Session D43: Focus Session: Vortices and Vortex Lattices in Fermi and Bose Superfluid Gases

Hardcore Bosons in a Rotating Lattice

Two of the most important themes in the developing area of quantum fluids and ultracold gases include the role of strong interactions and highly correlated effects. We study a novel and interesting problem combining these two key areas by looking at the experimentally relevant area of ultracold atoms in rotating optical lattices. This merges the effects of strong interactions generated by the lattice with the intriguing quantum effects present in the analogy of the quantum Hall effect at high rotation rate. Hardcore bosons in a 2D rotating square lattice are investigated via a modified Bose-Hubbard Hamiltonian. Our results show quantization of circulation and potential phase transitions between circulation values in which the symmetry of the ground state changes structure abruptly as a function of rotation.   

Vortex lattice melting in a stack of Bose Einstein Condensates

The observation of fractional Quantum Hall liquids in rapidly rotating ultracold Bose gases is a long desired goal. Until now the experimentally accessible ratio of the numbers of particles to the number of vortices is far too high to melt the vortex lattice and to observe these states. This can be solved by means of an one-dimensional optical lattice, which divides the condensate in a stack of two-dimensional condensates in which the number of particles is strongly reduced and the quantum fluctuations are enhanced. We study the melting of a vortex lattice in such a configuration by calculating the quantum fluctuations around the classical Abricosov lattice for realistic numbers of particles and vortices. We find that the fluctuations are inhomogeneous and the lattice melts from outward to inward. Coupling neigbouring pancakes by tunneling reduces the anharmonicity as well as the size of the fluctuations and brings in the 3D regime.   

Virial theorems and vortex states in confined Bose-Einstein condensates

We derive a class of virial theorems which provide stringent tests of both analytical and numerical calculations of vortex states in a confined Bose-Einstein condensate. In the special case of harmonic confinement we arrive at the surprising conclusion that the linear moments of the particle density, as well as the linear momentum, must vanish even in the presence of off-center vortices which lack axial or reflection symmetry. The effect of anharmonic confinement is also discussed. Two types of non-axisymmetric vortices have been observed to precess around the center of the condensate and they are refered to as the S-vortex and the U-vortex. We study numerically (Gross-Pitaevskii equation) and theoretically a single vortex in spherical and elongated condensates as a function of the interaction strength. For a given angular momentum the S-vortex has smaller precession frequency and a higher energy than the U-vortex in a rotating elongated condensate. We show that the S-vortex is related to the solitonic vortex and also to the dark soliton which are nonlinear excitations in the nonrotating system. In the dilute limit a lowest Landau level calculation provides an analytic description of these vortex modes. (Phys. Rev. A 72, 053609 (2005), Phys. Rev. A 72, 053624 (2005))   

Observation of High-Temperature Superfluidity in a Gas of Fermionic Atoms

Ultracold quantum degenerate Fermi gases provide a remarkable opportunity to study strongly interacting fermions. In contrast to other Fermi systems, such as superconductors, neutron stars or the quark-gluon plasma of the early Universe, these gases have low densities and their interactions can be precisely controlled over an enormous range. A major goal has been the realization of superfluidity in a gas of fermions. Our observation of vortex lattices in a strongly interacting rotating Fermi gas provide definitive evidence for superfluidity. By varying the binding energy between fermion pairs, we have studied the crossover from a Bose--Einstein condensate of molecules to a Bardeen-Cooper-Schrieffer superfluid of loosely bound pairs. The crossover is associated with a new form of superfluidity. The observed transition temperatures normalized for the density of the gas by far exceed the highest transition temperatures achieved in high-Tc superconductors. Recently, we have extended those studies to interacting Fermi gases with imbalanced spin populations and observed a quantum phase transition at a critical imbalance, which is the Pauli limit of superfluidity.   

Vortex lattice formation in Bose-condensed gases in rotating potentials

We study vortex lattice formation in trapped Bose-condensed gases in various types of rotating potentials by solving the time-dependent Gross-Pitaevskii equation. We discuss the detailed characteristics of the formation dynamics and the structure of vortex lattices depending on the geometry of rotating potentials.   

