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arXiv:0906.1686 · Journal of Physics B Atomic Molecular and Optical Physics

Quantum entanglement of spin-1 bosons with coupled ground states in optical lattices

B Öztop, Mehmet Özgür Oktel, Özgür Esat Müstecaplıoğlu, L You

Published Jun 17, 2009• 2 citations
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Abstract

We examine particle entanglement, characterized by pseudo-spin squeezing, of spin-1 bosonic atoms with coupled ground states in a one-dimensional optical lattice. Both the superfluid and Mott-insulator phases are investigated separately for ferromagnetic and antiferromagnetic interactions. Mode entanglement is also discussed in the Mott insulating phase. The role of a small but nonzero angle between the polarization vectors of counter-propagating lasers forming the optical lattice on quantum correlations is investigated as well.

DOI
10.1088/0953-4075/42/14/145505

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Abstract. We examine particle entanglement, characterized by pseudo-spin squeezing, of spin-1 bosonic atoms with coupled ground states in a one-dimensional optical lattice. Both the superfluid and Mott-insulator phases are investigated separately for ferromagnetic and antiferromagnetic interactions. Mode entanglement is also discussed in the Mott insulating phase. The role of a small but nonzero angle between the polarization vectors of counter-propagating lasers forming the optical lattice on quantum correlations is investigated as well. PACS numbers: 03.75.Lm, 03.75.Mn, 03.67.Bg Submitted to: J. Phys. B: At. Mol. Phys. Quantum entanglement of spin-1 bosons 2
The superfluid--Mott-insulator phase transition of ultracold spin-1 bosons with ferromagnetic and antiferromagnetic interactions in an optical lattice is theoretically investigated. Two counterpropagating linearly polarized laser beams with the angle $\ensuremath{\theta}$ between the polarization vectors ($\mathrm{lin}\text{\ensuremath{-}}\ensuremath{\theta}\text{\ensuremath{-}}\mathrm{lin}$ configuration), driving an Fg=1{F}_{g}=1Fg​=1 to Fe=1{F}_{e}=1Fe​=1 internal atomic transition, create the optical lattice and at the same time couple atomic ground states with magnetic quantum numbers $m=\ifmmode\pm\else\textpm\fi{}1$. Due to the coupling the system can be described as a two-component one. At $\ensuremath{\theta}=0$ the system has a continuous isospin symmetry, which can be spontaneously broken, thereby fixing the number of particles in the atomic components. The phase diagram of the system and the spectrum of collective excitations, which are density waves and isospin waves, are worked out. In the case of ferromagnetic interactions, the superfluid--Mott-insulator phase transition is always second order, but in the case of antiferromagnetic interactions for some values of system parameters it is first order and the superfluid and Mott phases can coexist. Varying the angle $\ensuremath{\theta}$ one can control the populations of atomic components and continuously turn on and tune their asymmetry.
In this work, we investigate the system of cold spin-1 atoms in a one dimensional optical lattice in relation with squeezing and entanglement. By using the corresponding Bose-Hubbard Hamiltonian, both superfluid and Mott-insulator phases are studied by using numerical methods in the mean-field approximation. To observe the presence of entanglement, we used a squeezing measure as a criterion for quantum correlations. We further investigate the two interaction regimes, namely ferromagnetic and antiferromagnetic in the case of zero and nonzero but very small angle between the counterpropagating laser beams that form the optical lattice. States in the superfluid phase are calculated analytically by using the perturbation theory.
We study the ground-state properties of spin-1 bosonic atoms trapped in a one-dimensional optical lattice with harmonic confinement. We have developed a highly efficient numerical method based on the Gutzwiller approximation to clarify the inhomogeneous magnetic phases induced by the harmonic confining potential. A quantum phase transition from a superfluid to a Mott insulator is examined for the respective cases with antiferromagnetic and ferromagnetic interactions. It is shown that the profile of local spins over the lattice sites changes as a function of the interaction strength forming the characteristic structures, which closely correlates with the average number of atoms at the sites. For antiferromagnetic cases, we find that there is a crossover from a superfluid polar condensate to Mott-insulator domains consisting of either a spin-singlet pair or a single spin at each site.
We study, using quantum Monte Carlo (QMC) simulations, the ground state properties of spin-1 bosons trapped in a square optical lattice. The phase diagram is characterized by the mobility of the particles (Mott insulating or superfluid phase) and by their magnetic properties. For ferromagnetic on-site interactions, the whole phase diagram is ferromagnetic and the Mott insulators-superfluid phase transitions are second order. For antiferromagnetic on-site interactions, spin nematic order is found in the odd Mott lobes and in the superfluid phase. Furthermore, the superfluid-insulator phase transition is first or second order depending on whether the density in the Mott is even or odd. Inside the even Mott lobes we observe a singlet-to-nematic transition for certain values of the interactions. This transition appears to be first order.
We analyze the behavior of cold spin-1 particles with antiferromagnetic interactions in a one-dimensional optical lattice using density matrix renormalization group calculations. Correlation functions and the dimerization are shown and we also present results for the energy gap between ground state and the spin excited states. We confirm the anticipated phase diagram, with Mott-insulating regions of alternating dimerized S=1S=1S=1 chains for odd particle density versus on-site singlets for even density. We find no evidence for any additional ordered phases in the physically accessible region, however for sufficiently large spin interaction, on-site singlet pairs dominate leading, for odd density, to a breakdown of the Mott insulator or, for even density, a real-space singlet superfluid.