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arXiv:cond-mat/0203143

"Fermionization" of Rotating Spin-1 Bose Clusters

Tin-Lun Ho, Erich J. Mueller

Published Mar 6, 2002• 0 citations
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Abstract

We propose a simple scheme of generating rotating atomic clusters in an optical lattices which produces states with quantum Hall and spin liquid properties. As the rotation frequencies increases, the ground state of a rotating cluster of spin-1 Bose atoms undergoes a sequence of (spin and orbit) transitions, which terminates at an angular momentum $L^{\ast}$ substantially lower than that of the boson Laughlin state. The spin-orbit correlations reflect "fermionization" of bosons facilitated by their spin degrees of freedom. We also show that the density of an expanding group of clusters has a scaling form which reflects the quantum Hall and the spin structure of a single cluster.

DOI
10.48550/arxiv.cond-mat/0203143

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We propose a simple scheme of generating rotating atomic clusters in an optical lattices which produces states with quantum Hall and spin liquid properties. As the rotation frequencies increases, the ground state of a rotating cluster of spin-1 Bose atoms undergoes a sequence of (spin and orbit) transitions, which terminates at an angular momentum L∗L^{\ast}L∗ substantially lower than that of the boson Laughlin state. The spin-orbit correlations reflect "fermionization" of bosons facilitated by their spin degrees of freedom. We also show that the density of an expanding group of clusters has a scaling form which reflects the quantum Hall and the spin structure of a single cluster.
We propose a simple scheme for generating rotating atomic clusters in an optical lattice which produces states with quantum Hall and spin liquid properties. As the rotation frequencies increase, the ground state of a rotating cluster of spin-1 Bose atoms undergoes a sequence of (spin and orbit) transitions, which terminates at an angular momentum L(*) substantially lower than that of the boson Laughlin state. The spin-orbit correlations reflect "fermionization" of bosons facilitated by their spin degrees of freedom. We also show that the density of an expanding group of clusters has a scaling form which reveals the quantum Hall and spin structure of a single cluster.
We study the quantum Hall phases that appear in the fast-rotation limit for Bose-Einstein condensates of spinless bosonic atoms. We use exact diagonalization in a spherical geometry to obtain low-lying states of a small number of bosons as a function of the angular momentum. This allows us to understand or guess the physics at a given filling fraction $\ensuremath{\nu}$, the ratio of the number of bosons to the number of vortices. This is also the filling factor of the lowest Landau level. In addition to the well-known Bose-Laughlin state at $\ensuremath{\nu}=1∕2$, we give evidence for the Jain principal sequence of incompressible states at $\ensuremath{\nu}=p∕(p\ifmmode\pm\else\textpm\fi{}1)$ for a few values of ppp. There is a collective mode in these states whose phenomenology is in agreement with standard arguments coming, e.g., from the composite-fermion picture. At filling factor 1, the potential Fermi sea of composite fermions is replaced by a paired state, the Moore-Read state. This is most clearly seen from the half-flux nature of elementary excitations. We find that the hierarchy picture does not extend up to the point of transition towards a vortex lattice. While we cannot come to any definite conclusions, we investigate the clustered Read-Rezayi states and show evidence for incompressible states at the expected ratio of flux versus number of Bose particles.
We study the physics of a rapidly rotating gas of ultracold atomic bosons, with an internal degree of freedom. We show that in the limit of rapid rotation of the trap the problem exactly maps onto that of noninteracting fermions with spin in the lowest Landau level. The spectrum of the real bosonic system is identical to the one of the effective fermions, with the same eigenvalues and the same density of states. When the ratio of the number of atoms to the spin degeneracy is an integer number, the ground state for the effective fermions is an integer quantum Hall state. The corresponding bosonic state is a fractional quantum Hall liquid whose filling factor ranges in the sequence $\ensuremath{\nu}=1/2,2/3,3/4,\dots{},$ as the spin degeneracy increases. Anyons with 1/2,1/3,1/4,…1/2,1/3,1/4,\dots{}1/2,1/3,1/4,… statistics can be created by inserting lasers with the appropriate polarizations. A special situation appears when the spin degeneracy equals the number of atoms in the gas. The ground state is then the product of a completely antisymmetric spin state and a $\ensuremath{\nu}=1$ Laughlin state. In this case the system exhibits fermionic excitations with fermionic statistics although the real components are bosonic atoms.
The notion of quasi-angular momentum is introduced to label the eigenstates of a Hamiltonian with a discrete rotational symmetry. This concept is recast in an operatorial form where the creation and annihilation operators of a Hubbard Hamiltonian carry units of quasi-angular momentum. Using this formalism, the ground states of ultracold gases of non-interacting fermions in rotating optical lattices are studied as a function of rotation, and transitions between states of different quasi-angular momentum are identified. In addition, previous results for strongly-interacting bosons are re-examined and compared to the results for non-interacting fermions. Quasi-angular momentum can be used to distinguish between these two cases. Finally, an experimentally accessible signature of quasi-angular momentum is identified in the momentum distributions of single-particle eigenstates.
We study incompressible ground states of bosons in a two-dimensional rotating square optical lattice. The system can be described by the Bose-Hubbard model in an effective uniform magnetic field present due to the lattice rotation. To study ground states of the system, we map it to a frustrated spin model, followed by Schwinger boson mean-field theory and projective symmetry group analysis. Using symmetry analysis, we identify bosonic fractional quantum Hall states, predicted for bosonic atoms in rotating optical lattices, with possible stable gapped spin-liquid states within the Schwinger boson formalism. In particular, our results indicate that previously obtained fractional quantum Hall states induced by the lattice potential, and with no counterpart in the continuum [M\"oller and Cooper, Phys. Rev. Lett. 103, 105303 (2009)], correspond to ``$\ensuremath{\pi}$-flux'' spin-liquid states of the frustrated spin model.