Vortex Structure and Dynamics in Fermi Superfluid Gas

In order to study a universal structure of the quantized vortex in Fermi superfluid Gas, we numerically calculate the generalized Bogoliubov de Gennes equation derived from the fermion-boson model and clarify how the vortex structure changes through the BCS-BEC crossover. In the numerical calculations, we concentrate on a singly quantized vortex and compare the structure for both the narrow and the broad Feshbach resonance. Numerical calculation results reveal that in the BEC regime the matter density depression at the vortex core is complete while in the BCS regime the depression at the vortex core is relatively obscure. This feature is qualitatively common for both the narrow and broad Feshbach resonances, while in profiles of the molecular boson condensate the narrow and broad cases differ. In the broad case, the profile of the molecular boson condensate is quite similar to that of the fermionic superfluid gap. In addition, we show quasi-particle spectra from BCS to BEC for both Feshbach resonance cases. The number of the low-lying quasi-particle excitations localized inside the vortex core drastically decreases as one goes to the BEC regime. This result indicates that an origin of the vortex dissipation alters between BCS and BEC.   

Critical Current, Vortices and Fermionic Bound States in the BEC to BCS Crossover

We have analyzed a single vortex at $T=0$ in a 3D superfluid atomic Fermi gas across a Feshbach resonance[1] using a fully self-consistent Bogoliubov-deGennes approach. From the current flow around a vortex we conclude that unitarity ($a_s = \infty$) is the most robust superfluid state in the entire BCS-BEC crossover, with the highest critical velocity $v_c$ of about $0.1v_F$. On either side of unitarity, $v_c$ decreases. It is determined by pair breaking on the BCS side and by collective excitations in the BEC regime. In the BCS limit, the order parameter near the vortex core shows a variation on both the scale of $k_{F}^{-1}$ and of the coherence length $\xi$, while away from the BCS limit only a variation on the scale of $\xi$ is seen. The density in the core rises quadratically with radial distance and is progressively depleted as one moves from BCS to BEC. The number of fermionic bound states in the core decreases as we move from the BCS to BEC regime. Remarkably, a bound state branch persists even on the BEC side reflecting the composite nature of bosonic molecules.\newline [1] R. Sensarma, M. Randeria and T.L. Ho, cond-mat/0510761   

Ground state description of a single vortex in an atomic Fermi gas: From BCS to Bose-Einstein condensation

We use a Bogoliubov-de Gennes (BdG) formulation to describe a single vortex in a neutral fermionic gas. It is presumed that the attractive pairing interaction can be arbitrarily tuned to exhibit a crossover from BCS to Bose-Einstein condensation. Our starting point is the BCS-Leggett mean field ground state for which a BdG approach is microscopically justified. At strong coupling, we demonstrate that this approach is analytically equivalent to the Gross-Pitaevskii description of vortices in true bosonic systems. We analyze the sizable density depletion found for the unitary regime and relate it to the presence of unoccupied (positive energy) quasi-bound states at the core center.\\ Reference: arXiv:cond-mat/0510647   

Fermionic Paired Superfluids at High Rotation Rate

I will describe our recent work on rotating resonantly-paired superfluids, mapping out the Feshbach resonance detuning, temperature and rotational frequency phase diagram. I will compare our predictions with the recent experiments on degenerate atomic $^6$Li gases across a Feshbach resonance [Zwierlein et al. Nature {\bf 435}, 1047 (2005)] and will make proposals for future experiments in such systems.   

Visualization and characterization of superfluid vortices in liquid helium

In superfluid helium 4, quantum vortices have been studied indirectly for nearly fifty years. We have discovered that micron sized solid hydrogen particles suspended within superfluid helium are attracted to and trapped by the vortex filaments and thereby make it possible to see individual vortex lines. The ability to produce the fine solid hydrogen particles is key to this new technique. We compare the line density in a steadily rotating superfluid with the Feynman prediction. Oscillating modes of the vortex array are also observed and characterized. Our observations also include periodic particle spacing on lines at low particle density, as well as complex vortex branching and networks. Our visualization technique makes it possible to observe the dynamics and geometry of vortices both in superfluid turbulence and in quench conditions passing through the phase transition.   

Nucleation and growth of vortices in a rotating BEC

An analytic solution of the Gross-Pitaevskii equation [1] for a rotating Bose-Einstein condensate of trapped atoms describes the onset of vorticity when the rotational speed is increased, starting with the entry of the first vortex [2] and followed by the formation of growing symmetric Wigner molecules. It explains the staircase of angular momentum jumps and the behavior of the bosonic occupancies observed in numerical studies. The universalities of this behavior [3] and its similarity to the mesoscopic superconductors are discussed. [1] O.K. Vorov, P. Van Isacker, M.S. Hussein, and K. Bartschat, Phys. Rev. Lett. 95, 230406 (2005). [2] O.K. Vorov, P. Van Isacker, and M.S. Hussein,, Phys. Rev. Lett., 90, 200402 (2003). [3] O.K. Vorov, P. Van Isacker, and M.S. Hussein, and K. Bartschat, subm. To Nature (London).