Rapidly Rotating Atomic Gases (0810.4398v2)

Abstract: This article reviews developments in the theory of rapidly rotating degenerate atomic gases. The main focus is on the equilibrium properties of a single component atomic Bose gas, which (at least at rest) forms a Bose-Einstein condensate. Rotation leads to the formation of quantized vortices which order into a vortex array, in close analogy with the behaviour of superfluid helium. Under conditions of rapid rotation, when the vortex density becomes large, atomic Bose gases offer the possibility to explore the physics of quantized vortices in novel parameter regimes. First, there is an interesting regime in which the vortices become sufficiently dense that their cores -- as set by the healing length -- start to overlap. In this regime, the theoretical description simplifies, allowing a reduction to single particle states in the lowest Landau level. Second, one can envisage entering a regime of very high vortex density, when the number of vortices becomes comparable to the number of particles in the gas. In this regime, theory predicts the appearance of a series of strongly correlated phases, which can be viewed as {\it bosonic} versions of fractional quantum Hall states. This article describes the equilibrium properties of rapidly rotating atomic Bose gases in both the mean-field and the strongly correlated regimes, and related theoretical developments for Bose gases in lattices, for multi-component Bose gases, and for atomic Fermi gases. The current experimental situation and outlook for the future are discussed in the light of these theoretical developments.

• The paper presents a comprehensive review of rotating Bose gases, highlighting the emergence of vortex arrays and distinct regimes from overlapping vortex cores to strongly correlated phases.
• It employs mean-field theory and numerical exact diagonalization to reveal transitions from triangular vortex lattices to bosonic quantum Hall states, including the Laughlin state at ν = 1/2.
• The study discusses experimental challenges and future prospects, emphasizing the role of optical lattices and tunable interactions in realizing novel states of matter.

Rapidly Rotating Atomic Gases: An Overview

The paper "Rapidly Rotating Atomic Gases" by N.R. Cooper provides a comprehensive review of the developments in the theoretical understanding of rapidly rotating degenerate atomic gases, particularly focusing on single-component atomic Bose gases. The paper explores various equilibrium properties and theoretical predictions for these gases subjected to fast rotation.

The formation of quantized vortices in a rotating Bose-Einstein condensate (BEC) leads to the emergence of a vortex array, similar to observations in superfluid helium. Under rapid rotation, where the vortex density increases significantly, novel physical regimes become accessible. This paper examines two primary regimes:

1. The regime where vortex cores overlap, simplifying theoretical descriptions by reducing to single-particle states in the lowest Landau level (LLL).
2. A regime characterized by vortex density comparable to particle number density, potentially giving rise to strongly correlated phases akin to bosonic analogues of fractional quantum Hall states.

The paper explores mean-field and strongly correlated regimes, assessing both experimental progress and theoretical advances.

Theoretical Developments and Numerical Insights

The analysis employs both mean-field theory and numerical exact diagonalization to unveil the properties of these gases at low filling factors. At high vortex densities, mean-field theory predicts a transition from a triangular vortex lattice to possible exotic strongly correlated phases.

Finite systems with contact interactions reveal exact solutions for ground states at specific angular momenta, elucidating the role of composite bosons. The emergence of these composite bosons in quantum Hall states reveals intriguing connections to FQHE phenomena, including the formation of incompressible liquid states at specific filling factors like the bosonic Laughlin state at $\nu = 1/2$.

Implications for Multi-Component Gases and Optical Lattices

The paper extends its discussion to multi-component Bose gases and atomic Fermi gases. Two-component systems exhibit diverse vortex lattice configurations influenced by inter-component interactions. Spinor condensates further diversify potential vortex lattice symmetries, with specific structures linked to the nature of interatomic interactions.

The interaction of rapidly rotating gases with optical lattices adds another intriguing dimension. Lattices introduce additional pinning potentials for vortices, enabling the exploration of commensurability effects, vortex pinning, and possible striped or bubble phases.

Future Prospects and Experimental Challenges

The paper outlines significant future challenges and opportunities in the experimental realization of these phases. Achieving the conditions for strongly correlated phases requires precise control over rotation speed, atomic interactions, and trap geometries. Advances in optical lattice technologies and manipulation of interatomic interactions through Feshbach resonances hold promise for deeper exploration of these states.

In conclusion, rapidly rotating atomic gases present a fertile ground for discovering new states of matter, bridging concepts from condensed matter and atomic physics. The predictions outlined for quantum Hall analogues in cold atoms suggest exciting experimental pursuits toward understanding non-abelian phases and topological quantum computing. The future of this field lies in overcoming technical challenges to realize and measure the significantly correlated phases described in theoretical studies.