Vortex lattices in the lowest Landau level for confined Bose-Einstein condensates

In this short review we present our recent results concerning the rotation of atomic Bose-Einstein condensates confined in quadratic or quartic potentials, and give an overview of the field. We first describe the procedure used to set an atomic gas in rotation and briefly discuss the physics of condensates containing a single vortex line. We then address the regime of fast rotation in harmonic traps, where the rotation frequency is close to the trapping frequency. In this limit the Landau Level formalism is well suited to describe the system. The problem of the condensation temperature of a fast rotating gas is discussed, as well as the equilibrium shape of the cloud and the structure of the vortex lattice. Finally we review results obtained with a quadratic + quartic potential, which allows to study a regime where the rotation frequency is equal to or larger than the harmonic trapping frequency.

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“…The minimization of (15) within the LLL has recently been discussed in [66,67,64]. Let us briefly sketch the main results.…”

Section: Equilibrium Shape In the Lllmentioning

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Bose-Einstein condensates in fast rotation

et al. 2005

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“…They started from the LLL wave functions for noninteracting particles in a trapping potential and switched interaction on after it. For a regular vortex lattice this yielded the Gaussian density profile [5] but it was unstable with respect to small distortions of the lattice, which transformed the Gaussian profile to the inverted parabola (Thomas-Fermi distribution) [4,6,7,8,9]. This Letter suggests another strategy.…”

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confidence: 99%

“…Kk, 67.40.Vs A rapidly rotating Bose-Einstein condensate (BEC) of cold atoms is now a subject of intensive experimental and theoretical investigations [1,2,3,4,5,6,7,8,9]. It is well known that rotation gives rise to a regular triangular vortex lattice.…”

mentioning

confidence: 99%

“…A number of papers addressed this issue using the analogy with the quantum Hall effect [4,5,6,7,8,9]. They started from the LLL wave functions for noninteracting particles in a trapping potential and switched interaction on after it.…”

mentioning

confidence: 99%

“…[6,7,8] also received the invertedparabola density profile. In their approach it looks as the effect of small distortions of the vortex lattice, which essentially transforms the Gaussian density profile predicted by Ho [5] for an ideally regular vortex lattice in a trap.…”

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confidence: 99%

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Ground state and Tkachenko modes of a rapidly rotating Bose-Einstein condensate in the lowest-Landau-level state

Sonin¹

2005

Phys. Rev. A

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The Letter considers the ground state and the Tkachenko modes for a rapidly rotating BoseEinstein condensate (BEC), when its macroscopic wave function is a coherent superposition of states analogous to the lowest Landau levels of a charge in a magnetic field. As well as in type II superconductors close to the critical magnetic field Hc2, this corresponds to a periodic vortex lattice. The exact value of the shear elastic modulus of the vortex lattice, which was known from the old works on type II superconductors, essentially exceeds the values calculated recently for BEC. This is important for comparison with observation of the Tkachenko mode in the rapidly rotating BEC.PACS numbers: 03.75. Kk, 67.40.Vs A rapidly rotating Bose-Einstein condensate (BEC) of cold atoms is now a subject of intensive experimental and theoretical investigations [1,2,3,4,5,6,7,8,9]. It is well known that rotation gives rise to a regular triangular vortex lattice. At moderate rotation speed this is a lattice of vortex lines (points in the 2D case) with the core size of the order of coherence length ξ, which essentially smallerHere Ω is the angular velocity of rotation and κ = h/m is the circulation quantum. One can call it the Vortex Line Lattice (VLL) regime. With increasing Ω, the vortex lattice becomes more and more dense and eventually enters the regime, in which the vortex cores start to overlap, i.e., ξ becomes larger than the b. This regime is analogous to the mixed state of a type-II superconductor close to the second critical magnetic field H c2 ∼ Φ 0 /ξ 2 (Φ 0 is the magnetic flux quantum), at which the transition to the normal state takes place. However, in a rotating BEC there is no phase transition at corresponding "critical" angular velocity Ω c2 ∼ κ/ξ 2 . Instead the crossover to the new regime takes place: At Ω ≫ Ω c2 all atoms condensate in a state, which is a coherent superposition of single-particle states similar to the Lowest Landau Levels (LLL) of a charged particle in a magnetic field (the LLL regime). An important method of investigation of the vortex structure is studying its collective modes. Coddington et al.[1] were able to detect the Tkachenko modes (transverse sound in the vortex lattice) in the VLL regime experimentally. Recently they increased the rotation speed in the attempt to reach the LLL regime [2]. They revealed softer Tkachenko modes as was predicted by the theory for the LLL regime [3,4].Theoretical study of the Tkachenko mode requires good knowledge of the equilibrium state. A number of papers addressed this issue using the analogy with the quantum Hall effect [4,5,6,7,8,9]. They started from the LLL wave functions for noninteracting particles in a trapping potential and switched interaction on after it. For a regular vortex lattice this yielded the Gaussian density profile [5] but it was unstable with respect to small distortions of the lattice, which transformed the Gaussian profile to the inverted parabola (Thomas-Fermi distribution) [4,6,7,8,9]. This Letter suggests another strategy. One c...

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Hydrodynamics of Rotating Superfluids with Quantized Vortices

Kagan

2013

Modern Trends in Superconductivity and Superfluidity

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Vortex lattices in the lowest Landau level for confined Bose-Einstein condensates

Cited by 72 publications

References 15 publications

Bose-Einstein condensates in fast rotation

Bose-Einstein condensates in fast rotation

Ground state and Tkachenko modes of a rapidly rotating Bose-Einstein condensate in the lowest-Landau-level state

Hydrodynamics of Rotating Superfluids with Quantized Vortices

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