Splitting of a Trapped Interacting Bose-Einstein Condensate by a Time-Dependent Barrier

Streltsov, Alexej I.; Alon, Ofir E.; Cederbaum, Lorenz S.

doi:10.1103/physrevlett.99.030402

Cited by 203 publications

(302 citation statements)

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“…Explicitly carrying out the variation (A3) leads to a coupled system of ordinary differential equations for the time-dependent coefficients C(t) and non-linear partial integro-differential equations for the time-dependent orbitals |φ j (t) , the MCTDHB equations of motion [31][32][33].…”

Section: Discussionmentioning

confidence: 99%

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

et al. 2013

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Following a 'bottom-up approach' in understanding many-particle effects and dynamics we provide a systematic ab initio study of the dependence of the breathing dynamics of ultracold bosons in a 1D harmonic trap on the number of bosons ranging from few to many. To this end, we employ (2013)]. The beating behavior for two bosons is found numerically and consequently explained by an analytical approach. Drawing on this, we show how to compute the complete breathing mode spectrum in this case. We examine how the two-mode breathing behavior of two bosons evolves to the single-frequency behavior of the many-particle limit when adding more particles. In the limit of many particles, we numerically study the dependence of the breathing mode frequency on both the interaction strength as well as on the particle number. We provide an estimate for the parameter region where the mean-field description provides a valid approximation.

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Section: Discussionmentioning

confidence: 99%

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

et al. 2013

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“…a time-independent basis. When applied to a single bosonic species only, ML-MCTDHB reduces to the Multi-Configuration TimeDependent Hartree Method for Bosons (MCTDHB), which was firstly introduced in [52,53]. In this case, the total wave function |Ψ t is expanded with respect to bosonic number states |n 1 , ..., n M t being based on time-dependent single-particle functions (SPFs) |φ i (t) , i = 1, ..., M : |Ψ t = n|N A n1,...,n M (t)|n 1 , ..., n M t , where n = (n 1 , ..., n M ) encodes the occupation numbers of the M SPFs and n|N indicates that the summation runs over all occupation numbers n i that sum up to N .…”

Section: B Computational Methodsmentioning

confidence: 99%

Many-body processes in black and gray matter-wave solitons

Krönke

Schmelcher

2015

Phys. Rev. A

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We perform a comparative beyond mean-field study of black and grey solitonic excitations in a finite ensemble of ultracold bosons confined to a one-dimensional box. An optimized densityengineering potential is developed and employed together with phase-imprinting to cleanly initialize grey solitons. Based on our recently developed Multi-Layer Multi-Configuration Time-Dependent Hartree Method for Bosons, we demonstrate that quantum fluctuations limit the lifetime of the soliton contrast, which prolongs with increasing soliton velocity. A natural orbital analysis reveals a two-stage process underlying the decay of the soliton contrast. The broken parity symmetry of grey solitons results in a local asymmetry of the orbital mainly responsible for the decay, which leads to a characteristic asymmetry of remarkably localized two-body correlations. The emergence and decay of these correlations as well as their displacement from the instantaneous soliton position are analysed in detail. Finally, the role of phase-imprinting for the many-body dynamics is illuminated and additional non-local correlations in pairs of counter-propagating grey solitons are unravelled.

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“…[7][8][9][10][11][12][13][14][15][16][17][18][19][20][21]. It is a common practice that in order to produce a fragmented BEC in the splitting process, the ground state must be fragmented.…”

mentioning

confidence: 99%

“…A suitable platform to study the many-body time evolution of trapped BECs is provided by the multiconfigurational time-dependent Hartree for bosons (MCTDHB) method [18,39]. The MCTDHB method has been shown to produce accurate many-body solutions in various applications [19,[40][41][42][43][44], and is well documented in the literature [45,46].…”

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confidence: 99%

Breaking the resilience of a two-dimensional Bose-Einstein condensate to fragmentation

et al. 2014

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A two-dimensional Bose-Einstein condensate (BEC) split by a radial potential barrier is investigated. We determine on an accurate many-body level the system's ground-state phase diagram as well as a time-dependent phase diagram of the splitting process. Whereas the ground state is condensed for a wide range of parameters, the time-dependent splitting process leads to substantial fragmentation. We demonstrate for the first time the dynamical fragmentation of a BEC despite its ground state being condensed. The results are analyzed by a mean-field model and suggest that a large manifold of low-lying fragmented excited states can significantly impact the dynamics of trapped two-dimensional BECs. [4][5][6]. While three-dimensional trapped BECs have been extensively studied since their discovery, the static and time-dependent properties of their two-dimensional counterparts are comparatively less explored.One of the most popular scenarios studied with ultracold bosonic atoms, both experimentally and theoretically, is the splitting of a BEC by a central barrier into two spatially-disjoint clouds, e.g., Refs. [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21]. It is a common practice that in order to produce a fragmented BEC in the splitting process, the ground state must be fragmented. This renders high barriers and strong interaction strengths necessary. Previous works dealt with splitting of a BEC in one or three spatial dimensions. To the best of our knowledge, splitting of a BEC in two spatial dimensions has not been explored experimentally or theoretically on the many-body level.In the present work we investigate theoretically, on an accurate many-body level, the physics of splitting a twodimensional (2D) BEC. A natural approach is to exploit the 2D symmetry of the system. We thus split a circular BEC by a radial potential barrier, see Fig. 1a for an illustration. This would lead to two concentric clouds, unlike the above-discussed common way of splitting a BEC and, as we shall see below, enrich the physics of BEC splitting.By analyzing the many-body time-independent and time-dependent wavefunctions of the system, we construct both static and dynamic phase diagrams of the splitting process. Whereas the ground state is condensed for a wide range of parameters, the time-dependent splitting process leads to substantial fragmentation. We therefore demonstrate the dynamical fragmentation of a BEC, despite its ground state being fully condensed. The results imply that a large manifold of fragmented excited states can significantly impact the dynamics of 2D BECs.We consider a repulsive BEC with N = 100 bosons in the 2D circular trap shown in Fig. 1a. Throughout this work dimensionless units are used, such that the single-particle kinetic-energy operator readsT (r) = − 1 2 ∇ 2 r [22]. The explicit form of the one-body potential is given by V (r) = V trap (r) + V barrier (r). Here V trap (r) = {200e −(r−rc) 4 /2 , r ≤ r c = 9; 200, r > r c } is a flat trap which has the shape of "a crater" and V barrier (r) = 200e ...

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Role of Excited States in the Splitting of a Trapped Interacting Bose-Einstein Condensate by a Time-Dependent Barrier

Cited by 203 publications

References 19 publications

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

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

Many-body processes in black and gray matter-wave solitons

Breaking the resilience of a two-dimensional Bose-Einstein condensate to fragmentation

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