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arXiv:cond-mat/0701464 · Physical Review Letters

Trapped Fermionic Clouds Distorted from the Trap Shape due to Many-Body Effects

Masudul Haque, Henk T. C. Stoof

Published Jun 29, 2007• 31 citations
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Abstract

We present a general approach for describing trapped Fermi gases, when the cloud shape is distorted with respect to the trap shape. Our approach provides a consistent way to explore physics beyond the local density approximation, if this is necessary due to the distortion. We illustrate this by analyzing in detail experimentally observed distortions in a trapped imbalanced Fermi mixture. In particular, we demonstrate in that case dramatic deviations from ellipsoidal cloud shapes arising from the competition between surface and bulk energies.

DOI
10.1103/physrevlett.98.260406

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We present a general approach for describing trapped Fermi gases, when the cloud shape is distorted with respect to the trap shape. Our approach provides a consistent way to explore physics beyond the local density approximation, if this is necessary due to the distortion. We illustrate this by analyzing in detail experimentally observed distortions in a trapped imbalanced Fermi mixture. In particular, we demonstrate in that case dramatic deviations from ellipsoidal cloud shapes arising from the competition between surface and bulk energies.
Many-body dipolar effects in Fermi gases are quite subtle as they energetically compete with the large kinetic energy at and below the Fermi surface (FS). Recently it was experimentally observed that its FS is deformed from a sphere to an ellipsoid due to the presence of the anisotropic and long-range dipole-dipole interaction. Moreover, it was suggested that, when the dipoles are rotated by means of an external field, the Fermi surface follows their rotation, thereby keeping the major axis of the momentum-space ellipsoid parallel to the dipoles. Here we generalise a previous Hartree-Fock mean-field theory to systems confined in an elongated triaxial trap with an arbitrary orientation of the dipoles relative to the trap. With this we study for the first time the effects of the dipoles' arbitrary orientation on the ground-state properties of the system. Furthermore, taking into account the geometry of the system, we show how the ellipsoidal FS deformation can be reconstructed, assuming ballistic expansion, from the experimentally measurable real-space aspect ratio after a free expansion. We compare our theoretical results with new experimental data measured with erbium Fermi gas for various trap parameters and dipole orientations. The observed remarkable agreement demonstrates the ability of our model to capture the full angular dependence of the FS deformation. Moreover, for systems with even higher dipole moment, our theory predicts an additional unexpected effect: the FS does not simply follow rigidly the orientation of the dipoles but softens showing a change in the aspect ratio depending on the dipoles' orientation relative to the trap geometry, as well as on the trap anisotropy itself. Our theory provides the basis for understanding and interpreting phenomena in which the investigated physics depends on the underlying structure of the FS, such as fermionic pairing and superfluidity.
Many-body dipolar effects in Fermi gases are quite subtle as they energetically compete with the large kinetic energy at and below the Fermi surface (FS).Recently it was experimentally observed in a sample of erbium atoms that its FS is deformed from a sphere to an ellipsoid due to the presence of the anisotropic and long-range dipole-dipole interaction Aikawa et al (2014 Science 345 1484).Moreover, it was suggested that, when the dipoles are rotated by means of an external field, the FS follows their rotation, thereby keeping the major axis of the momentum-space ellipsoid parallel to the dipoles.Here we generalise a previous Hartree-Fock mean-field theory to systems confined in an elongated triaxial trap with an arbitrary orientation of the dipoles relative to the trap.With this we study for the first time the effects of the dipoles' arbitrary orientation on the ground-state properties of the system.Furthermore, taking into account the geometry of the system, we show how the ellipsoidal FS deformation can be reconstructed, assuming ballistic expansion, from the experimentally measurable real-space aspect ratio after a free expansion.We compare our theoretical results with new experimental data measured with erbium Fermi gas for various trap parameters and dipole orientations.The observed remarkable agreement demonstrates the ability of our model to capture the full angular dependence of the FS deformation.Moreover, for systems with even higher dipole moment, our theory predicts an additional unexpected effect: the FS does not simply follow rigidly the orientation of the dipoles, but softens showing a change in the aspect ratio depending on the dipoles' orientation relative to the trap geometry, as well as on the trap anisotropy itself.Our theory provides the basis for understanding and interpreting phenomena in which the investigated physics depends on the underlying structure of the FS, such as fermionic pairing and superfluidity.
It is quite common that several different phases exist simultaneously in a system of trapped quantum gases of ultra-cold atoms. One example is the strongly interacting Fermi gas with two imbalanced spin species, which has received a great deal of attention owing to the possible occurrence of exotic superfluid phases. By using novel numerical techniques and algorithms, we self-consistently solve the Bogoliubov–de Gennes equations, which describe Fermi superfluids in the mean-field framework. From this study, we investigate the novel phases of spin-imbalanced Fermi gases and examine the validity of local density approximation (LDA), which is often invoked in the extraction of bulk properties from experimental measurements within trapped systems. We show how the validity of the LDA is affected by the trapping geometry, the number of atoms and the spin imbalance.