Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms

Greiner, Markus; Mandel, Olaf; Esslinger, Tilman; Hänsch, Theodor W.; Bloch, Immanuel

doi:10.1038/415039a

Cited by 5,560 publications

(6,451 citation statements)

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“…In the atomic limit it is therefore natural to expect a gapped collective mode in which particles belonging to the lower Hubbard band are cooperatively promoted to the upper Hubbard band. Such a mode has been observed in a Bose-Einstein condensate in a deep 3D optical lattice [91] and, more recently, in an artificial honeycomb lattice realized by nanopatterning the surface of a GaAs semiconductor [16] (see Fig. 5).…”

Section: Hubbard Correlations and Split Bandsmentioning

confidence: 80%

Artificial honeycomb lattices for electrons, atoms and photons

et al. 2013

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Artificial honeycomb lattices offer a tunable platform to study massless Dirac quasiparticles and their topological and correlated phases. Here we review recent progress in the design and fabrication of such synthetic structures focusing on nanopatterning of two-dimensional electron gases in semiconductors, molecule-by-molecule assembly by scanning probe methods, and optical trapping of ultracold atoms in crystals of light. We also discuss photonic crystals with Dirac cone dispersion and topologically protected edge states. We emphasize how the interplay between single-particle band structure engineering and cooperative effects leads to spectacular manifestations in tunneling and optical spectroscopies.

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Section: Hubbard Correlations and Split Bandsmentioning

confidence: 80%

Artificial honeycomb lattices for electrons, atoms and photons

et al. 2013

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“…Recent experiments on cold atoms trapped in optical lattices demonstrated that the Mott transition (MIT), originally introduced in electronic systems, [1] can be experimentally realized also in bosonic systems, [2] where the MIT is actually a superfluid-insulator transition. Recent experiments by Stoferle et al [3] have shown that a considerable amount of spectral weight is concentrated at high energy even within the superfluid phase.…”

mentioning

confidence: 99%

“…[18] This term is kept just to improve the variational accuracy (mainly in 2D and 3D) but does not introduce important correlation effects, that are instead contained only in the long-range tail of the two-body Jastrow potential v i,j . Both the Jastrow factor and the many-body operator ξ commute with the particle number, hence (2) belongs to the Fock space with N = L bosons.…”

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confidence: 99%

Superfluid to Mott-Insulator Transition in Bose-Hubbard Models

et al. 2007

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We study the superfluid-insulator transition in Bose-Hubbard models in one-, two-, and threedimensional cubic lattices by means of a recently proposed variational wave function. In one dimension, the variational results agree with the expected Berezinskii-Kosterlitz-Thouless scenario of the interaction-driven Mott transition. In two and three dimensions, we find evidences that, across the transition, most of the spectral weight is concentrated at high energies, suggestive of pre-formed Mott-Hubbard side-bands. This result is compatible with the experimental data by Stoferle et al. [Phys. Rev. Lett. 92, 130403 (2004)].

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“…We create a Mott insulator 6 of atomic 87 Rb starting from an atomic BEC in an optical dipole trap by slowly ramping up the depth of the optical lattice (see the Methods section). The typical lattice depth 6 seen by an atom is V 0 = 24E r , where E r =h 2 k 2 /(2m) is the recoil energy, where m is the mass of one atom,h is the reduced Planck constant and 2π/k = 830 nm is the wavelength of the lattice light. At this lattice depth, the atomic tunnelling amplitude is J = 2πh × 4 Hz.…”

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confidence: 99%

Preparation of a quantum state with one molecule at each site of an optical lattice

et al. 2006

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U ltracold gases in optical lattices are of great interest, because these systems bear great potential for applications in quantum simulations and quantum information processing, in particular when using particles with a longrange dipole-dipole interaction, such as polar molecules 1-5 . Here we show the preparation of a quantum state with exactly one molecule at each site of an optical lattice. The molecules are produced from an atomic Mott insulator 6 with a density profile chosen such that the central region of the gas contains two atoms per lattice site. A Feshbach resonance is used to associate the atom pairs to molecules 7-14 . The remaining atoms can be removed with blast light 13,15 . The technique does not rely on the moleculemolecule interaction properties and is therefore applicable to many systems.A variety of interesting proposals for quantum information processing and quantum simulations 1-5 require as a prerequisite a quantum state of ultracold polar molecules in an optical lattice, where each lattice site is occupied by exactly one molecule. A promising strategy for the creation of such molecules is based on the association of ultracold atoms using a Feshbach resonance, or photoassociation and subsequent transfer to a much lower rovibrational level using Raman transitions 16 . If the moleculemolecule interactions are predominantly elastic and effectively repulsive, then a state with one molecule per lattice site can finally be obtained using a quantum phase transition from a superfluid to a Mott insulator by ramping up the depth of an optical lattice 6 . However, many molecular species do not have such convenient interaction properties, so alternative strategies are needed. Here, we demonstrate a technique that is independent of the molecule-molecule interaction properties. The technique relies on first forming an atomic Mott insulator and then associating molecules. Several previous experiments 15,17-20 associated molecules in an optical lattice, but none of them demonstrated the production of a quantum state with exactly one molecule per lattice site. Another interesting perspective of the state prepared here is that after Raman transitions to the rovibrational ground state, the lattice potential can be lowered to obtain a Bose-Einstein condensate (BEC) of molecules in the rovibrational ground state 21,22 . Figure 1 Schematic diagram of the molecular n = 1 state. In the core of the cloud, each lattice site is occupied by exactly n = 1 molecule (shown in green). In the surrounding shell, each site is occupied by exactly one atom (shown in red). The atoms can be removed with a blast laser. In the experiment, the number of occupied lattice sites is much larger than shown here.The behaviour of bosons in an optical lattice is described by the Bose-Hubbard hamiltonian 23 . The relevant parameters are the amplitude J for tunnelling between neighbouring lattice sites and the on-site interaction matrix element U. We create a Mott insulator 6 of atomic 87 Rb starting from an atomic BEC in an optical dipol...

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Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms

Cited by 5,560 publications

References 23 publications

Artificial honeycomb lattices for electrons, atoms and photons

Artificial honeycomb lattices for electrons, atoms and photons

Superfluid to Mott-Insulator Transition in Bose-Hubbard Models

Preparation of a quantum state with one molecule at each site of an optical lattice

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