scholarly journals Characteristic Length Scale during the Time Evolution of a Turbulent Bose–Einstein Condensate

Symmetry ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 1865
Author(s):  
Lucas Madeira ◽  
Arnol D. García-Orozco ◽  
Michelle A. Moreno-Armijos ◽  
Francisco Ednilson Alves dos dos Santos ◽  
Vanderlei S. Bagnato
Keyword(s):  
Time Evolution ◽  
Quantum Turbulence ◽  
Characteristic Length ◽  
Three Dimensional ◽  
Einstein Condensate ◽  
Length Scale ◽  
Characteristic Length Scale ◽  
Bose Einstein Condensate ◽  
Momentum Distributions ◽  
Bose Einstein

Quantum turbulence is characterized by many degrees of freedom interacting non-linearly to produce disordered states, both in space and in time. In this work, we investigate the decaying regime of quantum turbulence in a trapped Bose–Einstein condensate. We present an alternative way of exploring this phenomenon by defining and computing a characteristic length scale, which possesses relevant characteristics to study the establishment of the quantum turbulent regime. We reconstruct the three-dimensional momentum distributions with the inverse Abel transform, as we have done successfully in other works. We present our analysis with both the two- and three-dimensional momentum distributions, discussing their similarities and differences. We argue that the characteristic length allows us to intuitively visualize the time evolution of the turbulent state.

scholarly journals Characteristic Length Scale during the Time Evolution of a Turbulent Bose-Einstein Condensate

2021 ◽  
Author(s):  
Lucas Madeira ◽  
Arnol D. García-Orozco ◽  
Michelle A. Moreno-Armijos ◽  
Francisco Ednilson Alves dos Santos ◽  
Vanderlei S. Bagnato
Keyword(s):  
Time Evolution ◽  
Quantum Turbulence ◽  
Characteristic Length ◽  
Three Dimensional ◽  
Einstein Condensate ◽  
Length Scale ◽  
Turbulent Regime ◽  
Characteristic Length Scale ◽  
Momentum Distributions ◽  
Bose Einstein

Quantum turbulence is characterized by many degrees of freedom interacting non-linearly to produce disordered states, both in space and time. The advances in trapping, cooling, and tuning the interparticle interactions in atomic Bose-Einstein condensates (BECs) make them excellent candidates for studying quantum turbulence. In this work, we investigate the decaying regime of quantum turbulence in a trapped BEC. Although much progress has been made in understanding quantum turbulence, other strategies are needed to overcome some intrinsic difficulties. We present an alternative way of investigating this phenomenon by defining and computing a characteristic length scale, which possesses relevant characteristics to study the establishment of the quantum turbulent regime. One intrinsic difficulty related to these systems is that absorption images of BECs are projected to a plane, thus eliminating some of the information present in the original momentum distribution. We overcome this difficulty by exploring the symmetry of the cloud, which allows us to reconstruct the three-dimensional momentum distributions with the inverse Abel transform. We present our analysis with both the two- and three-dimensional momentum distributions, discussing their similarities and differences. We argue that the characteristic length allows us to visualize the time evolution of the turbulent state intuitively.

λ-Transition to the Bose-Einstein Condensate

1995 ◽  
Vol 50 (10) ◽  
pp. 921-930 ◽  
Author(s):  
Siegfried Grossmann ◽  
Martin Holthaus
Keyword(s):  
Heat Capacity ◽  
Three Dimensional ◽  
Einstein Condensate ◽  
Einstein Condensation ◽  
Condensation Temperature ◽  
Harmonic Oscillator Potential ◽  
Bose Einstein Condensate ◽  
Bose Einstein ◽  
Analytical Expressions ◽  
Grand Canonical

Abstract We study Bose-Einstein condensation of comparatively small numbers of atoms trapped by a three-dimensional harmonic oscillator potential. Under the assumption that grand canonical statis­tics applies, we derive analytical expressions for the condensation temperature, the ground state occupation, and the specific heat capacity. For a gas of TV atoms the condensation temperature is proportional to N1/3, apart from a downward shift of order N-1/3. A signature of the condensation is a pronounced peak of the heat capacity. For not too small N the heat capacity is nearly discon­tinuous at the onset of condensation; the magnitude of the jump is about 6.6 N k. Our continuum approximations are derived with the help of the proper density of states which allows us to calculate finite-AT-corrections, and checked against numerical computations.

scholarly journals Three-Dimensional Skyrmions with Arbitrary Topological Number in a Ferromagnetic Spin-1 Bose-Einstein Condensate

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Huan-Bo Luo ◽  
Lu Li ◽  
Wu-Ming Liu
Keyword(s):  
Magnetic Field ◽  
Vortex Ring ◽  
Three Dimensional ◽  
Einstein Condensate ◽  
Laser Beams ◽  
Quantization Axis ◽  
Density Distributions ◽  
Bose Einstein Condensate ◽  
Bose Einstein ◽  
Topological Number

AbstractWe propose a new scheme for creating three-dimensional Skyrmions in a ferromagnetic spin-1 Bose-Einstein condensate by manipulating a multipole magnetic field and a pair of counter-propagating laser beams. The result shows that a three-dimensional Skyrmion with topological number Q = 2 can be created by a sextupole magnetic field and the laser beams. Meanwhile, the vortex ring and knot structure in the Skyrmion are found. The topological number can be calculated analytically in our model, which implies that the method can be extended to create Skyrmions with arbitrary topological number. As the examples, three-dimensional Skyrmions with Q = 3, 4 are also demonstrated and are distinguishable by the density distributions with a specific quantization axis. These topological objects have the potential to be realized in ferromagnetic spin-1 Bose-Einstein condensates experimentally.

scholarly journals IDEAL-MODIFIED BOSONIC GAS TRAPPED IN AN ARBITRARY THREE-DIMENSIONAL POWER-LAW POTENTIAL

2012 ◽  
Vol 27 (31) ◽  
pp. 1250181 ◽  
Author(s):  
E. CASTELLANOS ◽  
C. LÄMMERZAHL
Keyword(s):  
Dispersion Relation ◽  
Power Law ◽  
Three Dimensional ◽  
Particle Dispersion ◽  
Einstein Condensate ◽  
Gravity Models ◽  
Condensation Temperature ◽  
Bose Einstein Condensate ◽  
Bose Einstein ◽  
Number Of Particles

We analyze the effects caused by an anomalous single-particle dispersion relation suggested in several quantum-gravity models, upon the thermodynamics of a Bose–Einstein condensate trapped in a generic three-dimensional power-law potential. We prove that the shift in the condensation temperature, caused by a deformed dispersion relation, described as a non-trivial function of the number of particles and the shape associated to the corresponding trap, could provide bounds for the parameters associated to such deformation. In addition, we calculate the fluctuations in the number of particles as a criterium of thermodynamic stability for these systems. We show that the apparent instability caused by the anomalous fluctuations in the thermodynamic limit can be suppressed considering the lowest energy associated to the system in question.

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