We propose to induce topological defects in particle-hole-symmetric superfluids, with the prime example of the Bardeen-Cooper-Schrieffer state of ultracold atoms, and detect their time evolution and decay. We demonstrate that the time evolution is qualitatively distinct for particle-hole-symmetric superfluids and point out that the dynamics of topological defects is strongly modified in particle-hole-symmetric fluids. We obtain results for different charges and compare them with the standard Gross-Pitaevskii prediction for Bose-Einstein condensates. We highlight the observable signatures of the particle-hole symmetry in the dynamics of decaying solitons and subsequent vortices.
We propose to induce topological defects in particle-hole-symmetric superfluids, with the prime example of the Bardeen-Cooper-Schrieffer state of ultracold atoms, and detect their time evolution and decay. We demonstrate that the time evolution is qualitatively distinct for particle-hole-symmetric superfluids and point out that the dynamics of topological defects is strongly modified in particle-hole-symmetric fluids. We obtain results for different charges and compare them with the standard Gross-Pitaevskii prediction for Bose-Einstein condensates. We highlight the observable signatures of the particle-hole symmetry in the dynamics of decaying solitons and subsequent vortices.
Vortex lattices in rapidly rotating Bose-Einstein condensates are systems of topological excitations that arrange themselves into periodic patterns. Here we show how phase-imprinting techniques can be used to create a controllable number of defects in these lattices and examine the resulting dynamics. Even though we describe our system using the mean-field Gross-Pitaevskii theory, the full range of many-particle effects among the vortices can be studied. In particular we find the existence of localized vacancies that are quasistable over long periods of time and characterize the effects on the background lattice through the use of the orientational correlation function and Delaunay triangulation.
Cold atoms experiments offer invaluable information on superfluid dynamics, including decay cascades of topological defects. While the cascade properties are well established for Bose systems, our understanding of their behavior in Fermi counterparts is very limited, in particular in spin-imbalanced systems, where superfluid (paired) and normal (unpaired) particles naturally coexist giving rise to complex spatial structure of the atomic cloud. Here we show, based on a newly developed microscopic approach, that the decay cascades of topological defects are dramatically modified by the spin polarization. We demonstrate that decay cascades end up at different stages: "dark soliton," "vortex ring," or "vortex line," depending on the polarization. We reveal that it is caused by sucking of unpaired particles into the soliton's internal structure. As a consequence vortex reconnections are hindered and we anticipate that quantum turbulence phenomenon can be significantly affected, indicating new physics induced by polarization effects.
Since its realization in dilute bosonic atomic gases [], [], Bose-Einstein condensation of alkali atoms and hydrogen has been produced and studied extensively in the laboratory [], and has permitted an intriguing glimpse into the macroscopic quantum world. In view of potential applications [], [], [], the study of quantized vortices, which are well-known signatures of superfluidity, is one of the key issues. In fact, bulk superfluids are distinguished from normal fluids by their ability to support dissipationless flow. Such persistent currents are intimately related to the existence of quantized vortices, which are localized phase singularities with integer topological charge []. The superfluid vortex is an example of a topological defect that is well known in superconductors [] and in liquid helium []. The occurrence of quantized vortices in superfluids has been the focus of fundamental theoretical and experimental work []. Different research groups have obtained quantized vortices in Bose-Einstein condensates (BECs) experimentally, e.g., the JILA group [], [], the ENS group [] and the MIT group [], []. Currently, there are at least two typical ways to generate quantized vortices from a BEC ground state: (i) impose a laser beam rotating with an angular velocity on the magnetic trap holding the atoms to create a harmonic anisotropic potential [], [], []; or (ii) add to the stationary magnetic trap a narrow, moving Gaussian potential, representing a far-blue detuned laser [], [], [], [], [], [].
We present a numerical method for generating vortex rings in Bose-Einstein condensates confined in axially symmetric traps. The vortex ring is generated using the line-source approximation for the vorticity, i.e., the curl of the superfluid velocity field is different from zero only on a circumference of a given radius located on a plane perpendicular to the symmetry axis and coaxial with it. The particle density is obtained by solving a modified Gross-Pitaevskii equation that incorporates the effect of the velocity field. We discuss the appearance of density profiles, the vortex core structure, and the vortex nucleation energy, i.e., the energy difference between vortical and ground-state configurations. This is used to present a qualitative description of the vortex dynamics.
We study soliton oscillations in a trapped superfluid Fermi gas across the Bose-Einstein condensate to Bardeen-Cooper-Schrieffer (BEC-BCS) crossover. We derive an exact equation for the oscillation period in terms of observable quantities, which we confirm by solving the time-dependent Bogoliubov-de Gennes equations. Hence we reveal the appearance and dynamics of solitons across the crossover, and show that the period dramatically increases as the soliton becomes shallower on the BCS side of the resonance. Finally, we propose an experimental protocol to test our predictions.
1. Introduce soliton in quasi-one-dimensional time-dependent Gross-Pitaevskii equation. 2. Introduce the basic idea of topology and the homotopy groups. 3. Introduce vortex in spinless condensate as a typical example of topological defect. 4. Introduce the Berezinskii-Kosterlitz-Thouless transition as a topological defect driven phase transition, and emphasize the topological and energy requirements for such a transition. 5. Discuss the geometric configuration that minimizes the energy of a vortex lattice. 6. Introduce the Majorana stellar representation as a useful tool to visualise the symmetry of a high-spin wave function. 7. Introduce two different phases of spin-1 condensate. 8. Introduce the relation between a mean-field state and the singlet pair condensate. 9. Introduce spin vortex and half vortex in spinor condensate, and discuss various possibilities of spin vortex core. 10. Introduce two categories of topological excitations in a Bose condensate, and introduce monopole and skyrmion as the typical example of each category. 11. Introduce simulating Dirac monopole in synthetic magnetic field. 12. Discuss the symmetry of the Hamiltonian and the symmetry of various phases in a spin-orbit coupled BEC. 13. Discuss the relation between symmetry and phase transitions, using spin-orbit coupled condensate as an example. 14. Discuss the Galilean invariance and the superfluid critical velocity.