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

Symmetry ◽  
2019 ◽  
Vol 11 (11) ◽  
pp. 1344 ◽  
Author(s):  
Ofir E. Alon
Keyword(s):  
Angular Momentum ◽  
Mean Field ◽  
Interaction Model ◽  
Einstein Condensate ◽  
Two Dimensional ◽  
Bose Einstein Condensate ◽  
Spatial Dimensions ◽  
The Many ◽  
Harmonic Interaction ◽  
Bose Einstein

We analyze, analytically and numerically, the position, momentum, and in particular the angular-momentum variance of a Bose–Einstein condensate (BEC) trapped in a two-dimensional anisotropic trap for static and dynamic scenarios. Explicitly, we study the ground state of the anisotropic harmonic-interaction model in two spatial dimensions analytically and the out-of-equilibrium dynamics of repulsive bosons in tilted two-dimensional annuli numerically accurately by using the multiconfigurational time-dependent Hartree for bosons method. 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.

scholarly journals Morphology of an Interacting Three-Dimensional Trapped Bose–Einstein Condensate from Many-Particle Variance Anisotropy

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1237
Author(s):  
Ofir E. Alon
Keyword(s):  
Angular Momentum ◽  
Wave Packet ◽  
Infinite Number ◽  
Mean Field ◽  
Three Dimensional ◽  
Einstein Condensate ◽  
Many Body ◽  
Bose Einstein Condensate ◽  
Bose Einstein ◽  
Number Of Particles

The variance of the position operator is associated with how wide or narrow a wave-packet is, the momentum variance is similarly correlated with the size of a wave-packet in momentum space, and the angular-momentum variance quantifies to what extent a wave-packet is non-spherically symmetric. We examine an interacting three-dimensional trapped Bose–Einstein condensate at the limit of an infinite number of particles, and investigate its position, momentum, and angular-momentum anisotropies. Computing the variances of the three Cartesian components of the position, momentum, and angular-momentum operators we present simple scenarios where the anisotropy of a Bose–Einstein condensate is different at the many-body and mean-field levels of theory, despite having the same many-body and mean-field densities per particle. This suggests a way to classify correlations via the morphology of 100% condensed bosons in a three-dimensional trap at the limit of an infinite number of particles. Implications are briefly discussed.

scholarly journals Renormalization of the superfluid density in the two-dimensional BCS-BEC crossover

2018 ◽  
Vol 32 (17) ◽  
pp. 1840022 ◽  
Author(s):  
G. Bighin ◽  
L. Salasnich
Keyword(s):  
Field Equation ◽  
Equation Of State ◽  
Mean Field ◽  
Superfluid Density ◽  
Einstein Condensate ◽  
Two Dimensional ◽  
Theoretical Derivation ◽  
Bose Einstein Condensate ◽  
Bose Einstein ◽  
Mean Field Equation

We analyze the theoretical derivation of the beyond-mean-field equation of state for two-dimensional gas of dilute, ultracold alkali-metal atoms in the Bardeen–Cooper–Schrieffer (BCS) to Bose–Einstein condensate (BEC) crossover. We show that at zero temperature our theory — considering Gaussian fluctuations on top of the mean-field equation of state — is in very good agreement with experimental data. Subsequently, we investigate the superfluid density at finite temperature and its renormalization due to the proliferation of vortex–antivortex pairs. By doing so, we determine the Berezinskii–Kosterlitz–Thouless (BKT) critical temperature — at which the renormalized superfluid density jumps to zero — as a function of the inter-atomic potential strength. We find that the Nelson–Kosterlitz criterion overestimates the BKT temperature with respect to the renormalization group equations, this effect being particularly relevant in the intermediate regime of the crossover.

scholarly journals Derivation of the Landau–Pekar Equations in a Many-Body Mean-Field Limit

2021 ◽  
Vol 240 (1) ◽  
pp. 383-417
Author(s):  
Nikolai Leopold ◽  
David Mitrouskas ◽  
Robert Seiringer
Keyword(s):  
Mean Field ◽  
Einstein Condensate ◽  
Back Reaction ◽  
Many Body ◽  
Field Limit ◽  
Mean Field Limit ◽  
Phonon Field ◽  
Bose Einstein Condensate ◽  
Weakly Couple ◽  
Bose Einstein

AbstractWe consider the Fröhlich Hamiltonian in a mean-field limit where many bosonic particles weakly couple to the quantized phonon field. For large particle numbers and a suitably small coupling, we show that the dynamics of the system is approximately described by the Landau–Pekar equations. These describe a Bose–Einstein condensate interacting with a classical polarization field, whose dynamics is effected by the condensate, i.e., the back-reaction of the phonons that are created by the particles during the time evolution is of leading order.

scholarly journals Schemes for loading a Bose Einstein condensate into a two-dimensional dipole trap

2003 ◽  
Vol 5 (2) ◽  
pp. S155-S163 ◽  
Author(s):  
Yves Colombe ◽  
Demascoth Kadio ◽  
Maxim Olshanii ◽  
Brigitte Mercier ◽  
Vincent Lorent ◽  
...  
Keyword(s):  
Einstein Condensate ◽  
Two Dimensional ◽  
Dipole Trap ◽  
Bose Einstein Condensate ◽  
Bose Einstein

scholarly journals Polaron Problems in Ultracold Atoms: Role of a Fermi Sea across Different Spatial Dimensions and Quantum Fluctuations of a Bose Medium

Atoms ◽  
2021 ◽  
Vol 9 (1) ◽  
pp. 18
Author(s):  
Hiroyuki Tajima ◽  
Junichi Takahashi ◽  
Simeon Mistakidis ◽  
Eiji Nakano ◽  
Kei Iida
Keyword(s):  
Spectral Function ◽  
Einstein Condensate ◽  
Three Dimensions ◽  
Quantum Gas ◽  
Many Body ◽  
Bose Einstein Condensate ◽  
Spatial Dimensions ◽  
Three Body ◽  
Bose Einstein ◽  
The Impact

The notion of a polaron, originally introduced in the context of electrons in ionic lattices, helps us to understand how a quantum impurity behaves when being immersed in and interacting with a many-body background. We discuss the impact of the impurities on the medium particles by considering feedback effects from polarons that can be realized in ultracold quantum gas experiments. In particular, we exemplify the modifications of the medium in the presence of either Fermi or Bose polarons. Regarding Fermi polarons we present a corresponding many-body diagrammatic approach operating at finite temperatures and discuss how mediated two- and three-body interactions are implemented within this framework. Utilizing this approach, we analyze the behavior of the spectral function of Fermi polarons at finite temperature by varying impurity-medium interactions as well as spatial dimensions from three to one. Interestingly, we reveal that the spectral function of the medium atoms could be a useful quantity for analyzing the transition/crossover from attractive polarons to molecules in three-dimensions. As for the Bose polaron, we showcase the depletion of the background Bose-Einstein condensate in the vicinity of the impurity atom. Such spatial modulations would be important for future investigations regarding the quantification of interpolaron correlations in Bose polaron problems.

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