Cold Bosonic Atoms in Optical Lattices

We study the linear response to time-dependent probes of a symmetry-protected topological phase of bosons in one-dimension, the Haldane insulator (HI). This phase is separated from the ordinary Mott insulator (MI) and density-wave (DW) phases by continuous transitions, whose field theoretical description is here reviewed. Using this technique, we compute the absorption spectrum to two types of periodic perturbations and relate the findings to the nature of the critical excitations at the transition between the different phases. The HI-MI phase transition is topological and the critical excitations possess trivial quantum numbers: they correspond to particles and holes at zero momentum. Our findings are corroborated by a non-local mean-field approach, which allows us to directly relate the predicted spectrum to the known microscopic theory.

Section: The Haldane Insulatormentioning

confidence: 99%

Dynamical probing of a topological phase of bosons in one dimension

Torre

2013

“…In both cases, starting with a pure condensate or with a mixture of bosonic and fermionic atoms, we clearly observe a loss of interference contrast with increasing lattice depth marking the breakdown of long range phase coherence. As already mentioned, in case of the pure bosonic gas, the loss of coherence accompanies the well-known superfluid to Mott-insulator phase transition [18,20,112] which occurs as a result of competition between the minimization of kinetic energy, parameterized by the tunnelling matrix element J which tends to delocalize the atomic wavefunction over the crystal and the minimization of interaction energy U ( fig. 13(a)).…”

Section: Influence Of Fermions On Bosonic Coherencementioning

confidence: 97%

“…An intuitive definition of the contrast of the interference pattern is given by [113,114] V = n max − n min n max + n min (18) where n max is the total atom number in the first order interference fringes reflecting the p = 2 k momentum component and n min is the sum of number of atoms in equivalent areas at intermediate positions between the maxima. At first sight, the relation of the visibility to the bosonic many-body wavefunction is not clear.…”

Section: Characterizing the Phase Coherence Properties Of The Bosonicmentioning

confidence: 99%

“…b † i b j extends only over a few lattice sites in the case of short range coherence, resulting in a reduction of contrast and visibility. Note that based on the definition of equation (18), the Wannier envelope |ŵ| 2 cancels out and the visibility V is directly related to the Fourier transform of the correlation function. Figure 15(a) shows the visibility of a bosonic cloud of 10 5 atoms loaded into an optical lattice as a function of lattice depth.…”

Section: Characterizing the Phase Coherence Properties Of The Bosonicmentioning

confidence: 99%

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Heteronuclear quantum gas mixtures

Ospelkaus¹,

Ospelkaus²

2008

Abstract. In this PhD tutorial article, we present experiments with quantum degenerate mixtures of fermionic and bosonic atoms in 3-dimensional optical lattices. This heteronuclear quantum gas mixture offers a wide range of possibilities for quantum simulation, implementation of condensed matter Hamiltonians, quantum chemistry and ultimately dense and quantum degenerate dipolar molecular samples.We When loaded into a 3D optical lattice, a whole zoo of novel quantum phases has been predicted for Fermi-Bose mixtures. We present the first realization of Fermi-Bose mixtures in 3D optical lattices as a novel quantum many body system [3]. We study the phase coherence of the bosonic cloud in the 3D optical lattice as a function of the amount of fermionic atoms simultaneously trapped in the lattice. We observe a loss of phase coherence at much lower lattice depth than for a pure bosonic cloud and discuss possible theoretical scenarios including adiabatic processes, mean field FermiBose Hubbard scenarios, and disorder-enhanced localization scenarios.After considering this many-body limit of mixtures in lattices, we show how fermionic heteronuclear Feshbach molecules can be created in the optical lattice [4] as a crucial step towards all ground state dense dipolar molecular samples. We develop rf association as a novel molecule association technique, measure the binding energy, lifetime, and association efficiency of the molecules. We develop a simple theoretical single channel model of the molecules trapped in the lattice [5] which gives excellent quantitative agreement with the experimental data.

“…This basis is particularly well suited for the strongly correlated regime that is investigated here [28]. Then, the second quantization Hamiltonian reduces to the Fermi-Bose Hubbard (FBH) model [3,5,29] :…”

Section: The Fermi-bose Hubbard Hamiltonianmentioning

confidence: 99%

Strongly correlated Fermi–Bose mixtures in disordered optical lattices

Sanchez-Palencia¹,

Ahufinger²,

Kantian³

et al. 2006

Abstract. We investigate theoretically the low-temperature physics of a twocomponent ultracold mixture of bosons and fermions in disordered optical lattices. We focus on the strongly correlated regime. We show that, under specific conditions, composite fermions, made of one fermion plus one bosonic hole, form. The composite picture is used to derive an effective Hamiltonian whose parameters can be controlled via the boson-boson and the boson-fermion interactions, the tunneling terms and the inhomogeneities. We finally investigate the quantum phase diagram of the composite fermions and we show that it corresponds to the formation of Fermi glasses, spin glasses, and quantum percolation regimes.