Variance of an anisotropic Bose-Einstein condensate

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.

Section: Bosons In An Annulus Subject To a Tiltmentioning

confidence: 90%

“…Furthermore, the many-body and mean-field variances do not cross each other, see Fig. 3, indicating that the dynamics is mild and sufficiently close to the ground state manifold of states (compare to [18] with interaction-quench dynamics in a single trap).…”

Section: Bosons In An Annulus Subject To a Tiltmentioning

confidence: 94%

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

2019

Symmetry

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“…x,density = 0.777, 0.748, 0.519 and 1 N ∆ 2 P X = ∆ 2 px,density = 0.329, 0.340, 0.482, whereas at the many-body level we find 1 N ∆ 2X = 0.781, 0.794, 0.927 and 1 N ∆ 2 P X = 0.328, 0.322, 0.272 for the three interactions parameters Λ = −0.018, −0.18, −1.8, respectively. Just like for their repulsive sibling [42,45,48], the variance and density in the ground state of an attractive trapped BEC behave in an opposite manner. In summary, increasing the attraction amounts to enlarging the position variance, despite narrowing of the density, in as much as increasing the repulsion [42,45,48] leads to decreasing of the position variance, in spite of broadening of the density.…”

Section: Ground Statementioning

confidence: 99%

“…The interaction is quenched at t = 0 from Λ = λ 0 (N − 1) = −0.18 to Λ = −0.36. Following the quench of the interaction, the density performs breathing oscillations [45,48,[117][118][119]. The number of particles is N = 10, 100, .…”

Section: Out-of-equilibrium Dynamicsmentioning

confidence: 99%

Attractive Bose-Einstein condensates in anharmonic traps: Accurate numerical treatment and the intriguing physics of the variance

Cederbaum

2018

Chemical Physics

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The dynamics of attractive bosons trapped in one dimensional anharmonic potentials is investigated. Particular emphasis is put on the variance of the position and momentum many-particle operators. Coupling of the center-of-mass and relative-motion degrees-of-freedom necessitates an accurate numerical treatment. The multiconfigurational time-dependent Hartree for bosons (MCT-DHB) method is used, and high convergence of the energy, depletion and occupation numbers, and position and momentum variances is proven numerically. We demonstrate for the ground state and out-of-equilibrium dynamics, for condensed and fragmented condensates, for small systems and en route to the infinite-particle limit, that intriguing differences between the density and variance of an attractive Bose-Einstein condensate emerge. Implications are briefly discussed.

“…We solve the time-dependent many-boson Schrödinger equation presented in Eq. (1) using the MCTDHB method 36,39,40,49,57,58,61,[65][66][67][68][69][70][71][72][73][73][74][75][76][77][78][79][80][81][82] . The method is well documented and applied in the literature 59 .…”

Section: System and Methodologymentioning

confidence: 99%

Impact of the transverse direction on the many-body tunneling dynamics in a two-dimensional bosonic Josephson junction

Bhowmik

Halder

2020

Sci Rep

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Tunneling in a many-body system appears as one of the novel implications of quantum physics, in which particles move in space under an otherwise classically-forbidden potential barrier. Here, we theoretically describe the quantum dynamics of the tunneling phenomenon of a few intricate bosonic clouds in a closed system of a two-dimensional symmetric double-well potential. We examine how the inclusion of the transverse direction, orthogonal to the junction of the double-well, can intervene in the tunneling dynamics of bosonic clouds. We use a well-known many-body numerical method, called the multiconfigurational time-dependent Hartree for bosons (MCTDHB) method. MCTDHB allows one to obtain accurately the time-dependent many-particle wavefunction of the bosons which in principle entails all the information of interest about the system under investigation. We analyze the tunneling dynamics by preparing the initial state of the bosonic clouds in the left well of the double-well either as the ground, longitudinally or transversely excited, or a vortex state. We unravel the detailed mechanism of the tunneling process by analyzing the evolution in time of the survival probability, depletion and fragmentation, and the many-particle position, momentum, and angular-momentum expectation values and their variances. As a general rule, all objects lose coherence while tunneling through the barrier and the states which include transverse excitations do so faster. In particular for the later states, we show that even when the transverse direction is seemingly frozen, prominent many-body dynamics in a two-dimensional bosonic Josephson junction occurs. Implications are briefly discussed.