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arXiv:1204.5423 · Physical Review A

Non-Abelian spin-singlet states of two-component Bose gases in artificial gauge fields

Tobias Graß, Bruno Juliá-Díaz, N. Barberán, Maciej Lewenstein

Published Aug 9, 2012• 30 citations
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Abstract

We study strongly correlated phases of a pseudo-spin-$\frac{1}{2}$ Bose gas in an artificial gauge field using the exact diagonalization method. The atoms are confined in two dimensions and interact via a two-body contact potential. In Abelian gauge fields, pseudospin singlets are favored by pseudo-spin-independent interactions. We find a series of incompressible phases at fillings $\ensuremath{\nu}=2k/3$. By comparison with the non-Abelian spin singlet (NASS) states, constructed as zero-energy eigenstates of a $(k+1)$-body contact interaction, we classify the nontrivial topology of the states. An additional spin-orbit coupling is shown to switch between NASS-like states and spin-polarized phases from the Read-Rezayi series.

DOI
10.1103/physreva.86.021603

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We study strongly correlated phases of a pseudo-spin-12\frac{1}{2}21​ Bose gas in an artificial gauge field using the exact diagonalization method. The atoms are confined in two dimensions and interact via a two-body contact potential. In Abelian gauge fields, pseudospin singlets are favored by pseudo-spin-independent interactions. We find a series of incompressible phases at fillings \ensuremathν=2k/3\ensuremath{\nu}=2k/3\ensuremathν=2k/3. By comparison with the non-Abelian spin singlet (NASS) states, constructed as zero-energy eigenstates of a (k+1)(k+1)(k+1)-body contact interaction, we classify the nontrivial topology of the states. An additional spin-orbit coupling is shown to switch between NASS-like states and spin-polarized phases from the Read-Rezayi series.
We investigate strongly correlated phases of two-component (or pseudospin-1/21/21/2) Bose gases under rapid rotation through exact diagonalization on a torus geometry. In the case of pseudospin-independent contact interactions, we find the formation of gapped spin-singlet states at the filling factors $\ensuremath{\nu}=k/3+k/3$ (k/3k/3k/3 filling for each component) with integer kkk. We present numerical evidences that the gapped state with k=2k=2k=2 is well described as a non-Abelian spin-singlet (NASS) state, in which excitations feature non-Abelian statistics. Furthermore, we find the phase transition from the product of composite fermion states to the NASS state by changing the ratio of the intercomponent-to-intracomponent interactions.
We study the fractional quantum Hall phases of a pseudospin-1/2 Bose gas in an artificial gauge field. In addition to an external magnetic field, the gauge field mimics an intrinsic spin–orbit coupling of the Rashba type. While the spin degeneracy of the Landau levels is lifted by the spin–orbit coupling, the crossing of two Landau levels at certain coupling strengths gives rise to a new degeneracy. We therefore take into account two Landau levels and perform exact diagonalization of the many-body Hamiltonian. We study and characterize the quantum Hall phases which occur in the vicinity of the degeneracy point. Notably, we describe the different states appearing at the Laughlin fillings, ν = 1/2 and ν = 1/4. While for these filling factors incompressible phases disappear at the degeneracy point, we find gaps in the spectra of denser systems at ν = 3/2 and ν = 2. For filling factors ν = 2/3 and ν = 4/3, we discuss the connection of the exact ground states to the non-Abelian spin singlet states, obtained as the ground states of ( k + 1)-body contact interactions.
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We study bosonic atoms with two internal states in artificial gauge potentials whose strengths are different for the two components. A series of topological phases for such systems is proposed using the composite fermion theory and the parton construction. It is found in exact diagonalization that some of the proposed states may be realized for simple contact interaction between bosons. The ground states and low-energy excitations of these states are modeled using trial wave functions. The effective field theories for these states are also constructed and reveal some interesting properties.
The present thesis studies a variety of cold atomic systems in artificial gauge fields. In the first part we focus on fractional quantum Hall effects, asking whether interesting topological states can be realized with cold atoms. We start by making a close connection to solid-state systems and first consider fermionic atoms with dipolar interactions. Assuming the system to be in the Laughlin state, we evaluate the energy gap in the thermodynamic limit as a measure for the robustness of the state. We show that it can be increased by additionally applying a non-Abelian gauge field squeezing the Landau levels. We then switch to bosonic systems with repulsive contact interactions. Artificial magnetic fields for cold bosons have extensively been discussed before in the context of rotating Bose gases. We follow a different approach where the gauge field is due to an atom-laser coupling. Thus, transitions between different dressed states have to be included. They are shown to break the cylindrical symmetry of the system. Modifying the Laughlin state and the Moore-Read state accordingly, we determine the parameter regimes where they are good representations for the ground state of the system obtained via exact diagonalization. One of the most interesting feature of fractional quantum Hall states is the anyonic behavior of their excitations. We therefore also study quasiholes in the Laughlin state and the modified Laughlin state. They are shown to posses anyonic properties, which become manifest even in small systems. Moreover, the dynamics of a single quasihole causes visible traces in the density of the system which allow to clearly distinguish the Laughlin regime from less correlated phases. In the latter, a sequence of collapses and revivals of the quasihole can be observed, which is absent in the Laughlin regime. Extending our study to bosonic systems with a pesudospin-1/2 degree of freedom, we discuss the formation of strongly correlated spin singlets. Strikingly, at filling v=4/3, the system is described by a state with non-Abelian excitations, which is constructed as the zero-energy ground state of repulsive three-body contact interactions. Systems with internal degrees of freedom also allow for implementing artificial spin-orbit coupling. It is shown to give rise to a variety of incompressible states. In the second part of the thesis, we concentrate on condensed system. Bose-Einstein condensates with spin-orbit coupling are shown to have a degeneracy on the mean-field level, which is lifted by quantum and thermal fluctuations. The system becomes experimentally feasible in three dimensions, where the condensate depletion remains finite, and thus allow for an experimental observation of this order-by-disorder mechanism. Finally, we study the influence of Abelian and non-Abelian gauge fields on the quantum phase transitions of bosons in a square optical lattice. Re-entrant superfluid phases and superfluids at finite momenta are interesting properties featured by such systems.
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