scholarly journals Reliability of the Ginzburg–Landau Theory in the BCS-BEC Crossover by Including Gaussian Fluctuations for 3D Attractive Fermions

2021 ◽  
Vol 6 (4) ◽  
pp. 49
Author(s):  
Filippo Pascucci ◽  
Andrea Perali ◽  
Luca Salasnich
Keyword(s):  
Landau Theory ◽  
Landau Equation ◽  
Three Dimensional ◽  
Einstein Condensate ◽  
Unitary Limit ◽  
Ginzburg Landau ◽  
Gaussian Fluctuations ◽  
Bose Einstein Condensate ◽  
Bose Einstein ◽  
Physical Quantities

We calculate the parameters of the Ginzburg–Landau (GL) equation of a three-dimensional attractive Fermi gas around the superfluid critical temperature. We compare different levels of approximation throughout the Bardeen–Cooper–Schrieffer (BCS) to the Bose–Einstein Condensate (BEC) regime. We show that the inclusion of Gaussian fluctuations strongly modifies the values of the Ginzburg–Landau parameters approaching the BEC regime of the crossover. We investigate the reliability of the Ginzburg–Landau theory, with fluctuations, studying the behavior of the coherence length and of the critical rotational frequencies throughout the BCS-BEC crossover. The effect of the Gaussian fluctuations gives qualitative correct trends of the considered physical quantities from the BCS regime up to the unitary limit of the BCS-BEC crossover. Approaching the BEC regime, the Ginzburg–Landau equation with the inclusion of Gaussian fluctuations turns out to be unreliable.

scholarly journals Reliability of the Ginzburg–Landau Theory in the BCS-BEC Crossover by Including Gaussian Fluctuations for 3D Attractive Fermions

2021 ◽  
Author(s):  
Filippo Pascucci ◽  
Andrea Perali ◽  
Luca Salasnich
Keyword(s):  
Landau Theory ◽  
Landau Equation ◽  
Three Dimensional ◽  
Fermi Gas ◽  
Einstein Condensate ◽  
Unitary Limit ◽  
Ginzburg Landau ◽  
Gaussian Fluctuations ◽  
Physical Quantities ◽  
Different Levels

We calculate the parameters of the Ginzburg–Landau (GL) equation of a three-dimensional attractive Fermi gas around the superfluid critical temperature. We compare different levels of approximation throughout the Bardeen–Cooper–Schrieffer (BCS) to the Bose–Einstein Condensate (BEC) regime. We show that the inclusion of Gaussian fluctuations strongly modifies the values of the Ginzburg–Landau parameters approaching the BEC regime of the crossover. We investigate the reliability of the Ginzburg–Landau theory, with fluctuations, studying the behavior of the coherence length and of the critical rotational frequencies throughout the BCS-BEC crossover. The effect of the Gaussian fluctuations gives qualitative correct trends of the considered physical quantities from the BCS regime up to the unitary limit of the BCS-BEC crossover. Approaching the BEC regime, the Ginzburg–Landau equation with the inclusion of Gaussian fluctuations turns out to be unreliable.

Quantum fluctuations in the time-dependent BCS–BEC crossover

2008 ◽  
Vol 366 (1877) ◽  
pp. 2813-2820 ◽  
Author(s):  
B.M Breid ◽  
J.R Anglin
Keyword(s):  
Landau Theory ◽  
Einstein Condensate ◽  
Time Dependent ◽  
Integral Approach ◽  
Saddle Point Approximation ◽  
Ginzburg Landau ◽  
Bose Einstein Condensate ◽  
Fermionic Atoms ◽  
Molecular Fields ◽  
Bose Einstein

We describe the time-dependent formation of a molecular Bose–Einstein condensate from a BCS state of fermionic atoms as a result of slow sweeping through a Feshbach resonance. We apply a path integral approach for the molecules, and use two-body adiabatic approximations to solve the atomic evolution in the presence of the classical molecular fields, obtaining an effective action for the molecules. In the narrow resonance limit, the problem becomes semiclassical, and we discuss the growth of the molecular condensate in the saddle point approximation. Considering this time-dependent process as an analogue of the cosmological Zurek scenario, we compare the way condensate growth is driven in this rigorous theory with its phenomenological description via time-dependent Ginzburg–Landau theory.

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.

scholarly journals Resonant demagnetization of a dipolar Bose-Einstein condensate in a three-dimensional optical lattice

2013 ◽  
Vol 87 (5) ◽  
Author(s):  
A. de Paz ◽  
A. Chotia ◽  
E. Maréchal ◽  
P. Pedri ◽  
L. Vernac ◽  
...  
Keyword(s):  
Optical Lattice ◽  
Three Dimensional ◽  
Einstein Condensate ◽  
Bose Einstein Condensate ◽  
Bose Einstein

scholarly journals Stability analysis of three-dimensional breather solitons in a Bose–Einstein condensate

2005 ◽  
Vol 461 (2063) ◽  
pp. 3561-3574 ◽  
Author(s):  
M Matuszewski ◽  
E Infeld ◽  
G Rowlands ◽  
M Trippenbach
Keyword(s):  
Three Dimensional ◽  
Einstein Condensate ◽  
Dimensional Case ◽  
Two Dimensional ◽  
One Dimensional ◽  
Stability Properties ◽  
Bose Einstein Condensate ◽  
The Stability ◽  
Bose Einstein ◽  
Dimensional Soliton

We investigated the stability properties of breather soliton trains in a three-dimensional Bose–Einstein condensate (BEC) with Feshbach-resonance management of the scattering length. This is done so as to generate both attractive and repulsive interaction. The condensate is confined only by a one-dimensional optical lattice and we consider strong, moderate and weak confinement. By strong confinement we mean a situation in which a quasi two-dimensional soliton is created. Moderate confinement admits a fully three-dimensional soliton. Weak confinement allows individual solitons to interact. Stability properties are investigated by several theoretical methods such as a variational analysis, treatment of motion in effective potential wells, and collapse dynamics. Armed with all the information forthcoming from these methods, we then undertake a numerical calculation. Our theoretical predictions are fully confirmed, perhaps to a higher degree than expected. We compare regions of stability in parameter space obtained from a fully three-dimensional analysis with those from a quasi two-dimensional treatment, when the dynamics in one direction are frozen. We find that in the three-dimensional case the stability region splits into two parts. However, as we tighten the confinement, one of the islands of stability moves toward higher frequencies and the lower frequency region becomes more and more like that for the quasi two-dimensional case. We demonstrate these solutions in direct numerical simulations and, importantly, suggest a way of creating robust three-dimensional solitons in experiments in a BEC in a one-dimensional lattice.

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