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Physical Review Letters

Rotating Spin-1 Bose Clusters

Tin-Lun Ho, Erich J. Mueller

Published Jul 16, 2002• 38 citations
Publisher

Abstract

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.

DOI
10.1103/physrevlett.89.050401

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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 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 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.
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.
Two-dimentional systems of trapped samples of few cold bosonic atoms submitted to strong rotation around the perpendicular axis may be realized in optical lattices and microtraps. We investigate theoretically the evolution of ground state structures of such systems as the rotational frequency $\ensuremath{\Omega}$ increases. Various kinds of ordered structures are observed. In some cases, hidden interference patterns exhibit themselves only in the pair correlation function; in some other cases explicit broken-symmetry structures appear that modulate the density. For N<10N<10N<10 atoms, the standard scenario, valid for large sytems is absent, and is only gradually recovered as NNN increases. On the one hand, the Laughlin state in the strong rotational regime contains ordered structures much more similar to a Wigner molecule than to a fermionic quantum liquid. On the other hand, in the weak rotational regime, the possibility to obtain equilibrium states, whose density reveals an array of vortices, is restricted to the vicinity of some critical values of the rotational frequency $\ensuremath{\Omega}$.
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.